The familiar experiment of whirling a bu_Account of the Skerryvore lighthouse

head, so as to produce a ribbon of light, proves the possibility of

causing a continuous impression on the retina by intermittent images

succeeding each other with a certain rapidity. From the moderate

velocity at which this continuity of impression is obtained, we should

be warranted in concluding, _a priori_, that the time required to make

an impression on the retina is considerably less than the duration of

the impression itself; for the continuity of effect must, of course,

be caused by fresh impulses succeeding each other before the preceding

ones have entirely faded. If it were otherwise, and the time required

to make the impression were equal to the duration of the sensation, it

would obviously be impossible to obtain a series of impulses so close

or continuous in their effects as to run into and overlap each other,

and thus throw out the intervals of darkness; because the same velocity

which would tend to shorten the dark intervals, would also curtail

the bright flashes, and thus prevent their acting on the eye long

enough to cause an impression. Accordingly, we find that the duration

of an impression is in reality much greater than the time required

for producing the effect on the retina. It is stated by Professor

WHEATSTONE, in the London Transactions for 1834, that only about

_one millionth part_ of a second is required for making a distinct

impression on the eye; and it appears, from a statement made by Lamé,

at p. 425 of his Cours de Physique, that M. PLATEAU found that an

impression on the retina preserved its intensity unabated during _one

hundredth_ of a second, so that, however small those times may be in

themselves, the one is yet 10,000 greater than the other.

It has been ascertained by direct experiment,[78] that the eye can

receive a fresh impression before the preceding one has faded; and,

indeed, if this were impossible, absolute continuity of impression

from any succession of impulses, however rapid, would seem to be

unattainable; and the approach to perfect continuity would be inversely

as the time required to make an impression.

[78] Lamé, Cours de Physique, p. 424. “L’impression peut subsister

encore lorsque la suivante a lieu.”

~Effects of rapid motion on the power of Lights.~

From this property which bright bodies passing rapidly before the

eye possess of communicating a continuous impression to the sense of

sight, Captain HALL conceived the idea, not merely of obtaining all

the effects of a fixed light, by causing a system of lenses to revolve

with such a velocity as to produce a continuous impression, but, at

the same time, of obtaining a much more brilliant appearance, by

the compensating influence of the bright flashes, which he expected

would produce impulses sufficiently powerful and durable to make the

deficiency of light in the dark spaces almost imperceptible. The

mean effect of the whole series of changes would, he imagined, be

thus greatly superior to that which can be obtained from the same

quantity of light equally distributed, as in fixed lights, over the

whole horizon. Now this expectation, if it be considered solely in

reference to the physical distribution of the light, involves various

difficulties. The quantity of light subjected to instrumental action

is the same whether we employ the refracting zones at present used in

fixed dioptric lights, or attempt to obtain continuity of effect by

the rapid revolution of lenses; and the only difference in the action

of those two arrangements is this, that while the zones distribute

the light equally over the whole horizon, or rather do not interfere

with its natural horizontal distribution, the effect of the proposed

method is to collect the light into pencils, which are made to revolve

with such rapidity, that the impression from each pencil succeeds the

preceding one in time to prevent a sensible occurrence of darkness.

To expect that the mean effect of the light, so applied, should be

greater than when it is left to its natural horizontal divergence,

certainly appears at first to involve something approaching to a

contradiction of physical laws. In both cases, the same quantity of

light is acted upon by the instrument; and in either case, any one

observer will receive an impression similar and equal to that received

by any other stationed at a different part of the horizon; so that,

unless we imagine that there is some loss of light peculiar to one

of the methods, we are, in the physical view of the question, shut

up to the conclusion, that the impressions received by each class of

observers must be of equal intensity. In other words, the same quantity

of light is by both methods employed to convey a continuous impression

to the senses of spectators in every direction, and in both methods

equality of distribution is effected, since it does not at all consist

with our hypothesis, that any one observer in the same class should

receive more or less than his equal share of the light. Then, as to

the probability of the loss of light, it seems natural to expect that

this should occur in connection with the revolving system, because the

velocity is an extraneous circumstance, by no means necessary to an

equal distribution of the light, which can, as we already know, be more

naturally and at the same time perfectly, attained by the use of the

zones.

On the other hand, it must not be forgotten, that although the effect

of both methods is to give each part of the horizon an equal share

of light, there is yet this difference between them, that while the

light from the zones is equally intense at every instant of time,

that evolved by the rapidly circulating lenses is constantly passing

through every phase between total darkness and the brightest flash of

the lens; and this difference, taken in connection with some curious

physiological observations regarding the sensibility of the retina,

gives considerable countenance to the expectation on which Captain

HALL’S ingenious expedient is based. The fact which has already

been noticed, and which the beautiful experiments of M. PLATEAU and

Professor WHEATSTONE have of late rendered more precise, that the

duration of an impression on the retina is not only appreciable,

but is much greater than the time required to cause it, seems to

encourage us in expecting, that while the velocity required to produce

continuity of effect would not be found so great as to interfere

with the formation of a full impression, the duration of the impulse

from each flash would remain unaltered, and the dark intervals which

do not excite the retina would, at the same time, be shortened, and

that, therefore, we might in this manner obtain an effect on the

senses exceeding the brilliancy of a steady light distributed equally

in every direction by the ordinary method. Some persons, indeed, who

have speculated on this subject, seem even to be of opinion, that,

so far from the whole effect of the series of continuous impressions

being weakened by a blending of the dark with the bright intervals,

the eye would in reality be stimulated by the contrast of light and

darkness, so as thereby to receive a more complete and durable impulse

from the light. It is obvious, however, that this question regarding

the probable effect to be anticipated from a revolution so rapid as

to cause a continuous impression, could only have been satisfactorily

answered by an appeal to experiment.

In experimenting on this subject, I used the apparatus formerly

employed by Captain HALL. It consisted of an octagonal frame, which

carried eight of the discs that compose the central part of Fresnel’s

compound lens, and was susceptible of being revolved slowly or quickly

at pleasure, by means of a crank-handle and some intermediate gearing.

The experiments were nearly identical with those made by Captain HALL,

who contrasted the effect of a single lens at rest, or moving very

slowly, with that produced by the eight lenses, revolving with such

velocity as to cause an apparently continuous impression on the eye.

To this experiment I added that of comparing the beam thrown out by

the central portion of a cylindric refractor, such as is used at the

fixed light of the Isle of May, with the continuous impression obtained

by the rapid revolution of the lenses. Captain HALL made all his

comparisons at the short distance of 100 yards; and in order to obtain

some measure of the intensity, he viewed the lights through plates of

coloured glass until the luminous discs became invisible to the eye.

I repeated those experiments at Gullan, under similar circumstances,

but with very different results. I shall not, however, enter upon the

discussion of those differences here, although they are susceptible

of explanation, and are corroborative of the conclusions at which I

arrived, by comparing the lights from a distance of 14 miles; but shall

briefly notice the more important results which were obtained by the

distant view. They are as follows:--

1. The flash of the lens revolving slowly was very much larger than

that of the rapidly revolving series; and this decrease of size in the

luminous object presented to the eye, became more marked as the rate of

revolution was accelerated, so that, at the velocity of eight or ten

flashes in a second, the naked eye could hardly detect it, and only

a few of the observers saw it; while the steady light from the fixed

refractor was distinctly visible.

2. There was also a marked falling off in the brilliancy of the rapid

flashes as compared with that of the slow ones; but this effect was by

no means so striking as the decrease of volume.

3. Continuity of impression was not attained at the rate of five

flashes in a second, but each flash appeared to be distinctly separated

by an interval of darkness; and even when the nearest approach to

continuity was made, by the recurrence of eight or ten flashes in a

second, the light still presented a twinkling appearance, which was

well contrasted with the steady and unchanging effect of the cylindric

refractor.

4. The light of the cylindric refractor was, as already stated, steady

and unchanging, and of much larger volume than the rapidly revolving

flashes. It did not, however, appear so brilliant as the flashes of the

quickly revolving lenses, more especially at the lower rate of five

flashes in a second.

5. When viewed through a telescope, the difference of volume between

the light of the cylindric refractor and that produced by the lenses

at their greatest velocity was very striking. The former presented a

large diffuse object of inferior brilliancy, while the latter exhibited

a sharp pin-point of brilliant light.

Upon a careful consideration of these facts it appears warrantable to

draw the following general conclusions:--

1. That our expectations as to the effects of light, when distributed

according to the law of its natural horizontal divergence, are

supported by observed facts as to the visibility of such lights,

contrasted with those whose continuity of effect is produced by

collecting the whole light into bright pencils, and causing them to

revolve with great velocity.

2. It appears that this deficiency of visibility seems to be chiefly

due to a want of volume in the luminous object, and also, although in

a less degree, to a loss of intensity, both of which defects appear

to increase in proportion as the motion of the luminous object is

accelerated.

3. That this deficiency of volume is the most remarkable optical

phenomenon connected with the rapid motion of luminous bodies, and that

it appears to be directly proportional to the velocity of their passage

over the eye.

4. That there is reason to suspect that the visibility of distant

lights depends on the volume of the impression in a greater degree than

has perhaps been generally imagined.

5. That, as the size and intensity of the radiants causing these

various impressions to a distant observer were the same, the volume

of the light and, consequently, _cæteris paribus_, its visibility,

are, within certain limits, proportionate to the time during which the

object is present to the eye.

Such appear to be the general conclusions which those experiments

warrant us in drawing; and the practical result, in so far as

lighthouses are concerned, is sufficient to discourage us from

attempting to improve the visibility of fixed lights in the manner

proposed by Captain HALL, even supposing the practical difficulties

connected with the great centrifugal force generated by the rapid

revolution of the lenses to be less than they really are.

~Connection of the experiments with Irradiation.~

This decrease in the volume of the luminous object caused by the rapid

motion of the lights is interesting, from its apparent connection with

the curious phenomenon of irradiation. When luminous bodies, such as

the lights of distant lamps, are seen by night, they appear much larger

than they would do by day; and this effect is said to be produced by

irradiation. M. PLATEAU, in his elaborate essay on this subject, after

a careful examination of all the theories of irradiation, states it

to be his opinion, that the most probable mode of accounting for the

various observed phenomena of irradiation is to suppose, that, in the

case of a night-view, the excitement caused by light is propagated over

the retina beyond the limits of the day-image of the object, owing to

the increased stimulus produced by the contrast of light and darkness;

and he also lays it down as a law confirmed by numerous experiments,

that irradiation increases with the duration of the observation. It

appears, therefore, not unreasonable to conjecture, that the deficiency

of volume observed during the rapid revolution of the lenses may have

been caused by the light being present to the eye so short a time, that

the retina was not stimulated in a degree sufficient to produce the

amount of irradiation required for causing a large visual object. When,

indeed, the statement of M. PLATEAU, that irradiation is proportional

to the duration of the observation, is taken in connection with the

observed fact, that the volume of the light decreased as the motion

of the lenses was accelerated, it seems almost impossible to avoid

connecting together the two phenomena as cause and effect.

VARIOUS GENERAL CONSIDERATIONS CONNECTED WITH LIGHTHOUSES.

~Masking Lights.~

In the course of supplying the numerous wants of navigation, it will

often be found necessary to _cut off_, on a given bearing, the beam

proceeding from a Lighthouse, as a guide to the seaman to avoid some

shoal, or as a hint to put about and seek the opposite side of a

channel. This is attended with some little practical difficulty,

especially in lights from reflectors arranged externally on a circle,

because a certain portion of light, chiefly due to the divergence

caused by the size of the flames, and partly from the effects of the

diffraction or inflexion of the light, spreads faintly over a narrow

sector between the light arc and the dark one. It becomes necessary,

of course, to make allowance for this penumbral arc by increasing

the masked portion of the lantern; and, where a very sharp line of

demarcation is required, a board is sometimes placed on the outside of

the Lightroom, in such a position, and of such length, that while it

does not enter the boundaries of the luminous sector, it prevents the

more powerful part of the penumbral beam from reaching the observer’s

eye. This effect is, of course, more conveniently produced, where the

circumstances admit of its adoption, by distributing the reflectors

round the concave side of the lantern, towards the land; but such an

arrangement is inapplicable when the illuminated sector exceeds the

dark one. I have found, by observation, that the sector intercepted

between the azimuth on which the lantern is masked and that on which

total darkness is produced to an observer, at moderate distances, may

be estimated at not less than 3° for dioptric, and 7° for catoptric

lights of the highest class.[79]

[79] The method which I adopted for determining those quantities, was

to mask a certain portion of the lantern of a lighthouse subtending

an horizontal sector of about 30° or 40°, and at night to fix, by

actual observation, at the distance of 5 or 6 miles, two points on

the coast between which the light so masked was obscured. The angle

included between the lines joining those points and the centre of the

lantern was then determined by triangulation next day, and _half the

difference_ between the observed angle (which is always the _lesser_

of the two) and the computed subtense of the masked sector of the

lantern, is, in each case, the amount of the allowance stated in the

text.

Those quantities may therefore serve to guide the Lighthouse engineer

to approximate more rapidly to his object, as he will generally be safe

in increasing the dark sector, by one or other of the above constants,

according to the kind of apparatus employed. I need not add, that in a

matter of this kind, a final appeal to actual observation is, in all

cases, indispensable.

~Double Lights.~

A few words on the subject of double lights, naturally spring out

of what has been said about the masking of lights. The term _double

lights_ is properly and distinctly confined to lights on different

levels, but not _necessarily_ (as _leading-lights_ are) in separate

towers. The sole object of using double lights is for _distinction_

from neighbouring lights; and they are unquestionably most effective in

this respect, when they are placed in the same tower. In this point of

view, therefore, I shall speak of them; and it is obvious that all that

peculiarly belongs to them is, that the difference of level between

them shall be sufficiently great to present the lights as separate

objects to the eye of the seaman, when placed at the greatest distance

at which it may be desirable that he should be able to recognise their

characteristic appearance. In many cases it is not necessary (but

it is certainly always desirable) that the lights should, from the

first moment of their being seen, be known as _double lights_; but

in others, it may well consist with safety, that two lights, which

appear as a single light when first seen at the distance of 20 miles,

shall at 15 or 10 miles distance be discovered to be _double_. Now we

should at first be apt hastily to imagine, that all that is required

to produce that effect, is to raise the one light above the other to

such an extent, that the distance between them shall be somewhat more

than a _minimum visibile_ at the most distant point of observation,

or, in other words, that the difference of the height of the lights

should be such as to subtend to the eye at the point of observation,

an angle greater than 13″·02, which is the subtense of a _minimum

visibile_ during the day.[80] But the effect of irradiation, to which

I have already alluded, tends to blend together the images of the

lights long before their distance apart has become so low a fraction

of the observer’s distance from the Lighthouse, as to subtend so

small an angle; and I have accordingly found by experiments, conducted

under various circumstances, and at various distances, that repeated

observations gave me 3′ 18″ as the mean of the subtenses calculated in

reference to the distances at which the lights began to be blended into

_one_.

[80] This quantity is deduced from observations made by my friend

Mr JAMES GARDNER, while engaged on the Ordnance Survey, and may

be regarded as the _extreme_ limit of visibility, under the most

favourable circumstances as to the state of the atmosphere and also

the contrast of colours. The observed object, also, was a pole, not

a _round_ disc; and it is familiar to every one accustomed to view

distant objects, that _vertical length_ is an important constituent

in their visibility.

Adopting this as the smallest angle which the two lights should subtend

at the observer’s eye, we may find the least vertical distance between

them which will cause them to appear as separate objects by the

following formula:

H = 2 Δ . tan θ

in which Δ is the observer’s distance in feet; θ, half the subtense, =

1′ 39″; and H the required height of the tower between the two lights

in feet. The following Table gives the height in feet corresponding

to the distance in nautic miles, from 1 to 20 inclusive: the heights,

which are the bases of _similar_ isosceles triangles, increase, of

course, in an arithmetical series:

+---------------+-----------------++---------------+-----------------+

|Distance of the|Vertical distance||Distance of the|Vertical distance|

| observer in | in feet between || observer in | in feet between |

| Nautic Miles. | the Lights. || Nautic Miles. | the Lights. |

+---------------+-----------------++---------------+-----------------+

| 1 | 6·02 || 11 | 66·22 |

| 2 | 12·04 || 12 | 72·24 |

| 3 | 18·06 || 13 | 78·26 |

| 4 | 24·08 || 14 | 84·28 |

| 5 | 30·10 || 15 | 90·30 |

| 6 | 36·12 || 16 | 96·32 |

| 7 | 42·14 || 17 | 102·34 |

| 8 | 48·16 || 18 | 108·36 |

| 9 | 54·18 || 19 | 114·38 |

| 10 | 60·20 || 20 | 120·40 |

+---------------+-----------------++---------------+-----------------+

~Leading Lights.~

Akin to the subject of _Double Lights_, is that of _Leading Lights_,

the object of which is to indicate to the mariner a given line of

direction by their being seen _in one line_. In most instances, this

line of direction is used to point out the central part of a narrow

channel; and the alternate _opening_ of the lights, on either side of

their _conjunction_, serves to indicate to the mariner (who ought to

conjoin with his watching of the lights the observation of the elapsed

time and also frequent soundings) the proper moment for changing his

tack. In some places, the line of conjunction of the lights is placed

nearer to one side of a channel than the other, according as the set

of the tides, or the position of shoals, may seem to require. In other

situations, this line only serves as a _cross-bearing_ to shew the

mariner his approach to some danger, or to indicate his having passed

it, and thus to assure him of his entry on wider _sea-room_. Similar

considerations to those which determine the difference of elevation for

_double lights_ regulate the choice of the distance between two leading

lights; but the question is less narrow, and may be generally solved

graphically by simply drawing the lines on an accurate chart of the

locality. In some few situations, the configuration of the coast does

not admit of a separation between the lights, sufficient to cause what

is called a _sharp intersection_; but, in most cases, there is room

enough to place them so far apart, that but a few yards of deviation

in the vessel’s course, from the exact line of the conjunction of

the lights _in one_, produces a distinct opening between them on the

opposite side of that line. In order to insure the requisite sharpness

of intersection, the distance between the lights, wherever attainable,

should be not less than _one-sixth_ of the distance between the more

seaward of the two Towers and that point at which the seaman begins to

use the line of conjunction as his guide. I have only to add, that in

situations where the land prevents a considerable separation between

leading lights, they should be placed as nearly on _one level_ as is

consistent with their being seen as _vertically_ separated, so as in

some measure to compensate for their horizontal nearness, by rendering

their intersection more sharp and striking than it can be where the

observer must draw from the upper light an imaginary perpendicular

in his mind, and then estimate the separation of the lights by the

sine of an angle, which decreases as the difference of their apparent

elevations increases.

~Distribution of Lights on a Coast.~

The considerations which enter into the choice of the position and

character of the Lights on a line of coast, are either, on the one

hand, so simple and self-evident as scarcely to admit of being stated

in a general form, without becoming mere truisms; or are, on the

other hand, so very numerous and often so complicated as scarcely to

be susceptible of compression into any general laws. I shall not,

therefore, do more than very briefly allude to a few of the chief

considerations which should guide us in the selection of the sites and

characteristic appearance of the Lighthouses to be placed on a line of

coast. Perhaps those views may be most conveniently stated in the form

of distinct propositions:--

1. The most prominent points of a line of coast, or those first made

on _over-sea_ voyages, should be first lighted; and the most powerful

lights should be adapted to them, so that they may be discovered by the

mariner as long as possible before his reaching land.

2. So far as is consistent with a due attention to distinction,

revolving lights of some description, which are necessarily more

powerful than fixed lights, should be employed at the outposts on a

line of coast.

3. Lights of precisely identical character and appearance should not,

if possible, occur within a less distance than 100 miles of each other

on the same line of coast, which is made by over-sea vessels.

4. In all cases, the distinction of colour should never be adopted

except from absolute necessity.

5. Fixed lights and others of less power, may be more readily adopted

in narrow seas, because the _range_ of the lights in such situations is

generally less than that of open sea-lights.

6. In narrow seas also, the distance between lights of the same

appearance may often be safely reduced within much lower limits than is

desirable for the greater sea-lights; and there are many instances in

which the distance separating lights of the same character need not

exceed 50 miles, and there are peculiar cases in which even a much less

separation between similar lights may be sufficient.

7. Lights intended to guard vessels from reefs, shoals, or other

dangers, should in every case be placed, where practicable, to the

seaward of the danger itself, as it is desirable that seamen be enabled

to make the lights with confidence.

8. Views of economy in the first cost of a Lighthouse should never be

permitted to interfere with placing it in the best possible position;

and, when funds are deficient, it will generally be found that the

wisest course is to delay the work until a sum shall have been obtained

sufficient for the erection of the lighthouse on the best site.

9. The elevation of the lantern above the sea should not, if possible,

for sea-lights, exceed 200 feet; and about 150 feet is sufficient,

under almost any circumstances, to give the range which is required.

Lights placed on high headlands are subject to be frequently wrapped in

fog, and are often thereby rendered useless, at times when lights on a

lower level might be perfectly efficient. But this rule must not, and

indeed cannot, be strictly followed, especially on the British coast,

where there are so many projecting cliffs, which, while they subject

the lights placed on them to occasional obscuration by fog, would also

entirely and permanently hide from view lights placed on the lower land

adjoining them. In such cases, all that can be done is carefully to

weigh all the circumstances of the locality, and choose that site for

the lighthouse which seems to afford the greatest balance of advantage

to navigation. As might be expected, in questions of this kind, the

opinions of the most experienced persons are often very conflicting,

according to the value which is set on the various elements which enter

into the inquiry.

10. The best position for a sea-light ought rarely to be neglected for

the sake of some neighbouring port, however important or influential;

and the interests of navigation, as well as the true welfare of the

port itself, will generally be much better served by placing the

sea-light _where it ought to be_, and adding, on a smaller scale, such

subsidiary lights as the channel leading to the entrance of the port

may require.

11. It may be held as a general maxim, that the fewer lights that

can be employed in the illumination of a coast the better, not only

on the score of economy, but also of real efficiency. Every light

needlessly erected may, in certain circumstances, become a source of

confusion to the mariner, and, in the event of another light being

required in the neighbourhood, it becomes a _deduction_ from the means

of distinguishing it from the lights which existed previous to its

establishment. By the needless erection of a new Lighthouse, therefore,

we not only expend public treasure, but waste the means of distinction

among the neighbouring lights.

12. Distinctions of lights, founded upon the minute estimation of

intervals of time between flashes, and especially on the measurement of

the duration of light and dark periods, are less satisfactory to the

great majority of coasting seamen, and are more liable to derangement

by atmospheric changes, than those distinctions which are founded on

what may more properly be called the _characteristic appearance_ of the

lights, in which the times for the recurrence of certain appearances

differ so widely from each other as not to require for their detection

any very minute observation in a stormy night. Thus, for example,

flashing lights of five seconds interval, and revolving lights of half

a minute, one minute, and two minutes, are much more characteristic

than those which are distinguished from each other by intervals varying

according to a slower series of 5″, 10″, 20″, 40″, &c.

13. Harbour and local lights, which have a circumscribed range, should

generally be fixed instead of revolving; and may often, for the same

reason, be safely distinguished by coloured media. In many cases also,

where the purpose of guiding into a narrow channel is to be gained, the

leading lights which are used, should, at the same time, be so arranged

as to serve for a distinction from any neighbouring lights.

14. Floating lights, which are very expensive and more or less

uncertain from their liability to drift from their moorings, as well

as defective in power, should never be employed to indicate a turning

point in a navigation in any situation where the conjunction of lights

on the shore can be applied at any reasonable expense.

~Height of Lighthouse Tower, and its relation to range of Light.~

The spheroïdal form of the Earth requires that the height of a

Lighthouse Tower should increase proportionally to the difference

between the Earth’s radius and the secant of the angle intercepted

between the normal to the spheroïd at the Lighthouse and the normal

at the point of the light’s occultation from the view of a distant

observer. The effect of atmospheric refraction, however, is too

considerable to be neglected in estimating the _range_ of a light, or

in computing the height of a Tower which is required to give to any

light a given range; and we must, therefore, in accordance with the

influence of this element, on the one hand _increase_ the range due

to any given height, and _vice versa reduce_ the height required for

any given range, which a simple consideration of the form of the globe

would assign. In considering this height, we may proceed as follows:--

[Illustration: Fig. 92.]

Referring to the accompanying figure (No. 92), in which S′ _d_ L′ is

a segment of the ocean’s surface, O the centre of the earth, L′L a

Lighthouse, and S the position of the mariner’s eye, we obtain the

value of LL′ = H′, the height of the tower in feet by the formula,

2 _l_²

H′ = ------ (1.)

in which _l_ = the distance in English miles L′ _d_ at which the light

would strike the ocean’s surface. We then reduce this value of H′ by

the correction for mean refraction, which permits the light to be seen

at a greater distance, and which =

2 _l_²

------, (2.)

2 _l_² 2 _l_² 4 _l_²

So as to get, H = ------ - ------ = ------ (3.)

3 21 7

an expression which at once gives the height of the tower required, if

the eye of the mariner were just on the surface of the water at _d_,

where the tangent between his eye at S and the light at L would touch

the sea. We must, therefore, in the first instance, find the distance

_d_ S = _l′_, which is the radius of the visible horizon due to the

height SS′ = _h_ of his eye above the water, and is, of course, at once

obtained conversely by the expression:--

√(7 _h_)

_l′_ = -------- (4.)

Deducting this distance from SL, the whole effective range of the

light, we have L _d_ = _l_, and operating with this value in the former

equation,

4_l_²

H = -----

we find the height of the tower which answers the conditions of the

case.[81] From the above data the following Table has been computed.

[81] In the above expressions _l_ and _l′_ are given in English

miles, which in Scotland may be considered as bearing to nautical

miles the ratio of 5280 to 6088. In order to convert a distance given

in nautical miles to English miles, all that is needful is to add the

log of the number of nautical miles to log 5280, and subtract log

6088.

+-------+--------+--------++-------+--------+--------+

| | λ | λ′ || | λ | λ′ |

| H | Lengths|Lengths || H | Lengths|Lengths |

|Heights| in | in ||Heights| in | in |

| in |English |Nautical|| in |English |Nautical|

| Feet. | Miles. | Miles. || Feet. | Miles. | Miles. |

+-------+--------+--------++-------+--------+--------+

| 5 | 2·958 | 2·565 || 110 | 13·874 | 12·03 |

| 10 | 4·184 | 3·628 || 120 | 14·490 | 12·56 |

| 15 | 5·123 | 4·443 || 130 | 15·083 | 13·08 |

| 20 | 5·916 | 5·130 || 140 | 15·652 | 13·57 |

| 25 | 6·614 | 5·736 || 150 | 17·201 | 14·91 |

| 30 | 7·245 | 6·283 || 200 | 18·708 | 16·22 |

| 35 | 7·826 | 6·787 || 250 | 20·916 | 18·14 |

| 40 | 8·366 | 7·255 || 300 | 22·912 | 19·87 |

| 45 | 8·874 | 7·696 || 350 | 24·748 | 21·46 |

| 50 | 9·354 | 8·112 || 400 | 26·457 | 22·94 |

| 55 | 9·811 | 8·509 || 450 | 28·062 | 24·33 |

| 60 | 10·246 | 8·886 || 500 | 29·580 | 25·65 |

| 65 | 10·665 | 9·249 || 550 | 31·024 | 26·90 |

| 70 | 11·067 | 9·598 || 600 | 32·403 | 28·10 |

| 75 | 11·456 | 9·935 || 650 | 33·726 | 29·25 |

| 80 | 11·832 | 10·26 || 700 | 35·000 | 30·28 |

| 85 | 12·196 | 10·57 || 800 | 37·416 | 32·45 |

| 90 | 12·549 | 10·88 || 900 | 39·836 | 34·54 |

| 95 | 12·893 | 11·18 || 1000 | 41·833 | 36·28 |

| 100 | 13·228 | 11·47 || | | |

+-------+--------+--------++-------+--------+--------+

If the distance at which a light of given height can be seen by a

person on a given level be required, it is only needful to add together

the two numbers in the column of lengths λ or λ′ (according as Nautical

or English miles may be sought) corresponding to those in the column of

heights H, which represent respectively the height of the observer’s

eye and the height of the lantern above the sea. When the height

required to render a light visible at a given distance is required,

we must seek first for the number in λ or λ′ corresponding to the

height of the observer’s eye, and deduct this from the whole proposed

range of the light, and opposite the remainder in λ or λ′ seek for the

corresponding number in H.

~Diagonal Lantern.~

A considerable practical defect in all the lighthouse lanterns which

I have ever seen, with the exception of those recently constructed

for the Scotch Lighthouses, consists in the vertical direction of

the astragals, which, of course, tend to intercept the whole or a

great part of the light in the azimuth which they subtend.[82] The

consideration of the improvement which I had effected in giving a

diagonal direction to the joints of the fixed refractors, first led

me (as stated at p. 266, _ante_), to adopt a diagonal arrangement of

the framework which carries the cupola of zones and afterwards for the

astragals of the lantern. Not only is this _direction_ of the astragals

more advantageous for equalising the effect of the light; but the

greater stiffness and strength which this arrangement gives to the

frame-work of the lantern make it safe to use more slender bars and

thus also absolutely _less_ light is intercepted. The panes of glass

at the same time become triangular, and are necessarily stronger than

rectangular panes of equal surface. This form of lantern is extremely

light and elegant, and is shewn, with detailed drawings of some of its

principal parts, in Plate XXVI. To avoid the necessity of painting,

which, in situations so exposed as those which lighthouses generally

occupy, is attended with many inconveniences and no small risk, the

framework of the lantern is now formed of gun-metal and the dome is

of copper; so that a first order lantern of 12 feet diameter and 10

feet height of glass costs, when glazed, about L.1260. In order to

give the lightkeepers free access to cleanse and wash the upper panes

of the lantern (an operation which in snowy weather must sometimes

be frequently repeated during the night), a narrow gangway, on which

they may safely stand, is placed on the level of the top of the lower

panes, and at the top of the second panes, rings are provided of which

the lightkeepers may lay hold for security in stormy weather. A light

trap-ladder is also attached to the outside of the lantern by means of

which there is an easy access to the ventilator on the dome.

[82] I must also except the small pier light at Kirkcaldy, erected (I

believe in 1836) by my friend Mr EDWARD SANG.

~Glazing of the Lantern.~

Great care is bestowed on the glazing of the lantern, in order that

it may be quite impervious to water, even during the heaviest gales.

When iron is used for the frames, they are carefully and frequently

painted; but gun-metal, as just noticed, is now generally used in the

Scotch Lighthouses. There is great risk of the glass plates being

broken by the shaking of the lantern during high winds; and as much as

possible to prevent this, various precautions are adopted. The arris

of each plate is always carefully rounded by grinding; and grooves

about ¹⁄₂ inch wide, capable of holding a good thickness of putty, are

provided in the astragals for receiving the glass, which is ¹⁄₄ inch

thick. Small pieces of lead or wood are inserted between the frames and

the plates of glass against which they may press, and by which they

are completely separated from the more unyielding material of which

the lantern-frames are composed. Panes glazed in frames padded with

cushions, and capable of being temporarily fixed in a few minutes, in

the room of a broken plate, are kept ready for use in the Store-room.

Those framed plates are called _storm-panes_, and have been found very

useful on several occasions, when the glass has been shattered by large

sea-birds coming against it in a stormy night, or by small stones

violently driven against the lantern by the force of the wind.

~Ventilation of the Lanterns.~

The ventilation of the lanterns forms a most important element in the

preservation of a good and efficient light. An ill-ventilated lantern

has its sides continually covered with the water of condensation,

which is produced by the contact of the ascending current of heated

air; and the glass thus obscured obstructs the passage of the rays,

and diminishes the power of the light. In the Northern Lighthouses,

ventilators, capable of being opened and shut at pleasure, so as to

admit from without a supply of air when required, are provided in

the parapet-wall on which the lantern stands; the lantern roof also

is surmounted by a cover which, while it closes the top of an open

cylindric tube against the entrance of rain, and descends over it only

so far as is needful for that purpose, still leaves an open air-space

between it and the dome. This arrangement permits the current of

heated air, which is continually flowing from the lantern through the

cylindric tube, to pass between it and the outer cover, from which it

finally escapes to the open air through the space between the cover and

the dome. The door which communicates from the lightroom through the

parapet to the balcony outside, is also made the means of ventilating

the lightroom; and, for that purpose, it is provided with a sliding

bolt at the bottom, which, being dropped into one or other of the

holes cut in the balcony for its reception, serves to keep the door

open at any angle that may be found necessary. A useful precaution was

introduced by my predecessor, as Engineer to the Northern Lights Board,

in order to prevent the too rapid condensation of heated air on the

large internal surface of the lantern roof, which consists in having

two domes with an air-space between them, as shewn in the enlarged

diagrams in Plate XXVI.

An important improvement in the ventilation of Lighthouses was some

years ago introduced by Dr FARADAY into several of the Lighthouses

belonging to the Trinity House, and has since been adopted in all the

dioptric lights belonging to the Commissioners of Northern Lighthouses.

After mentioning several proofs of extremely bad ventilation in

Lighthouses, Dr FARADAY thus describes his apparatus:[83]

[83] Minutes of Institution of Civil Engineers, vol. i., p. 207.

“The ventilating pipe or chimney is a copper tube, 4 inches in

diameter, not, however, in one length, but divided into three or four

pieces; the lower end of each of these pieces for about 1¹⁄₂ inch

is opened out into a conical form, about 5¹⁄₂ inches in diameter at

the lowest part. When the chimney is put together, the upper end of

the bottom piece is inserted about ¹⁄₂ inch into the cone of the next

piece above, and fixed there by three ties or pins, so that the two

pieces are firmly held together; but there is still plenty of air-way

or entrance into the chimney between them. The same arrangement holds

good with each succeeding piece. When the ventilating chimney is fixed

in its place, it is adjusted so that the lamp-chimney enters about ¹⁄₂

inch into the lower cone, and the top of the ventilating chimney enters

into the cowl or head of the lantern.

“With this arrangement, it is found that the action of the ventilating

flue is to carry up every portion of the products of combustion into

the cowl; none passes by the cone apertures out of the flue into the

air of the lantern, but a portion of the air passes from the lantern

by these apertures into the flue, and so the lantern itself is in some

degree ventilated.

“The important use of these cone apertures is that when a sudden gust

or eddy of wind strikes into the cowl of the lantern, it should not

have any effect in disturbing or altering the flame. It is found that

the wind may blow suddenly in at the cowl, and the effect never reaches

the lamp. The upper, or the second, or the third, or even the fourth

portion of the ventilating flue might be entirely closed, yet without

altering the flame. The cone junctions in no way interfere with the

tube in carrying up all the products of combustion; but if any downward

current occurs, they dispose of the whole of it into the room without

ever affecting the lamp. The ventilating flue is in fact a tube, which,

as regards the lamp, can carry everything _up_ but conveys nothing

_down_.”

The advantages of this arrangement, as applied to the Northern

Lighthouses, were much less palpable than those which are described in

the beginning of Dr FARADAY’S paper, because their ventilation was very

good before its introduction; and the flame in particular was perfectly

steady, being by no means subject to derangement from sudden gusts of

wind from the roof in the manner noticed above.

~Arrangements and internal management of a Lighthouse.~

All the Lighthouses in the district of the Commissioners are under

the charge of at least two Lightkeepers, whose duties are to cleanse

and prepare the apparatus for the night illumination, to mount guard

singly after the light is exhibited, and to relieve each other at

stated hours, fixed by the printed regulations and instructions, under

which they act. The rule is, that no keeper on watch shall, under any

circumstances, leave the Lightroom until relieved by his comrade; and,

for the purpose of cutting off all pretext for the neglect of this

universal law, the dwelling-houses are built close to the Light Tower,

and means are provided for making signals directly from the Lightroom

to the sleeping apartments below. These signals are communicated by

air-tubes, through which, by means of a small piston, or a puff of wind

from the mouth, calls can be exchanged between the keepers, enabling

the man on guard in the Lightroom, at the end of the watch, or on any

sudden emergence, to summon his comrade from below, who, on being thus

called, answers by a counter-blast, to shew that the summons has been

heard and will be obeyed. For the purpose of greater security, in

such situations as the Bell Rock and the Skerryvore, four keepers are

provided for one lightroom; one being always ashore on leave with his

family, and the other three being at the Lighthouse, so that, in case

of the illness of one lightkeeper, an efficient establishment of two

keepers for watching the light may remain. At all the land-lighthouses

also, an agreement is made with some steady person residing in the

neighbourhood, who is instructed in the management of the light and

cleansing of the apparatus, and comes under an obligation to be ready

to do duty in the light-room when called upon, in the event of the

sickness or absence of one of the lightkeepers. This person is called

the _occasional keeper_, and receives pay only while actually employed

at the Lighthouse; but in order to keep him in the practice of the

duty, he is required to serve in the lightroom for a fortnight annually

in the month of January. The details of the lightkeeper’s duty may be

seen by referring to the instructions already alluded to, which will

be found in the Appendix.

Each of the two lightkeepers has a house for himself and family, both

being under a common roof, but entering by separate doors, as shewn

in Plates XXVII. and XXVIII., which exhibit the buildings for the

new Lighthouse at Ardnamurchan Point, on the coast of Argyllshire.

The principal keeper’s house consists of six rooms, two of which are

at the disposal of the visiting officers of the Board, whose duty in

inspecting the Lighthouse, or superintending repairs, may call them to

the station; and the assistant has four rooms, one of which is used as

a barrack-room for the workmen, who, under the direction of the Foreman

of the lightroom works, execute the annual repairs of the apparatus.

The early Lighthouses contained accommodation for the lightkeepers in

the Tower itself; but the dust caused by the cleaning of those rooms in

the Tower was found to be very injurious to the delicate apparatus and

machinery in the lightroom. Unless, therefore, in situations such as

Skerryvore, where it is unavoidable, the dwellings of the lightkeepers

ought not to be placed in the Light Tower, but in an adjoining building.

Great care should be bestowed to produce the utmost cleanliness in

everything connected with a Lighthouse, the optical apparatus of which

is of such a nature as to suffer materially from the effect of dust in

injuring its polish. For this purpose covered ash-pits are provided at

all the dwelling-houses, in order that the dust of the fire-places may

not be carried by the wind to the lightroom; and for similar reasons,

iron floors are used for the lightrooms instead of stone, which is

often liable to abrasion, and all the stonework near the lantern is

regularly painted in oil.

~Cleansing of Apparatus.~

If, in all that belongs to a lighthouse, the greatest cleanliness be

desirable, it is in a still higher degree necessary in every part of

the lightroom apparatus, without which the optical instruments and

the machinery will neither last long nor work well. Every part of

the apparatus, whether lenses or reflectors, should be carefully

freed from dust before being either washed or burnished; and without

such a precaution, the cleansing process would only serve to scratch

them. For burnishing the reflectors, prepared _rouge_ (tritoxide of

iron) of the finest description, which should be in the state of an

impalpable powder of a deep orange-red colour, is applied, by means

of soft chamois skins, as occasion may require; but the great art of

keeping reflectors clean consists in the daily, patient, and skilful

application of manual labour in rubbing the surface of the instrument

with a perfectly dry, soft, and clean skin, without rouge. The form

of the hollow paraboloid is such, that some practice is necessary in

order to acquire a free movement of the hand in rubbing reflectors; and

its attainment forms one of the principal lessons in the course of the

preliminary instruction, to which candidates for the situation of a

light-keeper are subjected at the Bell Rock Lighthouse. For cleansing

the lenses and glass mirrors, spirit of wine is used. Having washed

the surface of the instrument with a linen cloth steeped in spirit

of wine, it is carefully dried with a soft and dry linen rubber, and

finally rubbed with a fine chamois skin, free from any dust which would

injure the polish of the glass, as well as from grease. It is sometimes

necessary to use a little fine rouge with a chamois skin, for restoring

any deficiency of polish which may occur from time to time; but in

a well-managed lighthouse this application will seldom, if ever, be

required.

The machinery of all kinds, whether that of the mechanical lamp or the

revolving apparatus, should also be kept scrupulously clean, and all

the journals should be carefully oiled.

~Mode of measuring the relative intensity and power of Lights.~

As I have had frequent occasion to speak of the comparative power of

lights, it will not be out of place to present the reader with a few

practical observations, chiefly drawn from the excellent work of M.

PECLET to which I have so often referred, on the measurement of the

intensity of lights by the method of shadows.

[Illustration: Fig. 93.]

The intensity of light decreases as the observer recedes from the

luminous body, in proportion to the square of his distance. Suppose

a beam of light to proceed from a radiant at F, and we shall have the

rays which, of course, move in straight lines, gradually receding

from each other, as _b_, _b′_, _b″_, _b‴_, and _c_, _c′_, _c″_, _c‴_,

so that the section of the beam will increase with the distances

F _b_, and F _c_; and the same number of rays, being thus spread over

spaces continually increasing, will illuminate the surfaces with a

less intensity. This decrease of intensity will, therefore, be in the

inverse ratio of the extent of the transverse parallel sections of

the luminous cones at _b_ and _c_, which, we know, increase as the

square of their distances from the apex of the cone at F. Hence we

conclude, that the _intensity of any section of a divergent beam of

light decreases as the square of its distance from the radiant_. This

law furnishes us with a simple measure of the comparative intensity of

lights. If we suppose two lights so placed that they may separately

illuminate adjacent portions of a vertical screen of paper, we may, by

repeatedly comparing the luminousness of those surfaces, and moving

one of the lights farther from, or nearer to the screen, at length

cause the separate portions of the paper to become equally luminous.

This arrangement, however, has many practical difficulties, which I

shall not wait to specify; but shall at once indicate a more simple

and equally correct mode of obtaining the same result, by means of the

shadows cast by the lights from an opaque rod, in a vertical position

at O (fig. 94), placed between them, and a screen covered with white

paper on which the shadows fall. It is obvious that the light at F

would cause the object O to cast a shadow at SS, while the light at

F′ would cast a shadow at S′S′. But while the shadow at S would still

receive light from F′, S′ would receive light from F, so that those two

shadows are, in fact, the only portions of the screen which are each

illuminated only by one of the lights, while every other portion of

its surface receives light from both the radiants at F and F′. If we

suppose F to be the weaker light, we can bring it nearer the screen,

until the shadow S′S′, shall become similar in appearance to the shadow

SS; and we shall have the ratio of the intensity of the light at F to

that of the light at F′, as (FS′)² is to (F′S)², which distances must

be measured with the greatest exactness. Such is the mode commonly used

in estimating the comparative intensities of two lights; but there

are various precautions which are needful in order to prevent errors

in comparing the deepness of the shadows, and to insure the greatest

attainable accuracy in the estimate of the power of the lights, which I

shall endeavour briefly to describe.

[Illustration: Fig. 94.]

~More accurate comparison of the intensity of Lights.~

The difficulties of estimating the deepness or sharpness of the shadow

is very great, and many persons seem quite incapable of arriving at

any right judgment in this matter. The same person also will discover

such unaccountable variations in his decision after observations made

at short intervals of time, as, one would think, can only arise from

a sudden change of the intensity of one or both lights. M. Peclet, in

his _Traité de l’éclairage_, gives, as the result of his experience

(and I can fully confirm his result by my own), that those differences

depend less frequently on any real difficulty of estimating the

deepness of the shadows, than on variations in the position of the

observer, or rather in the angle at which he views the shadows, and

that, consequently, in proportion to the distance between the two

shadows, this source of error is increased. Any thing like a glossy

texture of the surface of the screen, which then, of course, becomes a

reflector, also tends to aggravate this evil. Thus, if the two lights

which are to be compared be placed on a table, in such situations as

to spread pretty far apart on the screen the shadows of a vertical rod

placed between them; and if the shadow nearer to the observer seem to

be a little deeper or sharper than the other, let the observer look

at them from the other side of the table, and their difference will

be reversed, and that which seemed the paler, will become the deeper.

Again, if the difference between the two shadows be very great when

seen from the right side of the screen, it may happen that, on viewing

them from the left hand, the difference may still be in favour of the

same shadow, but in a much less degree.

“When I observed this effect,” says M. Peclet,[84] “I tried to view

the shadows through a transparent screen, but I remarked the same

variations. They were indeed even more sensible; for a variation in the

distance of the eye of a few centimètres, made a prodigious change in

the deepness of the shadows. I observed also that the shadow was much

deeper when seen in the line of the light, and that in every other

direction, it became paler in proportion as the eye receded from that

direction.

[84] Traité de l’éclairage, p. 214.

“In all the cases which I have just described, the differences of

the tints when the position is changed, increase in proportion as

the shadows are farther separate; and they grow very minute when the

shadows are almost touching each other.

[Illustration: Fig. 95.]

“Let AB (fig. 95) be a white opaque surface, _a_, a luminous body, and

_m_, a black opaque body, then the shadow _b′_ cast on AB, will appear

deeper when observed from P, than as seen from Q. This is a fact which

may be easily verified, and the cause of which is easily conceived.

In fact, the surface AB, although it disperses the light, must still

reflect more of it, in the directions in which the regular reflection

takes place; and hence the rays which are reflected round about the

shadow, must have a greater intensity in the direction of P than in

that of Q, and, consequently, the shadow _b′_ must appear deeper from

the point P than from Q.

[Illustration: Fig. 96.]

“If we now place (fig. 96) two lights in front of the screen AB, at

such distances that the two shadows _a′_ and _b′_ should have equal

intensities, it is evident that if the eye be placed at P, the shadow

_b′_ must appear more intense than the shadow _a′_, and that the

reverse will take place if the eye be at Q. But the difference which is

then observed, arises not only from the difference in the brightness of

the parts surrounding the shadows, but also from a difference in the

intensity of the shadows themselves; for the shadow _b′_ is illuminated

by _b_, and radiates much more towards Q than towards P; and, on the

contrary, the shadow _a′_, which is illuminated by _a_, radiates much

more towards P than towards Q. We perceive also why the _differences_

of the tints increase with the separation of the two shadows, and

why they become very small when the shadows touch each other; it is

because, in proportion as the shadows are farther apart, each of them

is illuminated more obliquely, and a greater quantity of light is

radiated (by reflection) in the regular direction. When they touch each

other, on the contrary, they are illuminated almost perpendicularly,

and consequently the shadows radiate light almost equally on either

side.

“Those anomalies of a like kind which are observed when the shadows

are viewed through a translucent body, such as paper or linen, may

be referred to a similar cause. We know, in fact, that, in looking

through a translucent medium, we always, more or less, distinctly

perceive the luminous body behind it, and, also, that there is a very

large proportion of the rays which traverse the body, which stray but

a little from the direction which they would follow if the substance

were absolutely transparent. Consequently, the space which surrounds

the shadow is more luminous in proportion as we come nearer to the

direction of the shadow; and as the absolute intensity of the shadows

diminishes as we come nearer to the direction of the rays which light

them, those two effects concur to increase the intensity of that shadow

to which the eye is nearer.

“As the dispersion by reflection is much more complete than by

refraction, the variations of which we have just spoken are much

greater with a transparent screen, through which the shadows are

viewed, than with an opaque screen (from which they are reflected).

“This, then, is the mode of observing which has appeared to me the

best, and by means of which we may obtain very great precision in

measuring the intensity of two lights. I view, first, the two shadows

in such a manner that both of them may be seen in succession from

either side of the body which produces them, and at equal distances.

For this purpose I use a good opera-glass. I alter the distance of

the flames until in those two positions I perceive the differences

(of the intensity in the shadows) to be in opposite directions. The

distances of the lamps may then be considered as very nearly in the

proper proportion for producing equal shadows, and to make them exactly

so, the differences, which are observed on either side (of the centre

line between them), should be equal; and, of course, the two shadows

themselves, seen at one moment from either side of the opaque body,

should be perfectly equal also.[85] These three observations, which

mutually serve to verify or correct each other, will lead, with a

little practice, to very great precision in the result. We may, also,

by using a narrow screen, bring the shadows sufficiently near to touch

each other; the variations of the tints then become very small by any

change of our position, and we may, in this case, rest content with

observing them from one point. To get rid of large penumbrae which are

always an obstacle in forming a right estimate of the tints of the

shadows, I place the opaque body very near the screen.

[85] I prefer to view the exterior portions of both shadows from the

central line itself, in which case the opaque rod stands between

them, because, in this manner, I obtain a more correct comparison by

the direct contrast of the surfaces than by successive views of them,

however quickly taken.

[Illustration: Fig. 97.]

“When we wish to make a great many observations, it is very convenient

to mark divisions on the table (which carries the lights), in order

to read off, by means of them, the distance of the lamps from the

shadows which they illuminate. By this means, each observation need

not occupy more than two minutes. I generally use a table CC DD (fig.

97), about two mètres long (6 feet 6 inches), by 80 centimètres wide (2

feet 8 inches). At one end I place the screen AB, covered with white

paper, dull (or not glazed), and kept in a vertical plane by two small

pieces P and Q. Through the point M, the centre of the opaque body,

I draw two lines M _f_ and M _g_, equally inclined to the central line

_x_ _y_, whose extremities _b′_, _a′_ are the axes of the two shadows.

These lines must be inclined in such a manner that the distance of the

shadows may be a little less than the diameter of the opaque body, or

so that they may actually touch each other, according to the mode of

observing which you wish to follow. These lines M _f_, M _g_ I divide

into decimètres and centimètres, starting from the points _a′_, _b′_

and over these lines I place the centres of the flames; the distance

between the shadows remains always the same, whatever may be the

distance of the lamps: to determine the distance of each lamp from the

shadow which it illuminates, we ought, strictly speaking, to take the

distance of the centre of the flame _b_ from the point _a′_; but as

the distance from the point _b_ to the point _a′_ differs little from

the distance between the points _b_ and _b′_, we assume the latter

for the former, without causing any sensible error. That distance may

be obtained very conveniently by taking the half of the sum of the

distances of the two extremities _z_ and _z′_ of the diameter of the

pedestal of the lamp. When the burner is not placed over the centre of

the pedestal, we may suspend from it a small plummet, whose point will

touch some division and indicate the distance between the centre of the

burner and the shadow.

“When the lights are coloured, the shadows are coloured also, and it is

then far more difficult to judge accurately of their intensity. They

may in that case be much better seen from the point _x_, as the black

opaque body which is interposed between them renders the difference of

colour less sensible to the eye.

“The opaque body M is a cylindric rod of iron, whose upper part is

blackened in the flame of a lamp, in order to prevent the reflection

which might interfere with the _sharpness_ (_netteté_) of the shadows,

and to make them more distinct when they are viewed from the point

x.”[86]

[86] Those who feel a curiosity to look farther into this subject may

consult Count Rumford’s elaborate paper in the Phil. Trans. for 1794,

p. 67.

I shall make a few trifling additions to M. Peclet’s clear description

of his excellent mode of measuring the intensity of lights. It is, of

course, presumed throughout, that the centres of the flames should be

on one level; and I have found it most convenient to place the lamps

on small carriages with rollers, which are guided by means of fine

strips of wood nailed along the table in the directions _g_ M and _f_ M,

and carrying the divided scales of centimètres. This affords the means

of making any slight change in the position of the lamps so easily,

as entirely to avoid the disturbance of the flame which ensues from

lifting the lamp and readjusting it in another position; and will,

in practice, be found very convenient when many observations are to

be made. I have already said that my own experience has satisfied me

that, with the aid of a good opera-glass, the central observation

of the two shadows, with the opaque rod between them, is by far the

best, and conducts, at once, to a result which is confirmed by the

observations of two assistants who watch the shadows at the same time

on opposite sides of the table, and at equal distances from them. I

have found it convenient in comparing lights, to cover the table with

dull black linen cloth, and to surround it with curtains of the same

material, hung from slender brackets, in such a manner as to leave

space for the observer to move freely round the table within them. The

curtains prevent reflection from the walls of the chamber in which the

experiments may be conducted, and also lessen the disturbing effects

of currents of air. When a comparison of the _intensity_, and not of

the _aggregate power_ of two flames, is to be made, it is necessary

to adopt the precaution of inclosing the lights in opaque boxes, with

slits of equal area in each, placed on the same level, and so arranged,

in reference to the flames, as to be directly opposite the brightest

portion of each. After what has been said, it will be almost needless

to add that the _quotient of the square of the greater observed

distance divided by the lesser, is the ratio of the illuminating

power of the two flames_. The most convenient mode of registering

observations, and that which is generally practised, is in the form of

a Table like the following:--

+-------+---------------+---------------+---------------+

| +-------+-------+-------+-------+-------+-------+

+-------+-------+-------+-------+-------+-------+-------+

| 1 | 143 | 140 |20,449 |19,700 | 1·00 | 0·958 |

| 2 | 117 | 114 |13,689 |12,996 | 1·00 | 0·949 |

+-------+-------+-------+-------+-------+-------+-------+

As a standard lamp by which to test others, I believe few will be found

superior to the best Carcel lamp, which has a clockwork movement, and

whose flame continues to increase in power for about four hours after

it is lighted; after which it maintains its state permanently, until

the supply of oil fails. This fact was verified by M. Peclet with the

greatest care. “I took,” says he, “two similar lamps. They were lighted

at the same time, and their relative intensities were measured. One

was then extinguished, without touching the wick, and its clockwork

movement was stopped. One hour afterwards, I set the clockwork in

motion and relighted the lamp, but without touching the wick. It was

found in the same state as at the first comparison, and I measured its

intensity in reference to the first. Those experiments I repeated

every hour, and these are the results which I obtained. The lamp which

I call No. 1, is that which remained continually burning; No. 2, is

that which was only lighted during the continuance of the (successive)

observations.”

+------------++-------------------------+

| || Intensities. |

| Times of ++------------+------------+

|Observation.||Lamp, No. 1.|Lamp, No. 2.|

+-----+------++------------+------------+

| H. | M. || | |

| 5 | 30 || 100 | 100 |

| 6 | 30 || 103 | 100 |

| 7 | 30 || 106 | 100 |

| 8 | 30 || 110 | 100 |

| 9 | 30 || 117 | 100 |

| 10 | 30 || 117 | 100 |

| 11 | 30 || 117 | 100 |

| 12 | 30 || 117 | 100 |

+-----+------++------------+------------+

This curious scale of increase in power, seems to be solely due to a

peculiarity of the manner in which the lamp, that derives its supply

of oil by clockwork, becomes heated; and the effect may be described

as follows: The heating of the wicks, the chimney, and the oil in this

burner, as in that of all other lamps, tends to increase the light;

but, in an ordinary lamp, acting by a constant pressure, this _maximum_

of heat is soon attained; whereas in the clockwork-lamp, into the

burner of which the oil is thrown up by a pump, the whole of the oil in

the cistern must reach its maximum temperature before the _best_ effect

of that lamp is produced. After this state has been reached, there is

no disturbing influence at work, and the lamp burns steadily as long as

the oil lasts.

I have myself tried what may naturally appear to be the most simple

mode of obtaining an unvarying standard-light, by employing a

gas-burner, supplied from a gasometer under a constant pressure;

but I found it very difficult to obtain satisfactory proof of the

constancy of the pressure; and in a large town, where there are many

burners around one, their lighting or extinction is found to exercise

a material influence in changing the condition of the flame. I must

confess that I have always been disappointed in attempting to use a

gas-flame as a standard of comparison.

~Floating Lights.~

There are various dangers on the shores of Britain, more especially

at the entrance of the great estuaries of England and also in

Ireland, whose position is such as to put them beyond the reach of

regular lighthouses. Sand-banks which are too soft to sustain a solid

structure, and have too deep water on them to admit of the erection of

screw-pile lighthouses, are often the sites for mooring light-vessels,

to guide the mariner into the entrance of some estuary, or enable him

to thread his way through the mazes of _gats_ and channels, which, even

during the daytime, baffle the mariner, who sees no natural object on

the low sandy shores of the neighbouring coast to help him to guess at

his true position. The first Light-vessel moored on the coast of Great

Britain, was that at the Nore in 1734. There are now no fewer than 26

floating lights on the coast of England.

By the kindness of the Elder Brethren of the Corporation of Trinity

House of Deptford Strond, I am enabled to give the following brief

sketch of the nature and peculiarities of Floating Lights which was

communicated to me by Mr Herbert, the secretary of the Corporation:--

“The annual expense of maintaining a Floating Light, including the

wages and victualling of the crew, who are eleven in number, is,

on an average, L.1000; and the first cost of such a vessel, fitted

complete with lantern and lighting apparatus, anchors, cables, &c.,

is nearly L.5000. The lanterns are octagonal in form, 5 feet 6 inches

in diameter; and, where fixed lights are exhibited, they are fitted

with eight Argand lamps, each in the focus of a parabolic reflector of

twelve inches diameter; but, in the revolving lights, four lamps and

reflectors only are fitted. The greatest depth of water in which any

light-vessel belonging to the Corporation of Trinity House of Deptford

Strond at present rides, is about 40 fathoms (which is at the station

of the _Seven Stones_ between the Scilly Islands and the coast of

Cornwall).

“The Corporation’s light-vessels are moored with chain-cables of 1¹⁄₂

inch diameter, and a single mushroom anchor of 32 cwt., in which cases

the chain-cables are 200 fathoms in length; some of the said vessels

are moored to _span-ground_ moorings, consisting of 100 fathoms of

chain to each arm, and a mushroom anchor of similar weight at the end

of each; a riding cable of 150 fathoms being in such cases attached to

the centre ring of the ground chain. The tonnage and general dimensions

of the light-vessel are given on the drawing of the lines.” (See Plate

XXIX.)

~Beacons and Buoys.~

Still lower in the scale of “signs and marks of the sea,” are Beacons

and Buoys, which are used to point out those dangers which, either

owing to the difficulty and expense that would attend the placing

of more efficient marks to serve by night as well as by day, are

necessarily left without lights, or which, from the peculiarity of

their position, in passages too intricate for navigation by night,

are, in practice, considered to be sufficiently indicated by day-marks

alone. Beacons, as being more permanent, are preferred to Buoys; but

they are generally placed only on rocks or banks which are dry at some

period of the tide. On rocks, in exposed situations, the kind of Beacon

used is generally that of squared masonry, secured by numerous joggles

(as shewn at Plate XXXII.); and in situations difficult of access,

and in which works of uncompleted masonry could not be safely left

during the winter season, an open framework of cast-iron pipes, firmly

trussed and braced, and secured to the rock with strong _louis-bats_,

is preferred. The details of this framework are shewn at Plates XXX.

and XXXI. A stone Beacon of the form and dimensions shewn in Plate

XXXII., may be erected for about L.700, and the iron Beacon shewn at

Plate XXX., for about L.640. In less exposed places, where the bottom

is gravel or hard sand, a conical form of Beacon, composed of cast-iron

plates, united with flanges and screws, with rust-joints between them,

is sometimes used. A Beacon of this kind is shewn at Plate XXXII.,

which can be erected for about L.400.

Lastly, Buoys, which may be regarded as the least efficient kind

of mark, and as bearing the same relation to a Beacon that a

Floating-light does to a Lighthouse, are used to mark by day _dangers_

which are always covered even at low water, and also to line out the

fair-ways of channels. They are, for the most part, of one of the three

forms shewn in Plate XXXIII., viz., the _Nun-buoy_, in the form of a

parabolic spindle, generally truncated at one end, so as to carry a

mast or frame of cage-work, and loaded at the other end, so as to float

in a vertical position; the _Can-buoy_, which is a conoid floating

on its side; and, lastly, the _Cask-buoy_, which is a short frustum

of a spindle truncated at both ends, but almost exclusively used for

carrying the warps of vessels riding at moorings. Those buoys are of

various sizes and differ in cost. Mast-buoys, from 10 to 15 feet in

length, cost from L.23, 15s. to L.48; and those of the Ribble and the

Tay, which are 21 and 24 feet long, cost respectively L.105 and L.79;

the _Can-buoys_ are from 5 to 8 feet long, and cost from L.13, 13s. to

L.20, 5s. Large buoys are often built on _kneed_ frames resembling the

timbers of vessels. The Cask-buoy is generally 6 feet long, and costs

L.22, 15s. All these buoys are formed of strong oaken barrel-staves,

well hooped with iron rings, and shielded with soft timber; and the

nozzle-pieces at the small end of the _Nun_ and _Can_ buoys are

generally solid quoins of oak, formed with a _raglet_ or groove to

receive the ends of the staves. Much skill, on the part of the cooper,

is required in heating and moulding the staves to the required form;

and great care must be taken that they be of well-seasoned timber.

Buoys are not caulked with oakum, but with dry flags closely compressed

between the edges of the staves, which swell on being wet; and they are

carefully proved by _steaming_ them like barrels, to see if they be

quite tight. Buoys are also formed of sheet-iron, in which case they

are sometimes protected with fenders of timber; but they have been

found more troublesome for transport, and, for most situations, are

considered less convenient than those of timber.

In the beginning of 1845, I suggested the idea of rendering Beacons and

Buoys useful during night, by coating them with some phosphorescent

substance, or surmounting them with a globe of strong glass filled with

such a preparation, whose combustion is very slow, and emits a dull

whitish light and little heat. Some experiments were accordingly made

by my suggestion; but I cannot add that any practically useful result

has been obtained.

In laying down Beacons or Buoys, their position is fixed, as may be

seen in the Table in the Appendix, either by the intersection of two

lines drawn through two leading objects on the shore (the magnetic

bearings of which are given for the sake of easy reference on the spot,

in finding out the marks), or by means of the angles contained between

lines drawn to various objects on the shore, which meet at the Beacon

or Buoy from which they are measured by means of a sextant. In the

latter case, the angles are always measured around the whole horizon,

thus affording a check by the difference of their sum from 360°.

The magnetic bearing of one of those lines is afterwards carefully

ascertained, by means of the prismatic compass (if possible from one

of the objects on shore, and if not, conversely from the Beacon or

Buoy), so as to afford the means of translating the whole into magnetic

bearings for the use of seamen. The buoys are moored, as shewn in

Plate XXXIII., by means of chains and iron sinkers, with a sufficient

allowance in the length of the chain to permit them to _ride_ easily.

APPENDIX.

APPENDIX, No. I.

TABLE OF CO-ORDINATES OF AN HYPERBOLIC COLUMN WHOSE DIAMETER AT THE TOP

= 16 FEET, AT THE BASE = 42 FEET, AND HEIGHT = 120·25 FEET.

The column is generated by the revolution of a rectangular hyperbola

about one of its asymptotes. In the annexed figure (No. 98), _a_ _f_ is

the height of the column, _a_ _c_ and _f_ _h_ the radii of its base and

top; and we have to determine the particular hyperbola which will pass

through the points _c_, _h_.

Putting _b_ _e_ = _x_; _e_ _g_ = _y_, the equation to the curve,

referred to its asymptotes, is

_a_²

_x_ _y_ = ----,

in which the value of the constant

_a_²

----

is to be found. For this purpose we have the conditions _a_ _c_ = 21;

_f_ _h_ = 8; and _a_ _f_ = 120·25. Let the co-ordinates of the point

_c_ be _x′_, _y′_, and of _h_, _x″_, _y″_, then _y′_ = 21; _y″_ = 8;

_x″_ = _x′_ + 120·25.

[Illustration: Fig. 98.]

_a_²

And since _x′_ _y′_ = ---- = _x″_ _y″_

we have 21 _x′_ = 8 (_x′_ + 120·25)

from which _x′_ = 74

_a_²

and ---- = _x′_ _y′_ = 74 × 21 = 1554.

Therefore _x_ _y_ = 1554.

Transferring the origin to _a_, _x_ becomes _x_ - _x′_ = _x_ - 74, and

_y_ (_x_ - 74) = 1554, and the required equation by which the following

Table was computed is,

1554

_y_ = --------.

_x_ - 74

TABLE _of the Radii of the Hyperbolic Column at each foot of its

Height_.

+-------+-------++-------+-------++-------+-------++-------+-------+

|Height.|Radius.||Height.|Radius.||Height.|Radius.||Height.|Radius.|

+-------+-------++-------+-------++-------+-------++-------+-------+

| 0 | 21·000|| 31 | 14·800|| 62 | 11·426|| 93 | 9·305 |

| 1 | 20·720|| 32 | 14·660|| 63 | 11·343|| 94 | 9·250 |

| 2 | 20·447|| 33 | 14·523|| 64 | 11·261|| 95 | 9·195 |

| 3 | 20·182|| 34 | 14·389|| 65 | 11·180|| 96 | 9·141 |

| 4 | 19·923|| 35 | 14·257|| 66 | 11·100|| 97 | 9·088 |

| 5 | 19·671|| 36 | 14·127|| 67 | 11·021|| 98 | 9·035 |

| 6 | 19·425|| 37 | 14·000|| 68 | 10·944|| 99 | 8·983 |

| 7 | 19·185|| 38 | 13·875|| 69 | 10·867|| 100 | 8·931 |

| 8 | 18·951|| 39 | 13·752|| 70 | 10·792|| 101 | 8·880 |

| 9 | 18·723|| 40 | 13·632|| 71 | 10·717|| 102 | 8·830 |

| 10 | 18·500|| 41 | 13·513|| 72 | 10·644|| 103 | 8·780 |

| 11 | 18·282|| 42 | 13·397|| 73 | 10·571|| 104 | 8·730 |

| 12 | 18·070|| 43 | 13·282|| 74 | 10·500|| 105 | 8·681 |

| 13 | 17·862|| 44 | 13·170|| 75 | 10·430|| 106 | 8·633 |

| 14 | 17·659|| 45 | 13·059|| 76 | 10·360|| 107 | 8·586 |

| 15 | 17·461|| 46 | 12·950|| 77 | 10·291|| 108 | 8·539 |

| 16 | 17·267|| 47 | 12·843|| 78 | 10·224|| 109 | 8·492 |

| 17 | 17·077|| 48 | 12·738|| 79 | 10·157|| 110 | 8·446 |

| 18 | 16·891|| 49 | 12·634|| 80 | 10·091|| 111 | 8·400 |

| 19 | 16·710|| 50 | 12·532|| 81 | 10·026|| 112 | 8·355 |

| 20 | 16·532|| 51 | 12·432|| 82 | 9·962|| 113 | 8·310 |

| 21 | 16·358|| 52 | 12·333|| 83 | 9·898|| 114 | 8·266 |

| 22 | 16·188|| 53 | 12·236|| 84 | 9·835|| 115 | 8·222 |

| 23 | 16·021|| 54 | 12·141|| 85 | 9·774|| 116 | 8·179 |

| 24 | 15·857|| 55 | 12·046|| 86 | 9·712|| 117 | 8·136 |

| 25 | 15·697|| 56 | 11·954|| 87 | 9·652|| 118 | 8·094 |

| 26 | 15·540|| 57 | 11·862|| 88 | 9·593|| 119 | 8·052 |

| 27 | 15·386|| 58 | 11·773|| 89 | 9·534|| 120 | 8·010 |

| 28 | 15·235|| 59 | 11·684|| 90 | 9·476|| 120·25| 8·000 |

| 29 | 15·087|| 60 | 11·597|| 91 | 9·418|| ... | ... |

| 30 | 14·942|| 61 | 11·511|| 92 | 9·361|| ... | ... |

+-------+-------++-------+-------++-------+-------++-------+-------+

APPENDIX, No. II.

NOTES ON THE MANUFACTURE OF PARABOLOÏDAL REFLECTORS,

from Information furnished by Mr JAMES MURDOCH, OF THE NORTHERN LIGHTS

SERVICE.

[Illustration: Fig. 99.]

The reflector-plate consists of virgin-silver and the purest copper

(from the ingot), in the proportion of 6 oz. of silver to 16 oz. of

copper. The two metals are in pieces, forming a flat parallelopepid

of about nine inches of surface. Being first thoroughly scraped and

cleared from rust with a file, they are tied together with wire and

placed in the furnace, where they are united by means of a flux

composed of burnt borax and nitre, mixed to the consistence of cream.

Their thickness is sufficient to admit of their being repeatedly

passed through the rolling-mill, so as at last to come out a plate

twenty-eight inches square. Every time it is passed through the

rollers, the plate is annealed in the furnace before being again

pressed. It is then cut into a circular disc ready for working; and

great care should be taken to keep the metal perfectly clean during

the whole of the hammering and polishing processes. The first step

towards forming the plate to the curve, is to raise the back or copper

side to a slight convexity by beating, with the boxwood mallet (fig.

99), rounded at each end, _c_ and _d_, its inner or silver side upon a

large block of beechwood, of a form slightly concave. This beating is

begun at the edge of the plate, and gradually reaches the centre. After

the disc has been raised to the proper height on the wooden block,

the next step is to take it to the _horse_ (fig. 103, opposite page),

where it is beaten with the wooden mallet (fig. 100), its concave face

being in contact with the bright steel-head _a_ (fig. 103), until it

has nearly reached the proper height for the reflector, for which

the workman has a gauge or mould to guide him; in this course of

_raising_, as it is called, the _peened_ face _b_ _a_ _b_ (fig. 100)

is first used, and then recourse is had to the opposite or flat face

for smoothing it after being raised. In this last course of raising, as

well as in the process of smoothing the reflector all over, the workman

bestrides the _horse_.

[Illustration: Fig. 100.]

[Illustration: Fig. 101.]

During the process of raising with the peened side of the mallet,

an external mould FGHF (fig. 101), with a needle-point P, at its

vertex, is applied, to indicate its proper position with reference

to the mould; and allowance is made on the height and diameter

of the reflector to meet the expansion of the metal during the

_hard-hammering_ which is to follow. After each course of the raising

with the wooden mallets, the reflector must be annealed in the

following manner:--The reflector is first damped with clean water, and

its surface dusted over with a powder, composed of one pint of powdered

charcoal to one ounce of saltpetre, which is applied by means of a thin

flannel bag. The reflector is then put on a clear charcoal fire, where

it is turned round as the powder flies off, which is an indication that

the metal is duly heated. Over-heating is very injurious. When removed

from the fire, the reflector is plunged into a large tub, containing

what is called the _pickle_, which is a solution of one quart of

vitriol in five or six gallons of water. After this it is washed with

clean water, and scoured with Calais sand.

The next step is to put the reflector, thus raised _nearly_ to its

true form, into an iron stool, where a small hole being drilled in its

vertex, a circle is described from this point with a beam-compass, so

as to cut the paraboloïd to the proposed size.

[Illustration: Fig. 102.]

[Illustration: Fig. 103.]

[Illustration: Fig. 104.]

[Illustration: Fig. 105.]

The reflector is next _hard-hammered_ all over (or _planished_, as

it is technically termed) on the bright steel-head _a_ (fig. 103),

with the planishing hammer (fig. 102); and to facilitate working, the

reflector is slung in a flexible frame SS, and counterbalanced by

a weight _w_, hanging by a cord over the pulleys _p_ _p_. When the

reflector is all _planished_ over, the next process is the _smoothing_,

which is done on the steel-head _a_, with a lighter hammer (fig. 104),

muffled with fine parchment at each end. After it is smoothed comes the

_finishing_, or what is called the _filling up to the mould_. This is a

tedious process, and the workman requires continually to have recourse

to the marble table at M, on which he lays the reflector, as shewn in

fig. 105, and applies to successive portions of its surface the mould

_g_ _n_, which has a needle-point centred at _n_, in the small hole

drilled in the vertex. During this examination, he marks with a fine

slate-pencil those portions of the reflector which do not meet the

mould _g_ _n_. The parts, so marked, are gently gone over with the

muffled hammer, until every point touches the mould. This last process

requires great caution; for, if any part of the surface be raised above

the gauge, it is hardly possible to remedy it. Such a mistake, indeed,

can only be corrected by annealing the reflector afresh, and bringing

it back to the true form with the mallet; but reflectors so _cobbled_

are never good. The table M (fig. 105) rests on a square box C, in

which the tools and moulds are kept.

[Illustration: Fig. 106.]

When thus finished from the hammer, the reflector is put into the

apparatus shewn in fig. 106, which is placed at the end of a long

dark corridor. RR is a wooden frame fixed to the wall with projecting

brackets at K, which carry the reflector, fixed at E, E, by means of

screws, so as always to have a definite position with reference to the

bracket B, which carries the lamp and its fountain _f_, so arranged

that its flame may admit of perfect adjustment to the point which

_ought_ to be the focus of the reflector. For the purpose of this

adjustment, S shews screws for raising and depressing the level of

the burner; and the lines or marks M, M′ shewn at the sockets J being

brought _into line_, regulate the _position_ of the burner in _the

plane of the focus_, after it has been raised to the level of that

plane by means of the screws at S. The lamp being lighted and thus

properly placed, its effect on the reflector’s surface is observed by

some one stationed at a convenient distance; and if the whole surface

appear luminous, the instrument is considered fit for polishing;

but if any dark spaces be found in it, the whole reflector must be

again carefully tested by means of the mould, and the defective parts

remedied in the manner above described.

The next step is to turn over the edge of the reflector, so as to

stiffen it. For this purpose it is placed in the matrix P′P′ (fig.

107), and the needle-point at V is adjusted by the screw at D, so as

just to enter the small hole formerly drilled in the vertex of the

reflector. The die-plate PP (which is worked by means of the arms AA,

which turn the screw S) then descends and presses the edge _over_,

which is finished with a finely polished tool C, revolving round

the axis of the instrument, which coincides with the centre of the

matrix and die. In order to ensure a steady vertical movement of the

die-plate PP, cross-arms FF, which are provided with sockets HH, which

slide over the rods GG, GG, are added to prevent any lateral shake or

derangement. The whole frame is stiffened by the cross-head in which

the screw S works.

[Illustration: Fig. 107.]

[Illustration: Fig. 108.]

[Illustration: Fig. 109.]

The reflector is then placed on the circular cast-iron table (figs.

108, 109), to which it is attached by the clamp-screws S, S. In this

position, the bizzle W (fig. 108) and back-belt NAN (fig. 109), are

soldered on. After this the reflector is ready for being finally

polished; for which purpose, it is placed in a _chaise percée_,

padded round the edges, and is first scoured all over with a piece of

pure charcoal of hard wood, and next with a mixture of Florence oil

and finely washed rottenstone, applied by means of a large ball of

superfine cloth. It is then carefully cleansed with a piece of fine

flannel dipped in Florence oil, and afterwards dusted over with the

powder of well washed whiting, and wiped out with a soft cotton cloth.

Lastly, it is carefully rubbed by the naked hand, with finely washed

rouge and clean water, and wiped with a smooth chamois skin. In all

the polishing and cleansing processes, some skill in manipulation

is required, as the hand is generally moved in such a manner as to

describe successive circles with their planes parallel to the lips of

the reflector, and their centres in the axis of the generating curve.

The prices paid to the workmen for the various departments of the

reflector-making are generally as follows:--

Raising the plate to the curve, with the wooden mallet, L.0 10 0

Hammering and smoothing to the mould, 1 5 0

Finishing in the die, and putting on bizzle and back-belt, 0 6 0

Polishing, 0 12 0

-------

L.2 13 0

The prices paid to the manufacturer were for the large reflectors of 24

inches aperture, L.43; for the small ones of 21 inches, L.31, 12s. The

lamp with the sliding-carriage, required for each, costs L.6.

APPENDIX, No. III.

NOTES ON THE GRINDING OF THE VARIOUS PIECES COMPOSING THE INSTRUMENTS

USED IN DIOPTRIC LIGHTHOUSES, CHIEFLY FROM NOTES FURNISHED BY M.

THEODORE LETOURNEAU OF PARIS.

The glass used in all the parts of the optical apparatus of the

dioptric Lighthouses is that of St Gobain, whose index of refraction is

1·51.

As well on account of the difficulty experienced in producing at

all times regular castings of glass from the moulds, as in order

to compensate for the frequent accidents, which occur in the first

application of the rubbers to the inequalities of the surface of the

glass, the castings, whether for rings of lenses or prisms, are made

from moulds, exceeding the intended size of the finished pieces by

_one-eighth part_.

We shall take as an example, which is well calculated to illustrate the

difficulties of the grinding process, one of the prismatic rings of a

Catadioptric Light of the first order. The first operation will be to

take off the rough arris at the angles of the pieces as they come from

the moulds, and to reduce to equality the length of each of the four

quadrantal prisms or segments by removing from each the quantity that

may be necessary to make those four pieces, when placed on a circle,

exactly equal to that of the finished zones. Each of them must have an

excess of material at the various surfaces just sufficient to insure

the rubber having scope enough to remove all the flaws or defects of

the two surfaces to be first ground, which are the (concave and convex)

refracting faces of the zone (the sides AC and BC in the Table in the

Appendix, No. IV.)

[Illustration: Fig. 110.]

The pieces must be placed end to end on the horizontal plane or table

of the lathe at AA (fig. 110), and must rest on the exterior arris

A of the reflecting side, on which arris there is ground a narrow

plane whose width is proportionate to the projection of the outer edge

beyond the inner edge of the zone, _foreshortened_ by the _bevel_ or

inclination of the reflecting side, when resting (as in fig. 110) on

the circular iron belt, which is screwed to the table of the lathe

provided for its reception. This narrow plane at the arris A should

be sufficient to give the prism a solid and regular bearing on the

circular iron belt. In this figure (fig. 110) _a_ _b_ is the vertical

axis of the lathe, _n_ the point from which the co-ordinates for O,

the grinding centre for the exterior _concave_ refracting surface

AC, are measured, and _e_ AC the arc swept by the grinding surface.

Conversely, _n′_ is the origin of the co-ordinates for the grinding

centre O of the interior _convex_ refracting surface BC, and _e_ CB the

arc swept by its grinding surface. Some skill is required in fixing

the prism on the belt, for, on the one hand, there is an obstacle to

correct workmanship from the dragging motion of the platform, and, on

the other, by the unequal subdivision of the weight of the glass, which

should be nearly balanced. This narrow plane being perfectly adjusted

for all the segments so as to bed them quite level, the circular iron

belt on which the ring should be ground, is placed on its platform, in

the manner represented in the figure. It should be as truly levelled

as possible, otherwise all the subsequent operations will be deranged

by it. This iron belt is heated by means of heating _pans_; and the

degree of heat may be practically judged of by the ebullition of drops

of water let fall on it. The segments of glass are also at the same

time placed in a stove heated with steam, and are generally raised to

about 120° centigrade. The difference between the time required for

the two operations of heating the iron belt and the glass segments is

employed in laying or bedding a quantity of cement on the reflecting

side of the segment, so as to fill up the angular space between the

glass and the iron belt, and also to serve as a seat for the segment in

the manner shewn in fig. 110. This operation is performed on a plane

surface, in order that the lower part of the mastic may be precisely

on a level with the narrow plane already ground on the outer arris of

the reflecting side. After being sure that the heat is equally spread

over every part of the circular iron belt, the segment is arranged on

it; and the workman must, at this juncture, exert all his skill in

placing the parts of the segment in a position nearly concentric with

the belt, or in a truly circular form, making due allowance, however,

for the inequalities existing at various parts of the rough material,

and at the same time taking care that there should be an interval of at

least two millimètres (or about ¹⁄₁₂th inch) between the ends of each

of the two adjacent segments. Without this interval the heat evolved

during the polishing would either dilate the glass so much as to cause

the ends of the segments to fly into splinters, or make it needful

to remove the zone before this should take place, the inevitable

consequence of which would be the fracture of the pieces. Those

intervals between the segments are filled with statuary’s plaster,

which must be carefully washed and brushed at each change of the emery

employed in grinding.

The exterior diameter of the circular iron belt must be precisely

equal to that of the ring, because, if larger, the free movement of

the rubbers to and fro on the concave refracting surface AC (fig. 110)

could not take place.

By what is already said, it will be obvious that the grinding process

is begun at the refracting sides AC and BC, and a few words will shew

that this could hardly be otherwise. If a commencement be made on

the reflecting side, which appears at first sight more natural, the

consequence is obvious. Having provided for an excess of material

in every direction, the segment must consequently be larger than it

will be when finished; and the surfaces therefore cannot be true and

perfect, except they be ground throughout their entire segmental

section, from their centres of curvature, in reference to some given

apex of the generating triangle. Now, if the reflecting side were

finished first, it might continue to possess this excess of size after

being finished, and would, therefore, afford no accurate starting

point for the grinding of the other surfaces; it would also present

no _surface_ or narrow plane for resting firmly on the iron belt, but

would then depend merely on its own finished plane, which, being curved

and considerably inclined, would not give a solid bearing for the

glass. The other mode of commencing with the two refracting sides, on

the contrary, gives a solid bearing on the narrow plane already ground

on the reflecting side at A; and after these surfaces have been ground,

and the segments inverted (as shewn in fig. 111), the outer edge of

this narrow plane at the arris A, which has been fully defined by the

intersection of the finished surface AC just ground, and also the apex

at C, which has been determined by the intersection of AC and BC,

combine to fix an accurate starting point for the rubber, in grinding

the reflecting surface AB.

[Illustration: Fig. 111.]

_Dressing off the rough part of the Ring._

The ring is generally reduced from the rough state by means of fixed

rubbers, the adjustment of which is more easily regulated than that

of the moveable beam or radius of the arc, which is used to give the

exact curvature of the surface. Those fixed rubbers are 150 millimètres

(nearly 6 inches) wide, by 200 millimètres (nearly 8 inches) long,

and are of cast-iron. Three such rubbers are placed at equidistant

points of the circle. Two cutters of sheet-iron attached to arms placed

vertically (as are also those which carry the rubbers), and moving in

grooves radiating towards the centre of the lathe, so as to admit of

adjustment to suit the varying radii of the zones, serve gradually to

abrade the outer and inner arrises of the segments, so as to prevent

the splintering to which, from becoming too sharp, those arrises,

without this precaution, would be liable. Those rubbers are, besides,

fixed by stems to frames, in the form of quadrants of the circle, which

allow of a change in the direction of the planes, as occasion may

require.

Instead of the siliceous sand formerly used, the powder of pounded

freestone is employed, as it is found to wear the tools less, and to

form a better preparation for the subsequent grinding operations. It

is easy to conceive that the action of the fixed rubbers necessarily

produces ruts or inequalities in the circular direction. The operation

of rough dressing, therefore, is not finished until, when those first

rubbers are removed, the surfaces of the segments have been subject,

for the required time, to the action of moveable rubbers, attached to

arms working as radii of curvature, in a plane at right angles to the

horizontal movement of the lathe, which carries the zones.

_The Emery Grinding._

The form of the segment should be nearly perfect, after the rough

grinding is finished. The lathe and the zone are then subjected to an

extremely careful washing. Every place where the stone-powder might

adhere is dusted. The radius of curvature is verified afresh, agreeably

to the co-ordinates (Appendix, No. IV.); and emery is used instead of

powdered stone; beginning with that called No. 1, which is drawn after

suspension in water for one minute. Brushes are used for spreading the

emery on the surface of the glass. The quantity ought always to be

sufficient to prevent the direct contact of the cast-iron rubber with

the glass. Splintering or scratching, which cannot be easily effaced,

may result from the neglect of this precaution.

Practice alone, and an eye duly trained by continual experience,

can determine the point of time at which each kind of emery must be

discontinued. The celerity of the work depends on circumstances very

difficult to appreciate, such as the amount of the pressure of the

rubbers, or the degree of accuracy with which the radius of curvature

has been adjusted, during the rough grinding. Each kind of emery in

succession thus corrects the form of the zone and refines the grain of

the surface of the glass; and each change to a fresh material requires

the same attention to cleanliness, so as to remove every trace of the

substance last used in grinding, and thus to give each successive

process its full and legitimate effect. The _douci_ is the _fifth_

and _last_ kind of emery which precedes the _polish_. It is drawn off

after ten minutes’ suspension in water, and is extremely fine. Before

applying it, the greatest care is necessary to insure cleanliness,

as a single grain of any of the preceding kinds of emery might cause

scratches, which the polish cannot remove.

_The Polish._

The same considerations which induce the workman most carefully to

cleanse the lathe and everything connected with it, before employing

the last emery called the _douci_, are still more urgent in the case

of the final _polish_. The only change which is made at this last

stage of the work is to replace the first rubber by a new one, both

longer and wider by about 50 millimètres (nearly 2 inches). On its

lower face is attached with cement a piece of soft carpet, whose edges

are fixed to the rubber by means of flat bands of iron, attached with

screws. This security, added to that given by the cement, is necessary

to fit it to resist the great pressure it must sustain. A practical

question, which experience alone can resolve, occurs at this stage, as

the operation of polishing may, in the hands of unskilful persons, be

so inopportunely commenced, as to make that work almost endless. Thus,

the mere circumstance of spreading at the beginning too thick layers

of rouge, or using unsuitable kinds of carpet, would cut scratches in

the glass, and thus perhaps make it necessary to return to the use of

the emery called _douci_. Sometimes, also, if the carpets be not washed

at the very time of using them, scratches are formed by the dust which

they may contain. This shews, that the use of rouge should be rather

sparing than otherwise, at the commencement of the polish; and that the

carpet-cloths should be brushed and washed _twice_ rather than _once_.

In all cases, the quality of the carpet forms an important element in

the success of the working.

When the _polish_ is finished, the ring is detached from the circular

belt, simply by the tap of a hammer, on the inner edge of the circle.

The division of the zones (which are quarters of the circle) into

_eighths_, is done by means of a sawing machine consisting of a flat

copper-wheel, one-half millimètre (¹⁄₅₀th inch) in thickness, attached

to an arm with a counterpoise. This wheel descends and cuts the zone by

means of emery, which is continually applied to it; the direction of

the cut is radial. The two halves of the zone are detached from each

other, as soon as their weight exceeds the resistance of the part which

remains to be sawn.

_Adjustment of the Prisms._

The adjustment of the prisms in the frames, involves an operation

which is not without risk. Much care is required in handling the sharp

arrises of the glass, which are very acute and delicate and at the

same time lie in a curved direction, which makes them liable to be

splintered in the hands of unskilful persons.

With the exception of the plane vertical surfaces of the annular

lenses, and the central band and rings of the dioptric belts of

fixed lights, which are ground by means of vertical rubbers with a

reciprocating movement, every other plane surface is executed by hand

on a flat table.

_Composition of the Cement for fixing the glass on the lathe._

8 parts Swedish pitch.

1 do. of wood ashes.

The whole is heated in an iron pot until fully liquified and thoroughly

mixed. This cement is used almost in a state of ebullition, so that it

cannot be handled without the precaution of continually dipping the

hands in cold water.

_Composition of cement used for the adjustment of the pieces of glass

which touch each other._

12 parts white lead.

1 do. minium or red lead.

5 do. boiled lintseed oil.

The whole is pounded on an iron table by means of a flat mullet, like

that used by painters (fig. 112), whose grinding surface is _a_ _b_,

and _c_ the knob for the hand. This cement is applied liquid so as

to offer no resistance to the close union of the pieces, which it is

intended to unite.

[Illustration: Fig. 112.]

_Cement for filling up voids, and fixing the rings in the frames._

12 parts white lead.

3 do. whiting.

1 do. minium.

4 do. boiled lintseed oil.

This last composition differs from the former only in the introduction

of whiting, which, while like minium it has a desiccative property,

gives more body to the cement and prevents the formation of cracks. The

oil is also decreased in quantity, as the cement must be used in a more

compact state. The trituration of this cement is performed by means of

a cylindric iron roller _a_ _b_, with a centre-spoke _c_ _d_ for the

hand (fig. 113).

[Illustration: Fig. 113.]

It is essential for the production of good cement, that the mixture of

the ingredients be complete.

_Prices of the various parts of the Dioptric Apparatus._

The expense of the various parts of the Dioptric apparatus is as

follows: Great lens of first order, L.58 (8 of which are required);

pyramidal lens and mirror, L.14, 12s. (8 of which are required);

catadioptric cupola, L.480; catadioptric rings below lenses, L.360;

pannel of dioptric belt for fixed light of first order, L.56 (of which

8 are required for the whole circle); apparatus of fourth order, for a

fixed light, for whole horizon, L.128; apparatus of sixth order, for

whole horizon, L.44. The expense of the mechanical lamp of the first

order with four wicks, as made for the Scotch Lighthouses by Mr JOHN

MILNE of Edinburgh, is L.30.

_Diagrams illustrative of the Table, Appendix, No. IV._

[Illustration: Fig. 114.]

[Illustration: Fig. 115.]

[Illustration: Fig. 116.]

[Illustration: Fig. 117.]

APPENDIX, No. IV.

TABLE OF THE ELEMENTS OF CATADIOPTRIC ZONES SUITED FOR LIGHTS OF THE

FIRST ORDER IN THE SYSTEM OF AUGUSTIN FRESNEL.

NOTE.--The Six co-ordinates of the Generating Triangle of each Zone

in these Tables have the Focus of the Principal Lenses of the System

for their origin; it being considered more convenient, in executing

the necessary protractions, preparatory to the construction of the

grinding apparatus, at once to refer the whole of the grinding

machinery to the axis of the apparatus. To prevent the appearance of

any inconsistency, however, it is proper to mention, that the radiant

points of the series of Zones, do not exactly coincide with the Focus

of the Lenses nor with each other; and that to avoid the parallax

which the distance of the radiant points from the origin of the

co-ordinates would occasion, it is necessary to make some corrections

upon the linear dimensions, so as to find the line corresponding

to the angles θ, ξ, and the distance Δ. In the Hyperpyral series,

which stands _above_ the flame, the Zones have the radiant point

10 millimetres above the Focus of the Lenses, and each _y_ of this

series, therefore, requires a reduction of that quantity; while the

_x_ remains unchanged. In the Hypopyral series, which stands _below_

the flame, the Focus or radiant points of each Zone, varies its place

in the flame, moving upwards as the Zone is lower, so that the line

joining the Zones and the Foci, revolves as a radius vector round a

point between them. In this way, the _x_’s remain unaltered; but the

_y_’s will be lengthened successively by the addition of 10, 14, 19,

25, 32, and 40 millimetres. As these Tables contain the dimensions of

Zones which are intended as an addition to the apparatus of FRESNEL,

I have adopted the metric scale, so as to render them at once

applicable to the existing protractions of that system. It is only

necessary to add, that the conversion of millimetres into imperial

inches, is easily effected by adding the log. millimetres to the log.

̅2·59516, the sum being the log. of the equivalent of the first term

in imperial inches.

+-------+-----++--------+--------++---------+--------+--------++

| | || θ | ξ || BCA, | ABC, | BAC, ||

| | || | || | | ||

| | || Incli- | || | | ||

| | || nation | || Obtuse | | ||

| | || of | Inci- || Angle | | ||

| | || Ray FC | dence || of the | | ||

| | || to the | of Ray || Gener- |Angle of|Angle of||

| | ||Vertical| FC on || ating | Gener- | Gener- ||

| | || Axis | Side || Triangle| ating | ating ||

| | || of the | BC of || of the |Triangle|Triangle||

| | || System.| Zone. || Zone. |of Zone.|of Zone.||

| | No. || | || | | ||

| | of || (Fig. | (Fig. || (Fig. | (Fig. | (Fig. ||

| |ZONE.|| 114.) | 114.) || 114.) | 114.) | 114.) ||

| +-----++--------+--------++---------+--------+--------++

| | || ° ′ ″| ° ′ ″|| ° ′ ″| ° ′ ″| ° ′ ″||

| | 1 ||60 45 38|44 06 09||117 26 40|31 48 10|30 45 10||

| | 2 ||56 55 38|41 28 10||116 00 42|32 32 01|31 27 17||

| | 3 ||53 05 38|38 48 29||114 31 20|33 17 30|32 11 10||

| | 4 ||49 15 38|36 07 09||112 58 40|34 04 36|32 56 44||

|HYPER- | 5 ||45 25 38|33 24 19||111 23 00|34 53 07|33 43 53||

| PYRAL | 6 ||41 35 38|30 40 05||109 44 32|35 42 57|34 32 31||

|SERIES | 7 ||37 45 38|27 54 34||108 03 30|36 34 01|35 22 29||

| OF | 8 ||33 55 38|25 07 52||106 20 06|37 26 11|36 13 43||

|ZONES. | 9 ||30 05 38|22 20 07||104 34 36|38 19 23|37 06 01||

| | 10 ||26 15 38|19 31 25||102 47 12|39 13 27|37 59 21||

| | 11 ||22 25 38|16 41 54||100 58 10|40 07 14|38 54 36||

| | 12 ||18 42 02|13 56 26|| 99 10 50|40 59 53|39 49 17||

| | 13 ||15 06 03|11 16 04|| 97 26 07|41 51 03|40 42 49||

+=======+=====++========+========++=========+========+========++

| | || ° ′ ″| ° ′ ″|| ° ′ ″| ° ′ ″| ° ′ ″||

| | 1 ||59 49 16|43 27 36||117 05 56|31 58 37|30 55 27||

| HYPO- | 2 ||55 48 55|40 42 01||115 35 07|32 44 43|31 40 09||

| PYRAL | 3 ||51 48 33|37 54 32||114 00 31|33 28 16|32 27 13||

|SERIES.| 4 ||47 51 11|35 07 32||112 23 53|34 20 23|33 15 44||

| | 5 ||43 59 40|32 23 06||110 46 32|35 08 23|34 05 05||

| | 6 ||40 16 34|29 43 19||109 10 04|35 55 37|34 54 18||

+-------+-----++--------+--------++---------+--------+--------++

+-------+-----++-------+-------+-------++

| | || BA, | BC, | AC, ||

| | || | | ||

| | || | | ++

| | || | | ||

| | || Re- | | ||

| | || flect-| | ||

| | || ing | | ||

| | ||Side of| | ||

| | ||Zone in| Inner | Outer ||

| | || Milli-| Re- | Re- ||

| | || metres| fract-| fract-||

| | || being | ing | ing ||

| | || Chord |Side of|Side of||

| | || of |Zone in|Zone in||

| | ||the Arc| Milli-| Milli-||

| | ||_b_ A. |metres.|metres.||

| | No. || | | ||

| | of || (Fig. | (Fig. | (Fig. ||

| |ZONE.|| 115.) | 115.) | 115.) ||

| +-----++-------+-------+-------++

| | || | | ||

| | 1 ||160·331| 92·379| 95·209||

| | 2 ||155·430| 90·249| 93·011||

| | 3 ||151·551| 88·729| 91·434||

| | 4 ||148·580| 87·768| 90·424||

|HYPER- | 5 ||146·444| 87·332| 89·947||

| PYRAL | 6 ||145·087| 87·403| 89·986||

|SERIES | 7 ||144·481| 87·977| 90·536||

| OF | 8 ||144·609| 89·060| 91·604||

|ZONES. | 9 ||145·476| 90·671| 93·209||

| | 10 ||147·089| 92·843| 95·384||

| | 11 ||145·361| 93·000| 95·413||

| | 12 ||143·362| 93·000| 95·271||

| | 13 ||141·379| 93·000| 95·127||

+=======+=====++=======+=======+=======++

| | || | | ||

| | 1 ||159·369| 92·000| 94·806||

| HYPO- | 2 ||158·051| 92·000| 94·783||

| PYRAL | 3 ||156·592| 92·000| 94·719||

|SERIES.| 4 ||155·083| 92·000| 94·619||

| | 5 ||153·489| 92·000| 94·488||

| | 6 ||151·863| 92·000| 94·334||

+-------+-----++-------+-------+-------++

+-------+-----++--------------------------------------------------++

| | || Co-ordinates of the Apices of the Generating ||

| | || Triangle, in Millimetres, having the Axis of the ||

| | || System cut by the horizontal plane of the focus ||

| | ||of the Annular Lenses, for its origin. (Fig. 116.)||

| | ++--------+-------+--------+-------+--------+-------++

| | || | | | | | ||

| | No. || | | | | | ||

| | of || | | | | | ||

| |ZONE.|| A_{_y_}|A_{_x_}| B_{_y_}|B_{_x_}| C_{_y_}|C_{_x_}||

| +-----++--------+-------+--------+-------+--------+-------++

| | || | | | | | ||

| | 1 || 593·369|986·260| 551·481|831·497| 525·000|920·000||

| | 2 || 663·063|957·410| 617·423|808·832| 593·369|895·816||

| | 3 || 734·313|926·908| 684·958|783·619| 663·063|869·605||

| | 4 || 807·357|894·222| 754·267|755·451| 734·313|840·920||

|HYPER- | 5 || 882·445|858·858| 825·547|723·921| 807·357|809·337||

| PYRAL | 6 || 959·847|820·325| 899·011|688·608| 882·445|774·426||

|SERIES | 7 ||1039·852|778·108| 974·899|649·051| 959·847|735·730||

| OF | 8 ||1122·784|731·645|1053·471|604·730|1039·852|692·742||

|ZONES. | 9 ||1209·000|680·322|1135·025|555·059|1122·784|644·900||

| | 10 ||1298·900|623·433|1219·892|499·354|1209·000|591·556||

| | 11 ||1390·290|559·378|1308·183|439·428|1288·900|531·963||

| | 12 ||1482·755|490·169|1398·007|374·538|1390·290|467·217||

| | 13 ||1576·048|415·991|1488·972|304·611|1482·755|397·403||

+=======+=====++========+=======+========+=======+========+=======++

| | || | | | | | ||

| | 1 || 593·815|985·212| 550·915|831·725| 525·000|920·000||

| HYPO- | 2 || 682·731|981·810| 634·862|831·183| 610·872|920·000||

| PYRAL | 3 || 779·464|978·917| 726·831|830·694| 704·730|920·000||

|SERIES.| 4 || 885·046|974·441| 827·926|830·261| 807·657|920·000||

| | 5 ||1000·663|970·608| 939·385|829·882| 920·871|920·000||

| | 6 ||1127·665|966·771|1062·591|829·557|1045·740|920·000||

+-------+-----++--------+-------+--------+-------+--------+-------++

+-------+-----++--------------------------++

| | || Inclination of the Sides ||

| | ||of the Generating Triangle||

| | || to the Vertical Axis of ||

| | || the System. (Fig. 117.) ||

| | ||--------+--------+--------++

| | || | | ||

| | || Incli- | Incli- | Incli- ||

| | No. || nation | nation | nation ||

| | of || of | of | of ||

| |ZONE.|| AB. | BC. | AC. ||

| +-----++--------+--------+--------++

| | || ° ′ ″| ° ′ ″| ° ′ ″||

| | 1 ||74 51 19|73 20 31|44 06 09||

| | 2 ||72 55 27|74 32 32|41 28 10||

| | 3 ||70 59 39|75 42 51|38 48 29||

| | 4 ||69 03 53|76 51 31|36 07 09||

|HYPER- | 5 ||67 08 12|77 58 41|33 24 19||

| PYRAL | 6 ||65 12 36|79 04 27|30 40 05||

|SERIES | 7 ||63 17 03|80 08 56|27 54 34||

| OF | 8 ||61 21 35|81 12 14|25 07 52||

|ZONES. | 9 ||59 26 08|82 14 29|22 20 07||

| | 10 ||57 30 46|83 15 47|19 31 25||

| | 11 ||55 36 30|84 16 16|16 41 54||

| | 12 ||53 45 43|85 14 24|13 56 26||

| | 13 ||51 58 53|86 10 02|11 16 04||

+=======+=====++========+========+========++

| | || ° ′ ″| ° ′ ″| ° ′ ″||

| | 1 ||74 23 03|73 38 20|43 27 36||

| HYPO- | 2 ||72 22 10|74 53 06|40 42 01||

| PYRAL | 3 ||70 21 45|76 05 59|37 54 32||

|SERIES.| 4 ||68 23 16|77 16 21|35 07 32||

| | 5 ||66 28 11|78 23 26|32 23 06||

| | 6 ||64 37 37|79 26 45|29 43 19||

+-------+-----++--------+--------+--------++

+-------+-----++----------------------------------------++

| | || ||

| | || AB, Reflecting Surfaces (convex). ||

| | || (Fig. 115.) ||

| | ++-------+-------+-------+-------+--------++

| | || | | Verti-| | ||

| | || | Hori- | cal | | ||

| | || | zontal| dis- | | ||

| | || | dis- | tance | | ||

| | || | tance | of | | ||

| | || | of | centre| | ||

| | || | centre| of | | ||

| | || | of | curva-| | ||

| | || | curva-| ture X| | ||

| | || | ture |_below_| | ||

| | || | X from| the | | ||

| | || Radius| the |_outer_| |Inclina-||

| | || of | axis | arris | In- | tion ||

| | || Curva-| of the| of the| clina-| of the ||

| | ||ture in| System| _Zone_|tion of| Outer ||

| | || Milli-| in |at A in|the Two| Radius ||

| | No. ||metres,| Milli-| Milli-| Radii | in A ||

| | of || XA or | metres| metres| in A | to the ||

| |ZONE.|| X _b_.| = OX. | = OA. | and B.| Vertex.||

| +-----++-------+-------+-------+-------+--------++

| | || | | |° ′ ″| ° ′ ″||

| | 1 ||8750·19|3194·76|8466·88|1 02 59|14 38 11||

| | 2 ||8253·90|3306·80|7909·94|1 04 45|16 32 11||

| | 3 ||7850·30|3411·75|7446·67|1 06 22|18 27 11||

| | 4 ||7527·08|3514·22|7056·39|1 07 51|20 22 11||

|HYPER- | 5 ||7275·23|3617·56|6730·66|1 09 12|22 17 11||

| PYRAL | 6 ||7082·17|3723·81|6459·63|1 10 25|24 12 11||

|SERIES | 7 ||6944·09|3835·23|6234·93|1 11 31|26 07 11||

| OF | 8 ||6857·03|3954·67|6052·36|1 12 30|28 02 11||

|ZONES. | 9 ||6817·87|4081·70|5902·53|1 13 20|29 57 11||

| | 10 ||6824·46|4226·67|5795·68|1 14 05|31 52 11||

| | 11 ||6880·52|4385·63|5718·52|1 12 37|33 47 11||

| | 12 ||6980·89|4558·83|5672·64|1 10 36|35 38 59||

| | 13 ||7123·05|4747·24|5654·92|1 08 15|37 26 59||

+=======+=====++=======+=======+=======+=======+========++

| | || | | |° ′ ″| ° ′ ″||

| | 1 ||8674·74|3243·48|8375·64|1 03 09|15 05 22||

| HYPO- | 2 ||8419·60|3456·44|8047·72|1 04 31|17 05 32||

| PYRAL | 3 ||8278·82|3685·41|7823·68|1 05 01|19 05 13||

|SERIES.| 4 ||8252·95|3941·89|7701·00|1 04 36|21 04 24||

| | 5 ||8335·86|4228·06|7673·05|1 03 18|23 00 10||

| | 6 ||8522·64|4549·97|7732·80|1 01 15|24 51 43||

+-------+-----++-------+-------+-------+-------+--------++

+-------+-----++----------------------------------------++

| | || ||

| | ||AC, Outer Refracting Surfaces (concave).||

| | ++-------+-------+-------+-------+--------++

| | || | | Verti-| | ||

| | || | | cal | | ||

| | || | Hori- | dis- | | ||

| | || | zontal| tance | | ||

| | || | dis- | of | | ||

| | || | tance | centre| | ||

| | || | of | of | | ||

| | || | centre| curva-| | ||

| | || | of | ture | | ||

| | || | curva-|_above_| | ||

| | || | ture | the | | In- ||

| | || | from | outer | | clina- ||

| | || | the | arris | In- | tion ||

| | || Radius| axis | of the| clina-| of the ||

| | || of | of the| _Zone_| tion | Outer ||

| | || Curva-| System| at | of the| Radius ||

| | No. ||ture in| in | A in | Radii | at A ||

| | of || Milli-| Milli-| Milli-| in A | to the ||

| |ZONE.||metres.|metres.|metres.| and C.| Vertex.||

| +-----++-------+-------+-------+-------+--------++

| | || | | |° ′ ″| ° ′ ″||

| | 1 ||4000·00|3825·31|2817·77|1 21 50|45 12 56||

| | 2 || ... |3923·65|2683·55|1 19 56|47 51 52||

| | 3 || ... |4015·06|2542·31|1 18 34|50 32 14||

| | 4 || ... |4098·54|2394·23|1 17 42|53 14 00||

|HYPER- | 5 || ... |4173·08|2239·64|1 17 18|55 57 02||

| PYRAL | 6 || ... |4237·70|2078·82|1 17 20|58 41 15||

|SERIES | 7 || ... |4291·45|1912·18|1 17 48|61 26 32||

| OF | 8 || ... |4333·30|1740·12|1 18 44|64 12 46||

|ZONES. | 9 || ... |4362·26|1563·10|1 20 06|66 59 50||

| | 10 || ... |4377·24|1381·63|1 21 58|69 47 36||

| | 11 || ... |4376·72|1194·94|1 22 00|72 37 06||

| | 12 || ... |4360·70|1009·41|1 21 12|75 22 58||

| | 13 || ... |4329·31| 828·19|1 21 46|78 03 02||

+=======+=====++=======+=======+=======+=======+========++

| | || | | |° ′ ″| ° ′ ″||

| | 1 ||4000·00|3855·83|2785·60|1 21 28|45 51 40||

| HYPO- | 2 || ... |3983·21|2644·16|1 21 28|48 37 15||

| PYRAL | 3 || ... |4104·84|2494·82|1 21 24|51 24 46||

|SERIES.| 4 || ... |4218·56|2340·02|1 21 20|54 11 48||

| | 5 || ... |4322·95|2182·17|1 21 12|56 56 18||

| | 6 || ... |4416·91|2023·99|1 21 04|59 36 09||

+-------+-----++-------+-------+-------+-------+--------++

+-------+-----++----------------------------------------++-------++

| | || || Δ, ||

| | || || ||

| | || BC, Inner Refracting Surfaces (convex).|| ||

| | ++-------+-------+-------+-------+--------++ ||

| | || | | | | || ||

| | || | | Verti-| | || ||

| | || | Hori- | cal | | || ||

| | || | zontal| dis- | | || ||

| | || | dis- | tance | | || Dis- ||

| | || | tance | of | | || tance ||

| | || | of | centre| | || of ||

| | || | centre| of | | || C from||

| | || | of | curva-| | || the ||

| | || | curva-| ture | | || Focus ||

| | || | ture |_below_| | In- ||for the||

| | || | from | the | | clina- || Zones,||

| | || | the | outer | In- | tion of|| in ||

| | || Radius| axis | arris | clina-| of the || Milli-||

| | || of | of the| of the| tion | Outer || metres||

| | || Curva-| System| _Zone_| of the| Radius || = FC. ||

| | No. ||ture in| in |at A in| Radii | in C || ||

| | of || Milli-| Milli-| Milli-| in C | to the || (Fig. ||

| |ZONE.||metres.|metres.|metres.| and B.| Vertex.|| 114.) ||

| +-----++-------+-------+-------+-------+--------++-------++

| | || | | |° ′ ″| ° ′ ″|| ||

| | 1 ||4000·00|2021·19|3777·07|1 19 24|15 58 47||1054·34||

| | 2 || ... |1918·37|3797·40|1 17 34|14 48 41||1069·02||

| | 3 || ... |1813·60|3815·77|1 16 16|13 39 01||1087·52||

| | 4 || ... |1707·55|3831·95|1 15 26|12 30 46||1109·85||

|HYPER- | 5 || ... |1599·72|3846·04|1 15 04|11 23 47||1136·14||

| PYRAL | 6 || ... |1489·62|3858·14|1 15 08|10 17 59||1166·57||

|SERIES | 7 || ... |1376·71|3868·30|1 15 36| 9 13 16||1201·46||

| OF | 8 || ... |1260·38|3876·59|1 16 32| 8 09 30||1241·16||

|ZONES. | 9 || ... |1139·94|3883·03|1 17 56| 7 06 33||1286·15||

| | 10 || ... |1014·67|3887·66|1 19 48| 6 04 19||1336·99||

| | 11 || ... | 884·95|3893·00|1 19 56| 5 03 46||1394·36||

| | 12 || ... | 752·78|3897·32|1 19 56| 4 05 38||1457·22||

| | 13 || ... | 618·37|3901·10|1 19 56| 3 10 00||1525·43||

+=======+=====++=======+=======+=======+=======+========++=======++

| | || | | |° ′ ″| ° ′ ″|| ||

| | 1 ||4000·00|2002·52|3781·91|1 19 04|15 42 08|| -- ||

| HYPO- | 2 || ... |1918·55|3801·51|1 19 04|14 27 22|| -- ||

| PYRAL | 3 || ... |1836·22|3818·93|1 19 04|13 14 29|| -- ||

|SERIES.| 4 || ... |1756·33|3834·20|1 19 04|12 04 07|| -- ||

| | 5 || ... |1679·85|3847·38|1 19 04|10 57 02|| -- ||

| | 6 || ... |1607·39|3858·56|1 19 04| 9 53 43|| -- ||

+-------+-----++-------+-------+-------+-------+--------++-------++

APPENDIX, No. V.

NOTICE TO MARINERS.--SKERRYVORE LIGHTHOUSE.

The Commissioners of the Northern Lighthouses hereby give notice, that

a Lighthouse has been erected upon the Skerryvore Rock, which lies off

the Island of Tyree, in the county of Argyll, the Light of which will

be exhibited on the Night of the 1st February 1844, and every Night

thereafter, from sunset to sunrise.

A specification of the bearings of the Lighthouse and character of the

Light will be found on the next page.

And the Commissioners hereby further give notice, that by virtue of a

Warrant from the Queen in Council, of date the 13th December 1843, the

following Tolls will be levied for voyages in respect of which benefit

will be derived from this Light, viz., from every British Vessel

(the same not belonging to Her Majesty, or being navigated wholly in

ballast), and for every Foreign Vessel which, by any Act of Parliament,

Order in Council, Convention, or Treaty, shall be privileged to enter

the Ports of the United Kingdom of Great Britain and Ireland, upon

paying the same duties of tonnage as are paid by British Vessels (the

same not being navigated wholly in ballast), the Toll of One Penny per

Ton of the Burden of every such Vessel; and for every Foreign Vessel

not so privileged, the Toll of Two Pence per Ton.

_By Order of the Commissioners_,

(Signed) C. CUNINGHAM, }

ALEX. CUNINGHAM, } _Joint Secs._

EDINBURGH, _23d December 1843_.

The following is a Specification of the Position of the Lighthouse,

and the Appearance of the Light, by Mr ALAN STEVENSON, Engineer to

the Commissioners.

The Skerryvore Rock lies off the Island of Tyree, in Lat. 56° 19′ 22″

N.; Long. 7° 6′ 32″ W.

By Compass, the Lighthouse bears from Barrahead Lighthouse S. ¹⁄₄ E.,

distant 33 nautic miles; from Hynish Point, in Tyree, WSW. ¹⁄₂ W.,

distant 10¹⁄₃ miles; from Iona Island, WNW. ³⁄₄ N., distant 20 miles;

from Rhinns of Islay Lighthouse, N. ¹⁄₄ E., distant 44 miles; and from

Innistrahull Lighthouse in Ireland, NE. by N., distant 53¹⁄₂ miles.

Owing to the distance to which the foul ground extends on every side of

the rock on which the Lighthouse is placed, and the weight of sea which

breaks on the shallow ground all round it, it is necessary to give

the Light a wide berth. The better to enable seamen to judge of this,

their attention is called to the prefixed Chart,[87] which exhibits

the relative position of the Skerryvore Rock, and the various dangers

around it. In particular, it is necessary to notice the position of

those rocks which lie seaward of the Lighthouse, viz. Mackenzie’s Rock,

about 3 miles W. by S. ¹⁄₄ S. from the Lighthouse; Stevenson’s, 2¹⁄₄

miles W. ¹⁄₂ N.; and Fresnel’s, which lies between these two Rocks. To

the left of the prefixed Chart is a small diagram, which exhibits the

position of the Skerryvore Rock in reference to the principal landmarks

above noticed.

[87] A copy of the Chart referred to will be found at Plate II. at

the end of this volume.

The Skerryvore Light will be known to mariners as a Revolving Light,

producing a Bright Flash once every minute. The Lantern, which is

open all round, is elevated 150 feet above the level of the sea. In

clear weather the flashes of the Light will be seen at the distance

of six leagues, and at lesser distances according to the state of the

atmosphere; and to a near observer, in favourable circumstances, the

Light will not wholly disappear between the flashes.

APPENDIX, No. VI.

ACCOUNT OF THE EXPENSE OF ERECTING THE SKERRYVORE LIGHTHOUSE AND OF THE

SUBSIDIARY WORKS.

ESTABLISHMENT AT HYNISH.

Wages of the different workmen quarrying

and dressing the stones, and building

the dwelling-houses, barracks,

storehouses, inclosure and subdivision

dykes, draining and trenching the

ground, &c., at Hynish, and the wages of

joiners preparing and fitting up the

joiner work, £2996 7 7

Timber, pavement, bricks, ironmongery,

glass, &c., &c., used in the erections, 1376 16 9¹⁄₂

Slater, plaster, and plumber work of

the houses, 436 1 0

Paid the tenant of Hynish for a barn

which was used as a barrack to

accommodate the workmen when they first

landed at Tyree, 13 0 0

---------------

£4822 5 4¹⁄₂

NOTE.--Although these buildings had been erected for

the purposes of the works, yet the greater part of them

were designed to serve as part of the permanent

accommodation required at Tyree in connection with the

Lighthouse Establishment, and have accordingly been so

applied.

ROCK BARRACK, No. 1.

Cost of the barrack on the Rock, which

was destroyed, including the

contractor’s account for extra work,

&c., £742 17 7

Lead for running up the bats and for

other purposes about the barrack, 14 11 6¹⁄₂

A smith’s forge, bellows, anvil, and

smith’s tools used at Rock in erecting

the barrack, 32 19 1¹⁄₄

---------------

790 8 2³⁄₄

ROCK BARRACK, No. 2.

Cost of the carpenter and joiner work

on the second barrack, the expense of

fitting and erecting it at Greenock,

the wages of four joiners and a smith,

furnished by the contractor to assist

in its erection at Skerryvore,

including sundry other minor charges, £911 14 4

Cost of the iron-work of the barrack, 369 11 8

Lead for running up the bats and

protecting the timber of cooking

apartment, &c., 29 11 10

Cooking apparatus for the cook-room of

barrack, sheet-iron smoke tube, cooking

utensils, &c., 54 16 6

Bedding for beds of barrack, 90 9 1

Expense of upholding and making sundry

small repairs on the barrack since its

erection, 22 18 6¹⁄₂

---------------

1479 1 11¹⁄₂

Cost of the furniture, bedding, and

other utensils required for the

dwelling-houses, barracks, &c.,

connected with the different

establishments of the works, 830 19 2

ESTABLISHMENT AT NORTH BAY.

Wages of the quarriers, masons,

joiners, &c., quarrying stones,

building the barracks, storehouses,

&c., &c., and fitting up the joiner

work, £378 11 9

Timber and other furnishings for the

erections, the expense of making the

doors and windows, including

furnishings required for erecting the

habitable part of Skerryvore Barrack at

North Bay as a temporary accommodation

for the workmen, and sundry other

charges, 361 4 7

Sundry furnishings--such as utensils

for provision store, smithy, &c., 13 2 5

---------------

752 18 9

QUARRIES AT NORTH BAY.

Cost of rails and timber for railway

and timber, &c., for shipping-pier at

North Bay, £131 5 1

Wages of workmen who were employed at

quarries in North Bay, quarrying the

lighthouse blocks, constructing the

pier, railway, &c., 1752 5 3

---------------

1883 10 4

TEMPORARY WHARF AND RAILWAY AT THE SKERRYVORE ROCK.

Cost of timber used in the wharf and

railway at the Skerryvore Rock, £103 18 6

Iron bats, bolts, &c., for fastening

the timber, rails for railway, and

sundry furnishings connected with an

apparatus for blasting under water, 119 7 6

Wages of the workmen constructing the

railway, fastening the timber of wharf,

&c., 34 10 5

---------------

257 16 5

EXCAVATION AT ROCK AND PLATFORM, &c.

Wages of the workmen excavating the

foundation for the Lighthouse Tower, on

the Skerryvore Rock, £609 2 3¹⁄₂

A portable forge, and other smith’s

tools, used at the rock for this work, 21 15 10

Wages of the workmen excavating the

site of a platform at the workyard in

Hynish, and quarrying and dressing

stones for sill of platform, £107 16 5

Cost of freestone from Garscube Quarry,

Glasgow, for part of the sill of

platform, 24 14 0

---------------

763 8 6¹⁄₂

DRESSING LIGHTHOUSE BLOCKS.

Wages of masons, including the

assistance of labourers, carters, &c.,

in dressing the blocks for the

Lighthouse Tower at Hynish, £8589 8 7¹⁄₂

Timber for moulds of the various

blocks, and the joiners’ wages making

the moulds, 384 18 10

Timber, &c., and wages of joiners in

erecting sheds for the masons, 955 4 5

---------------

9929 11 10¹⁄₂

Expense of victualling the workmen and

others who were employed at the rock

during the operation of the whole

works, 1503 18 6

IMPLEMENTS AND TOOLS FOR MASONS, SMITHS, &c.

Amount paid to sundry persons for the

implements and tools used by the

workmen in all the departments of the

works, £1176 9 6¹⁄₂

Wages of the smiths and their hammermen

keeping these tools in repair and

making others, 908 16 5

---------------

2085 5 11¹⁄₂

MACHINERY FOR THE WORKS AT THE ROCK, HYNISH, AND NORTH BAY.

Cost of cranes, crabs, winches, trucks,

iron blocks, chains, rope-guys, &c.,

with sundry other furnishings connected

with these articles, £1516 9 5

1 Woolwich or sling-cart, a janker for

wood, and four jack-screws, 89 6 4

Large balance crane used in building

the Lighthouse Tower, 533 10 0¹⁄₂

Hoisting beams or needles, and a pair

of strong sheer-poles, used in building

the Lighthouse Tower, 42 11 2

---------------

2181 16 11¹⁄₂

CARTAGE ACCOUNT.

Cost of 3 large draught horses and a

pony, for the use of the works, £127 9 10¹⁄₂

Carts and stable utensils, 65 14 2¹⁄₂

Harness and other furniture, and

keeping them in repair, 52 2 3¹⁄₂

Provender for the horses for seven

years, 858 14 8

---------------

1104 1 0¹⁄₂

MORTAR ACCOUNT.

Cost of the lime which was used for all

the departments of the works, £331 9 8

Pozzolano which was used for the

building of the Lighthouse Tower,

excepting a small portion for the works

of the harbour or dock, 376 16 4

Mastic, cements, and stucco, 39 6 10

Wages of labourers grinding and sifting

Pozzolano at Hynish, and burning and

sifting a portion of the lime, 121 18 8

Packages to contain Pozzolano, to

prevent its admixture with other cargo

when on board ship, 20 0 1

---------------

889 11 7

SIGNAL TOWER AT HYNISH.

Expense of quarrying, dressing, and

building the stones, and executing the

joiner work of the Signal Tower at

Hynish, £370 13 2

Pavement and bricks for the interior, 32 13 1

Cast-iron floor, with lintels and sole

plates for windows, and cast-iron

supports for do., 110 13 4

Timber for joisting of floors, lining

of walls and windows, including the

glazing of them, a wooden trap,

flag-pole, and other furnishings for

interior, 284 9 0

Plumber work of roof, 35 9 6

A 5 feet achromatic telescope, with

stand, &c., for Signal Tower, 35 10 0

Cost of a code of signals, flags,

return books, and other furnishings, 11 10 6

---------------

880 18 7

LIGHTS ACCOUNT.

Expense of the apparatus required for

the lights at the Pier and Signal Tower

at Hynish, including fitting up, &c., £66 7 0

Cost of oil and other requisites for

upholding these lights, 136 5 8

Salary of the Lightkeepers, &c., 131 11 7

---------------

334 4 3

“SKERRYVORE” STEAMER.

First cost and complete outfit of the

steamer Skerryvore, £5930 0 11

Alteration on the engines, by raising

the shafts, &c., 423 5 0

Repairs on the hull and engines, on

various occasions, during the progress

of the works, 1057 4 2

Sailing expenses (exclusive of the cost

of coals supplied when the steamer was

at Hynish), and sundry other minor

charges, 5538 10 11¹⁄₄

---------------

12,949 1 0¹⁄₄

“QUEEN” TENDER.

First cost and complete outfit of the

“Queen” Tender, £935 13 3

Sailing expenses and other charges, 1010 7 9

Repairs on the hull, rigging, sails,

&c., 77 12 8¹⁄₄

---------------

2023 13 8¹⁄₄

STONE LIGHTERS

First cost and outfit of four lighters

for transporting the Lighthouse blocks,

&c., from Hynish to the Skerryvore Rock, £1666 15 6¹⁄₂

Hawsers for towing, mooring-ropes,

heaving-lines, &c., used in the course

of transporting the stones to the Rock, 249 1 6

Upholding the lighters in repair, and

sundry other charges, 178 9 9¹⁄₂

Expense transporting the lighters on

various occasions to different places, 58 15 10

Expense shifting and attending upon the

lighters when lying at Leith, and

advertising them for sale, 19 9 10¹⁄₂

---------------

2172 12 6¹⁄₂

MOORINGS.

Cost of the buoys for mooring the

vessels belonging to the works in

Hynish Bay, and at the Rock, when lying

there, £240 1 3

Cast-iron mushroom anchors for mooring

the buoys, 118 7 4

Wrought-iron common anchors, grapnels,

&c., for mooring the vessels, warping,

kedging, &c., 48 16 1

Chains and shackles for do., &c., 354 2 7

Upholding and keeping in repair the

buoys, 4 17 1

---------------

766 4 4

BOATS AND ATTENDANCE.

Cost of 8 boats, with oars, sails,

tackling, &c., £207 19 11¹⁄₂

Upholding these boats in repair, 28 13 9

Amount paid for the use of boats and

their crews assisting to discharge

cargoes from vessels previous to the

pier being built, 119 6 0

---------------

355 19 8¹⁄₂

Amount paid the owners of hired

vessels, as freights of the Lighthouse

blocks from the quarries at North Bay,

in Mull, to the workyard at Hynish, 1300 14 8¹⁄₂

FREIGHT AND SAILING EXPENSES.

Freights and other charges paid the

owners of hired vessels, vessels, for

the materials which were imported for

the use of various departments of the

works, exclusive of the Lighthouse

blocks from North Bay, 4045 9 7¹⁄₂

Wages of labourers, &c., discharging

the cargoes from the vessels at the

Pier at Hynish, and the wages of

workmen quarrying stones for ballast,

and putting it on board the vessels, 933 12 10

Amount paid for travelling expenses,

and other charges connected with the

transport of the workmen, including the

expenses of the Officers, &c.,

travelling on the business of the works, 1711 11 2

The familiar experiment of whirling a burning stick quickly round the