LEVELLING STAVES--CONSTRUCTION--VARIOUS _Surveying and Levelling Instruments, Theoretically and Practically Described. For construction, qualities, selection, preservation, adjustments, and uses; with other apparatus and appliances used by civil engineers and surveyors in the field.

SOPWITH'S--FIELD'S--STRANGE'S--STANLEY'S NEW--METRICAL--SIMPLE

CONSTRUCTION MINING STAFF--PAPERED LEVELLING STAFF--

PRESERVATION--PACKING PADS--STAFF PLATE--STAFF LEVEL--PRACTICE

OF LEVELLING--INDEX OF BUBBLE--LAMP--CURVATURE CORRECTIONS--STATION

PEGS--REFINEMENT OF LEVELLING--LEVELLING BOOKS--INK BOTTLE, ETC.

258.--=Levelling Staves.=--Since great improvements have been made

in the telescopes used as part of all modern surveyors' levels,

particularly by increasing their light-receiving capacity, all systems

of vanes which were formerly made to be seen distinctly at a distance

have disappeared from use by British surveyors; it is now found that

the plain reading of a divided staff can be taken by means of the

telescope at a sufficient distance from the observer for all practical

purposes. In this country one construction of staff is now generally

adopted; and the only variations that are made in this are found

occasionally in the readings. The construction of the level staff in

common use is that invented by the late Thomas Sopwith,[7] called

the _telescopic staff_, the face view of which is shown Fig. 96.

For ordinary open field work this is made 14, 16, or 18 feet in its

extended length; but generally, except for levelling on mountainous

land, the 14 feet is used. This staff when closed is about the same

length as the tripod, 5 _feet_ 4 _inches_, and may be conveniently

stowed away under the seat of a railway carriage. Sopwith's staff, as

it was formerly made, consisted of two square parallel tubes and one

inner solid parallel slide. Made in this manner it was liable to be

rather shaky when extended, besides which it frequently got jammed in

the telescopic boxes if put away damp from rain: this tended at first

to limit its use. It is now usual to make the boxes slightly conical,

that is, diminished towards the upper part, so that they are rigid when

opened out but are very free when closed, which quite remedies the

defects just mentioned.

[Illustration: Figs. 93, 94.--_Section of Sopwith's staff._]

259.--The ordinary construction of Sopwith's staff and the best mode of

manufacture is shown, with the joints grooved together, in section Fig.

93. The outer tube or case _A_, which in the 14-feet staff is 5 feet in

length, is made of mahogany 5/16 inch thick, the front being ¼ inch.

The outer dimensions of the section are 3-1/8 inches by 2 inches. The

second tube _B_ is 5 feet 1 inch long, of outer dimensions 2-3/8 inches

by 1¼ inches. The inner slide _C_ is solid, 5 feet 2 inches long,

1¾ inches by ¾ inch. All the slides are sunk on the face about

1/16 inch to prevent the divisions being rubbed by exposure in sliding

together. The slides have each a brass shoe and cap. They are held when

extended by a spring catch, the detail of which is shown in Fig. 94,

section _y_ to _z_ of Fig. 93--S spring of T form screwed firmly to the

edges of the box. The catch is made at _A_ over the edge of the brass

cap _A′_. The spring should be of very hard rolled brass. It is well

to have one or two brass bands round the body of the outer casing to

secure this as far as possible from being split by accident.

260.--The most important consideration in the manufacture is that the

telescopic work should fit well, and that the boxes should be glued up

quite square and out of winding. The boxes should, after the glue is

quite set, be screwed with brass screws at distances of about 6 inches

apart, to secure the joints which may afterwards in use be exposed to

long-continued rain. The fittings should be carefully made, so that

when the staff is extended there should be no shakiness sufficient to

cause serious vibration when it is used in windy weather. The interior

of the slides when finished should be thoroughly oiled with raw linseed

oil, and the outer surfaces be well soaked in shellac dissolved in

spirit, and then French polished over this. The brass work should be

well lacquered.

[Illustration: Fig. 95.--_Section of semi-cylindrical staff._]

261.--=Semi-circular Staff.=--This is another kind of telescopic staff,

with Sopwith sliding arrangement, which possesses a certain merit, but

is more expensive to make. It is semi-cylindrical, the cylindrical part

being made without any joint. This is shown in the section Fig. 95.

The general dimensions of the face of the staff are the same as those

given for the Sopwith staff. This staff is a little stiffer, but there

is more risk of its not standing true. As in the union of four pieces

of wood in the square form, previously described, the tendency of one

piece to warp in a certain direction is resisted by the other pieces;

but in this cylindrical form there is no such resistance, so that it

is found that these staves when exposed to wet are much more liable to

become warped and fixed in their slides. There is also more difficulty

in getting the conical form fairly accurate in the working. One

particular merit, when a pair of staves of this kind is used, is that

the two go together and form a cylinder, which is a very compact form,

but perhaps a little more difficult to carry, owing to the tendency of

a cylinder to roll off the shoulder.

[Illustration: Fig. 96.--_Sopwith pattern staff._]

[Illustration: Fig. 97.--_Field's pattern._]

[Illustration: Fig. 98.--_Stanley's old pattern._]

262.--What was originally considered as the defect of the Sopwith

staff, besides its shakiness, as it was first made, was the diminished

width of reading of the upper length, this being only 1¼ inches

wide. This caused for a long period other forms of staves, which

maintained the same width of reading surface quite to the top, to be

preferred by many. This fault has been partly remedied by the author

in making the feet readings of the upper staff by dots, instead of the

narrow figures, which were very difficult to read. In other respects

the light and portable form of the Sopwith staff has ensured its

general use.

[Illustration: Fig. 99.--_Sopwith's staff._]

[Illustration: Fig. 100.--_Rogers Field's staff._]

[Illustration: Fig. 101.--_Col. Strange's staff._]

263.--The original form of reading designed by Sopwith is still much

more in use than any other. It is similar in pattern to Fig. 96, shown

in detail for 1 foot Fig. 99. The dots at the end of the lines shown

in the figure were introduced by the author to render this staff more

distinct than when lines only are used, as in the ordinary pattern.

264.--Sopwith's pattern is sometimes printed on paper for pasting on

the staff, and in this manner the staff comes out much cheaper than

by drawing the readings in solid paint. Paint, however, is strongly

recommended, not only because it wears much better and keeps cleaner,

but that the painting and varnishing add very much to the durability of

the staff, exposed as it must necessarily be to rainy weather; further,

the paper, however well it is fixed at first, is liable to creep away

from the edges of the staff, and leave a space into which rain enters

very freely by capillary attraction; but it does not again freely

evaporate, so that it rots the staff and makes the paper reading after

a time mouldy. It is, nevertheless, convenient to take a set of first

length papers if a surveyor is going abroad, as from accidents--grazing

by carrying the staff with the tripod of the level, etc.--the first

length of surface is very liable to become too much injured and effaced

for fair reading. A description of fixing the paper will be given

further on.

265.--_For Reading the Sopwith Staff_, the foot readings are taken from

the tops of the red figures. The ·1 foot figures are in black, and

are all odd numbers, 1, 3, 5, 7, 9. These read also from the top. The

height of the figure is exactly ·1 foot, so that the bottom of each

figure reads the lower even number--thus the bottom of 3 reads 2, of 5

reads 4, of 7 reads 6, and of 9 reads 8. The 6 and 9 foot figures if

made alike, from effect of telescopic inversion, may cause error. The

author has for many years made the head of the 9 a solid black block to

avoid this.

266.--=Various Readings.=--A very large number of surveyors design

their own staff readings. This was formerly very much the fashion,

consequently a great number of patterns come before the manufacturer.

The author for about twelve years kept a copy of what he considered

the most meritorious of these patterns, both for future reference and

to judge of their comparative merits. This was discontinued, as it was

found that the number of designs became a little perplexing, and they

were rather dangerous to show to a customer, who often selected from

its appearance a pattern which proved afterwards unsatisfactory in use.

267.--_Rogers Field's and Colonel Strange's Readings._--The author

made some experiments to obtain a clear staff, readable beyond the

ordinary range of staves with a 14-inch level; but much more complete

experiments were made with the author's set of patterns by Mr. Rogers

Field, C.E., whose ingenuity is well known. This gentleman finally

designed a staff which in the author's opinion is still one of the

best, but it has not generally pleased the profession: this is

illustrated, Figs. 97, 100. The author has tried it at all distances:

at 20 chains he has found a reading of ·01 foot could be taken

approximately with a good 14-inch level with his point index-stop

level, Fig. 75. The late Colonel Strange made a series of experiments

with the author's patterns placed at 10 and 20 chains distance. He

also had for these experiments one of Mr. Rogers Field's staves. He

arrived at the conclusion, for distant reading particularly, that the

black markings on all the twenty staff patterns he had were excessively

heavy, so that the lightest and most open readings were the clearest.

This led him to design a staff, a part of which is shown in Fig. 101,

which has been since generally used on the great India survey. This

staff somewhat resembles the English ordnance pattern. The fault found

with these patterns is that they do not read the ·01 foot, which is

necessary for close reading in hilly districts, otherwise they may

be read very clearly at a distance of 20 chains, where the Sopwith

becomes a blur. We may take it that the surveyor, if he be a fairly

good draughtsman, would subdivide the ·05 block to the ·01 foot; but

it is argued that his assistant, who might be a fair leveller, might

not. Another objection is that the reading is on one side and is not

cut through by the horizontal web, so that a white margin can be seen

in the telescope on both sides of the vertical webs, between which

it is most pleasant and exact that the reading should be taken. This

objection does not, however, hold for the point reading, Fig. 75.

Colonel Strange's pattern has not been very generally accepted by civil

engineers. The author tried to meet the matter by making the block ·05

foot, but so subdivided as to indicate ·01 foot. This has frequently

been preferred to his dotted Sopwith.

[Illustration: Fig. 102.--_Details of Stanley staff; A bottom length, B

middle, C top with dot figures._]

268.--The author designed another staff especially for his point index.

This is shown above, Fig. 102. It has had a very fair popularity,

being good both for distant and near sighting. In this staff for the

close figures 11, 12, 13, on a 14-feet staff, which are with great

difficulty distinguishable at a distance, the author employs dots only

as before mentioned--one dot for the 11, two for the 12, and three

for the 13, as shown _C_ for the 12 and 13 in the right-hand figure.

It must be remembered that a good clear staff is a great desideratum,

as it means less size, weight, and cost in the level necessary to be

used with it for equal exactness. A clear staff with a 14-inch level

is quite equal to a complex misty one with a 16-inch level, with the

advantage of saving expense in the purchase, and about 2 lbs. in the

weight of the level to be carried in work.

269.--Our space will not permit the discussion of the various staff

readings that have been designed, many of which are, in the author's

opinion, superior to the Sopwith; but some variations are necessary

occasionally for personal reasons. Some surveyors, from imperfect

colour vision perhaps, strongly object to the red foot figure as being

indistinct at a distance, hence in many patterns a clear black figure

is employed. Some get confused with the number of equal lines of ·01

foot in the Sopwith, what is sometimes termed _Sopwith's ladder_. In

this case these lines may be made unequal in different ways: several

patterns have this peculiarity. Some persons cannot get over the

inverted figure as seen in the telescope. In this case it would be

much better, perhaps, to read with an erecting eye-piece to the level;

but practically the manufacturer has to invert the figures. Other less

important variations are common.

270.--=Metrical Staves.=--These are in this country generally made 14

feet, to keep the length the same as the tripod. The most approved

patterns are shown Figs. 103 and 103A. In using the metre pattern at

short distances often a complete metre cannot be taken in the field of

view, so that there is a little difficulty in being certain to what

metre interspace the subdivisions belong. To avoid this the author

places a dot or dots after the decimetre figures that follow the

metre--one dot for 1 metre, two dots for 2 metres, three dots for 3

metres. Thus 1·4 metre reads ·4; 2·4 metre reads :4. The dots need

only be very small, as they are not required except for very close

readings, that is, within about 30 metres: at 40 metres distance one

complete metre comes into the ordinary telescopic field.

[Illustration:

Fig. 103.--_Metres and Half Centimetres._ Fig. 103A.--_Centimetres._

Stanley's metre levelling staves.]

271.--=Feet and Inches Staff.=--For building works, drainage, and some

other cases, the staff is divided into feet and inches, and subdivided

again into eighths or tenths of inches. This is most convenient when

the work has to be carried out with 5 or 10 feet rods and the 2-feet

rule. The intermediate inches between the feet are better marked 3,

6, 9 only than fully figured. For rough usage the author has made a

solid 10-feet pine staff, well painted. This has a strong hinge in

the centre, and is kept stiff when open by a strong open hook. It

closes face to face in two parts, which keeps the face clean. This is

important for dock and drainage works, where the staff holder's hands

in many cases necessarily get dirty by climbing; otherwise it bears

much more rough usage than the telescopic staff, and is much cheaper to

make. Fig. 104.

[Illustration: Fig. 104.--_Stanley's rough levelling staff._]

272.--=Mining Staves.=--For levelling in mines, large sewers, and other

cases were there is no height for the ordinary staff, the Sopwith staff

is made in its closed form commonly 2 feet 3 inches and 3 feet 3 inches

only in length, to open out respectively 5 feet and 8 feet, or in some

few instances even shorter than these dimensions. The mine staff is in

every way, except its length, similar to the ordinary Sopwith, art. 259.

[Illustration: Fig. 105.--_Stanley's patented mine staff._]

273.--=Stanley's Portable Staff.=--The writer has made a portable staff

in lengths of 18 inches, somewhat like a French folding rule. It may be

formed of three, four, five, or six lengths, opening out respectively 4

feet 6 inches, 6 feet, 7 feet 6 inches, and 9 feet. The separate pieces

are flat boards, slightly sunk on the face to prevent the divisions

being scratched in opening and closing, but left solid at the joint

ends. The boards are attached together with a kind of rivet at each

joint. A strong spring at the end of each piece with a catch and notch

keeps the length opened or closed with sufficient rigidity.[8] The

entire length of the staff when closed in 20½ inches. The same kind

of staff forms a very useful builder's or drainage staff, divided in

this case in feet and inches; and it is conveniently portable for

carrying abroad. Fig. 105--_E_ shows back view, _F_ front view, _G_

cross section, _A_ longitudinal section. The holding springs are shown

at _BB′B″_.

274.--A portable mine staff designed by Mr. G. J. Jee,[9] is said

to be a useful staff for colliery work. It is constructed in three

lengths, sliding one into the other. The bottom length of three feet

is graduated in the ordinary way. The top of this length has a band

attached to it, painted to continue the lower division of the staff

upwards. The other end of the band passes over a roller attached to the

top division of the staff. The roller contains a spring which keeps a

constant tension on the band. By extending the lengths of the staff and

clamping them, the staff may be lengthened out any distance to 9 feet.

The weight of the staff is 5 lbs.

275--=Papering or Repapering a Sopwith Staff.=--The staff, if new,

is painted with three coats of rather flat, thin white-lead paint on

the face, and left to season till the paint is quite hard. It is then

washed thoroughly with a sponge dipped in stout, until this adheres

without beading, and is again left to dry. For repapering an old staff,

this is soaked with hot water in which there is some washing soda, and

rubbed until the old paper is brought off. After the staff is in either

of the states described above, it has to be made warm and coated with

one or two coats of size. The size may be made of a piece of glue left

in water for a night, and then melted in a jam-pot placed in a saucepan

of water over a slow fire. When the staff is sized and dry, if

ordinary papers be used, it has to be divided carefully into foot

lengths, which are marked with a set square in pencil across the face

of the staff. The foot lengths may be set off accurately from an

engine-divided chain scale, or by beam compasses. The papers, which

are printed short, are then pasted over, preferably with paste made of

starch with boiling water, but not afterwards boiled. As the lengths

of paper are pasted they are laid aside, pasted side upon pasted side,

to thoroughly absorb the paste for a few minutes, the time varying

according to the increased length required above that of the original

printed paper. While still wet, the upper paper of the two is lifted up

and cut with scissors, at the same time fitting to the boundary lines.

This wet cutting ensures the paste being equally distributed quite up

to the edges. The foot length of pasted paper is then laid by setting

the upper edge exact to the upper foot line, and gradually bringing

the paper down from this by dabbing with a clean cloth or straight

hat-brush. If the paper does not reach the foot mark when laid, it is

again lifted, and a little more pressure used in laying it the second

time, which will lengthen it out as required. Other lengths are laid in

the same manner. The skilled workman requires no lap to the joins of

the papers, but brings them up edge to edge; with the amateur a lap of

1/8 inch is advisable.

To avoid the trouble of marking off and stretching each foot, the

author has introduced jointless levelling staff papers, so that the

entire length of each section may be put on in one piece. These are of

special paper, and it is only necessary to paste the face of the staff

well and smoothly, and lay the paper unpasted down in position upon it.

After the papers are thoroughly dry they require two coats of thin

isinglass size, and then a coat or two of varnish. Paper varnish can be

bought; but in defect a varnish may be made of Canada balsam dissolved

in oil of turpentine. This should be laid on with a flat bristle brush

(varnish brush), and set in a warm room to dry for a day or two.

276.--=Preservation of the Levelling Staff in Use.=--Where two staves

are used they may be placed face to face for carrying, and be strapped

together, and will take little harm with moderate care. Where one only

is used it is generally strapped to the tripod. A strip of wood is

sometimes used to protect the face of the staff.

[Illustration: Fig. 106.--_Pad for holding a staff and tripod._]

277.--For carrying the staff with the tripod, a convenient plan is to

have two pads formed of stout ox-hide butt, each pierced with two slots

near their ends at the exact distance apart of the width of the staff,

Fig. 106. The strap of calf leather is passed from one slot round the

staff into the other slot, and then passed round the tripod and pulled

up tightly and buckled. The pad of course protects the front of the

staff from grazing by the friction of the tripod against it.

There is a certain amount of risk, under any circumstances, of the

cylindrical tripod pressing against the front of the staff and

splitting it. To avoid this the author has lately made the pads with a

mahogany bridge piece, so that the pressure is distributed, coming upon

the edges of the front where the staff is strongest to resist it. This

is shown, Fig. 107.

278.--For the entire protection of the staff a leather-bound sailcloth

case is very generally used. This may be divided into two compartments

for the staff and the tripod, with pads between. The whole case has a

neat appearance, and forms a protection from slight bruises and dirt,

either in travelling or when set up in an office corner for future use.

[Illustration: Fig. 107.--_Improved pad for staff and tripod._]

279--=Repairing Figures and Divisions.=--Surveyors going abroad

will find it very convenient to have a few tubes of artist's oil

colours--white, black, and vermilion, with one or two sable brushes

to touch up any divisions or figures upon the staves that have become

accidentally injured or worn off by friction. A tube of medium is also

useful, which will cause the colour to dry quickly and leave it bright.

The tubes of colour will keep any number of years if the caps are

carefully replaced. The brushes after use should be well washed with

soap and hot water, rubbing the soap in quite thickly till they are

quite clean, and then well rinsed before putting them by.

[Illustration: Fig. 108.--_Iron triangle to support a staff._]

280.--=Iron Triangle.=--For use of the staff in the field, particularly

in open grass or moist lands, a triangular plate of iron, as

represented Fig. 108, is very useful. This is trodden down firmly by

the staff holder before he places the staff upon it. In use it gives a

certain base to turn the staff upon from fore to back sight. It is very

inexpensive.

281.--=Staff Level.=--This is a small circular level, shown at

Fig. 109, the upper surface of which is formed of a glass worked

slightly concave and fixed into a short cylindrical box. The glass is

hermetically sealed after being nearly filled with spirit. The circular

level is mounted on a plate with a dovetail fitting which fits in a

slot in the holding plate attached to the back of the staff. In use the

staff holder has to observe when the bubble under the concave glass is

in its centre. A very little practice is required to hold the staff

vertically by means of this little contrivance, which only weighs,

about 2 oz.

[Illustration: Fig. 109.--_Staff level, ½ scale._]

[Illustration: Fig. 110.--_Staff-holder, 1/10 scale._]

282.--=Staff-holder.=--This implement, shown Fig. 110, striding a

staff, is very generally used in Germany and other parts of the

Continent. The staff is sunk into one side of a hardwood block. The

block is turned at one end to form a handle. A second similar handle

is cut with a strong screw and screwed into the end of the block. This

screw handle by turning brings up a following piece, shown inside

next the staff, which is covered with leather. When it is screwed up,

the staff may be held firmly by the handles only, without the risk of

the fingers coming in front. With this accessory it is also held more

easily and truly vertical. It is a comfort in use in cold weather.

283.--=Practice of Levelling with the Staff.=--This subject can be

followed here only so far as to exemplify the uses of the instruments

and of accessories connected with such instruments. For practical

levelling we have the standard original works of Simms, Ainsley, and

others, with many modern works.[10]

284.--_For Holding the Staff_, Mr. Holloway, in the work referred

to in the last note, gives instructions in such concise form that

they may be quoted with advantage. He says:--"I generally enter into

confidential chat with my staff holder, in which I explain to him the

vast importance of his duties, _i.e._, I endeavour to make him a man of

importance in his way, and I never fail to get those duties properly

performed. My instructions to him are seven in number:--

"1. Draw out the slides of the staff, and be sure the

joints are properly locked. Draw out one length

only unless signalled to do otherwise.

"2. When the staff is once on a point never move it

unless signalled to do so.

"3. Examine the staff regularly before setting it down

to see that no dirt is sticking to the bottom of it.

"4. Always stand erect behind the staff, so that the

figures face the level.

"5. Do not let any part of the hand come before the

face of the staff.

"6. In no case put a downward pressure on the staff.

"7. If the grass be long, mossy, or spongy, tread

it down, so that the staff shall have a firm

footing--select a firm spot if the selection is

left to yourself."[11]

285.--The manner of setting up a level has been already described in

the previous chapter. The leveller generally follows a definite track

which he has previously arranged and marked out on a map. The distances

apart for placing the staves or staff are measured by the chain, or

by the subtense system to be fully described hereafter. Where the

levelling is very important, as for canal work, topographical survey,

etc., wooden pegs are driven down at the measured stations where the

staff is to be placed from which the levels are to be taken. A general

rule followed, as far as practicable, for starting is to select an

easily recognised, permanent, solid station for first placing of the

staff--a mile-stone, large boulder, or other solid object answers: a

datum line is generally assumed to be at a certain depth below this,

to which all levels are referred. From this station, if the ground be

fairly level, 5 chains is the ordinary advanced position where the

level is set up and the first staff reading taken. The level is set up

at the measured distance from the staff, which is indicated by a mark

left by the chainman.

[Illustration: Fig. 111.--_Level height tape._]

286.--Occasionally in town surveys the height of the level has to be

taken. For this a small steel spring pocket tape is used to take the

height of the axis of the telescope, Fig. 111. The tape may be adjusted

by taking a piece off the first end, and allowing for the width of the

tape case, so that by placing the ring of the tape upon the hook under

the instrument and bringing the case just to the ground, the height of

the axis of the telescope above the ground may be read off at the point

where the tape leaves its case.

287.--_The Reading of the Staff._--The first position, which is

afterwards termed the _back reading_, is taken at a distance behind the

first forward position of the level. This is recorded exactly as it

appears in the telescope, the height of the telescope being also noted

in the levelling book, to be described. Thus in Fig. 112, _S_ the first

staff; _L_ the first station for taking levels. The fore reading _L_ to

_S′_ reads to a higher part of the staff _S′_; _L′_ next level station

back sight. _L′S′_ reads high on the staff _S′_; fore sight _L′S″_

reads low; back sight _L″S″_ again low, following the contour; fore

sight _L″S‴_ low; thus giving data in the levelling book from which

the contour can be plotted from the datum line, which is taken low to

make all readings plus.

[Illustration: Fig. 112.--_Practice of levelling._]

288.--The staff reading, as already described, is divided into feet,

with two places of decimals. The safest method of taking this reading

is to take the second decimal place first and then record it, then

the first decimal, and finally the foot. In this manner no effort of

memory is required, and the staff being sighted three times assures the

certainty of the reading. The telescope should not be touched during

the operation, so that the reading in this manner is only a cautious

transfer.

289.--If two staves are used on fairly level ground, the second staff

is now advanced 5 chains from the level to a measured station, the

staff holder here sighting the line through the level to the back

staff, and firmly treading down the staff plate if the land is soft

or grass, or otherwise requires it, or an iron triangle is used. When

time is given to hold the staff vertically by means of the staff level,

the reading is taken in this position by the leveller as before, and

this is recorded in the levelling book. The level is now moved forward

10 chains, that is, 5 chains ahead of the forward staff. The staff is

carefully turned half round without pressure upon its standing place

or plate to face the level as now placed, in which position it is then

read off by the level as the back sight, the back staff now being moved

5 chains forward of the level, and so on alternately staff and level

until the distance required to be levelled is completed, if there is no

obstruction which causes another method of procedure to be adopted. A

similar plan is pursued with a single staff; but care has to be taken

in securing the right line of march, which will be by placing the staff

in a sight line through the level with a fixed landmark instead of the

back staff mentioned.

290.--The equal back and fore sights as far as practicable are insisted

upon by all levellers, as by this means any inaccuracy in the level, if

the run of the bubble is kept constantly true, is thereby compensated;

but it is not always convenient, and when it is not the accuracy of the

work must depend largely upon the qualities of the level. It is not

necessary or convenient at all times to take the back and fore sight

in a line--obstructions of woods, rivers, etc., may occur. In these

cases very often what is quite equivalent may be done by taking equal

angular back and fore sights from the apex of an equilateral triangle

thus:--Say an obstruction occurs for the chain by a pond or wood, but

that both points to which the levels are to be taken are visible at

some lateral position. Levels may be taken from this place, and if the

intermediate point of distance is equal from both stations there will

be no instrumental error. Thus, suppose the direct level line east

(90°), and that the two stations can be seen and the staves read at

150° and 210°; here, evidently, this is equivalent to a direct back and

fore sight, the right angle to the level course being 180°--the one

station is 150° = 180° - 30°, and the other 210° = 180° + 30°. If these

equal angles can be even approximated with a fairly good level the

error will be small. In this manner intermediate and extended points

may often be conveniently taken by previous arrangement with a good

staff holder. It is in this angular levelling that the greatest use of

the compass is found to give the angles, to make entries of the work in

the levelling book.

291.--In levelling hilly ground great loss of time would sometimes be

incurred from taking equal back and fore sights; the best plan in this

case is to make as much use as possible of the length of the staff in

use. It is in hilly districts only that a staff longer than 14 feet

is advantageous. With any staff in descending a hill only 5 feet of

the staff can be used for the back sight, that is, a part of it equal

to the height of the level, and sometimes 4 feet or less if there is

grass, brambles, or other obstruction. Whereas for the foresight all

the staff upwards of the height of the level, that is, about 9 feet in

a 14-feet staff, can be used with certainty. The distance of setting

up of the levels and staves must in this case entirely depend upon the

length of the staff and other conditions present.

292.--For near reading of the staff on sharp inclines, reading to

two places of decimals is not near enough, as errors may accumulate

rapidly. It is in such cases that a fully divided staff is best. The

divisions upon a near staff appear in the telescope much magnified; and

three places of decimals may easily be taken by anyone used to reading

a chain scale, particularly if a point diaphragm be used. Through

valleys the level may be often checked at some point from hill to hill

by a back sight: the contour must nevertheless be followed for the

section. It is in these shorter unequal ranges and in distant sights

that accuracy in the level is demanded; and it becomes interesting to

know how nearly this may be depended upon for such readings.

293.--As already mentioned, a sensitive 14-inch level of Y

construction, or a dumpy in perfect adjustment supported on the

tribrach system, will work with a level tube divided to read 5 seconds

in divisions 1/20 inch apart. There will be a little personal error

in reading the bubble from difference of reflection, according to

the direction of the light from the two ends of the bubble, as before

discussed; but the bubble may be assumed to be read within less than

half a division, that is, within 2½ seconds--say 2 seconds. A

distinct staff may be read with a good glass within ·1 foot at one

mile. A second of arc subtends ·025598 of a foot = approximately ·3

inch at a mile distance. Therefore a back reading at this distance can

be taken within an inch or so of allowance for instrumental errors.

A reading taken in this way at a mile distance would require a plus

allowance for curvature of the earth of 8 inches, minus say 1 inch for

refraction = 7 inches. From these data we can get a fair check level

for hilly ground, possibly more accurate than by contour levelling for

a distant station, even if we allow double the probable error, say ·1

foot for error of reading the staff at a mile distance.

[Illustration: Fig. 113.--_Calder stove used as a lamp._]

294.--=Lamp.=--At heights between hills in wide valleys check levels

may be taken from five to ten miles very well with a good 14-inch

level in still clear weather in dark nights by the use of an oil lamp.

Coincident points above datum being selected, the lamp is set upon

the ground, or at a measured height at a calculated point, or raised

or lowered to lantern signals, allowance being made for curvature and

refraction. The wide band of light is read very easily by shifting the

observer's position and raising or lowering his tripod. The "Calder"

lamp stove answers very well as a lamp. It has a wick about 3½

inches wide, and by means of a masked chimney may be made to present a

clear white line of light of 1 inch in depth, Fig. 113.

The heliostat is sometimes used for check levelling in sunlight. This

will be described further on with the theodolite.

295.--=Curvature Corrections of the earth and of Refraction= to be

made use of occasionally for check levelling. The rule for finding

curvature is "_That the difference between true and apparent level is

equal to the square of the distance between two places or stations

in miles--divided by the earth's mean diameter, 7916 miles_";

consequently, by this rule the correction is always proportional to

the squares of the distances. By proportioning the excesses of height

to the squares of the distances, we may obtain a curvature table for

corrections. This is, however, always in excess of the true curvature

by the refraction caused by the increase of density of the air towards

the earth's surface, which bends the visual ray. The curvature of the

earth may be corrected for refraction one-fifth to one-sixth,[12] which

varies according to the atmospheric pressure.

296.--The following table, which takes curvature minus refraction,

will be found useful to have at hand: it may be written out and pasted

inside the lid of the level case:--

_Table of Differences of Apparent and True Level for Distances in

Chains._

Distances in Curvature minus Distances in Curvature minus

Chains. Refraction in Chains. Refraction in

Dec. Ft. Dec. Ft.

1 ·000089 14 ·0175

2 ·000358 17 ·0258

3 ·000804 20 ·0357

4 ·001435 22 ·05

5 ·002233 24 ·06

6 ·003216 26 ·07

7 ·00437 28 ·08

8 ·0057 30 ·09

9 ·0072 40 ·14

10 ·089 60 ·31

11 ·011 80 ·56

Where great precision in levelling is required, as for important

trigonometrical surveys, many precautions are required to be taken

which would be quite superfluous, for instance, in railway work. Thus

much greater exactness and freedom from personal error is secured by

having two levellers to go over the same ground simultaneously. Errors

by two persons in the same part of the track are very unlikely to

occur, and by comparing books every part may be checked.

297.--=Pegs.=--Where the work is to be entirely pegged for chain

measurements, the pegs may be made of natural sticks sawn off and

pointed up with a bill hook. If they are sawn from timber they are

generally made about 9 inches long and sawn to a point, the head

being full 2 inches by 2 inches. Where great precision is required a

cast-brass or iron nail is driven into the head after the peg itself is

driven down. This is used to turn the staff upon, Fig. 114. _A_ the peg

shown with a nail in its head, 1/8 size. _B_ nail about full size.

[Illustration: Fig. 114.--_A, staff pegs of sawn timber, 1/8 scale; B,

nail, full size._]

298.--It is considered a precaution with an ordinary level to mark

one leg of the tripod and always place this in the same position to

the staff. Thus, if the marked leg is placed to the forward staff at

first, it is put at the next station backward to the back staff. This

corrects any general error from defective work in the instrument and

want of adjustment; and if the staves are placed at equal stations

any instrumental defect whatever, to act cumulatively upon a distant

station, is then prevented, as this principle produces an alternate

plus and minus error.

299.--Differences of true level have been found between working

southward towards the sun from working northward from it, which are

caused by the expansion of the instrument and bubble tube upon the side

heated by his rays. These matters of higher refinement may be followed

in some of our best works on levelling. Most excellent instructions in

this matter will be found in the appendix of _A Manual of Surveying for

India_,[13] in a paper by Colonel J. T. Walker, R.E., F.R.S., etc., of

the great Trigonometrical Survey of India, wherein levels have been

carried across from ocean to ocean for over 1500 miles of land surface.

300.--=Levelling Books= which record the levels as they are taken are

considerably varied in form, much influenced, no doubt, by the method

pursued by the civil engineer for the execution of his work. The

illustration, Fig. 115, shows the most general forms, but there are

many others.

301.--Entries are very generally made in levelling books in black lead.

Faber's artists' pencils, which require no cutting, are very generally

used, No. 2 being black and moderately hard. It is very convenient to

carry a small file for sharpening the lead frequently. In the author's

surveyor's knife, described further on, a file forms one of the blades.

302.--Where it is desirable to make the original levelling book

readings permanent for reference or otherwise, they are very commonly

written in ink, Morrell's registration ink being very generally used,

or the author's drawing ink answers; this being permanent is not liable

to corrode the pen, nor permit the writing to be effaced in any degree

by moisture.

[Illustration: Fig. 115.--_Specimens of levelling books, 1/3 scale._

_Ordinary Level Book_ with columns for No., Back Sight, Intermediate,

Rise, Fall, Reduced Level, Distance, Remarks.

_Collimation Level Book, with columns for Back Sight, Intermediate,

Fore Sight, Height of Collimation, Reduced Level, Distance, Remarks._

_Railway Engineers' Level Book_, ruled for Back, Intermediate, Fore

Sight, Rise, Fall, Distance, Reduced Level, Formation Levels, Cutting,

Embankment, Remarks.

_Tacheometer Survey Book, ruled as above illustration._

_Traverse Survey Book, ruled as above illustration._]

303.--_The Ink Bottle_ mostly used is that known as the excise bottle.

This is of a smooth, oval form, covered with black leather, with a tab

and buttonhole to hang upon a button of the coat, Fig. 116. One of the

numerous fountain pens is now generally used instead of the bottle

described.

[Illustration: Fig. 116.--_Excise ink bottle._]

FOOTNOTES:

[7] _Brit. Assoc. Report_, 1838, p. 154.

[8] Patent No. 12590, 1889.

[9] _Colliery Guardian_, vol. xxxviii. p. 576, 1879.

[10] _A Treatise of the Principles and Practice of Levelling_, by

F. W. Simms, 1842; _A Treatise on Land Surveying_, by John Ainsley,

revised by William Galbraith, 1849. Quite modern works--_Aid to Survey

Practice_, L. D'A. Jackson, Crosby Lockwood, 1910; _On Levelling and

its General Application_, by Thomas Holloway, Spon, 1887; revised 1914.

[11] _Levelling_, p. 49.

[12] Deschanel's Natural Philosophy, by Prof. Everett, p. 1018, 1876.

[13] _A Manual of Surveying for India_, by Colonel H. L. Thuillier,

C.S.I., F.R.S., etc., and Lieutenant-Colonel R. Smith. Thacker,

Calcutta, 1875. (Now out of print).

CHAPTER VI.

DIVISION OF THE CIRCLE AND METHODS EMPLOYED IN TAKING ANGLES--DIVIDING

ENGINE--SURFACES FOR GRADUATION--VERNIER--VARIOUS SECTIONS--READING

MICROSCOPES--SHADES--MICROMETERS--CLAMP AND TANGENT MOTIONS--OF

LIMBS--OF AXES--USE AND WEAR--DIFFERENCE OF HYPOTENUSE AND BASE.

304.--=Division of the Circle.=--_Sexagesimal Division._--All true

surveying instruments depend, as their special function, upon taking

the direction, or angular position, of surrounding objects or definite

parts of the surface of the earth from positions which are at first

accurately measured or ascertained. The instruments required for such

work must possess an accurately divided circle or arc, with means of

subdividing the visible divisions of this to greater closeness than

any possible method of drawing lines simply would permit. The lines

upon the circle in general practice in Great Britain are divided into

degrees, which are subdivided to 30, 20, 10, or 5 minutes, according

to the size of the instrument, and arranged for further subdivisions

by means of a vernier into minutes or 30, 20, or 10 seconds of arc.

Upon large circles, say of 10 and 12 inches diameter, and with modern

5, 6, and 8 inch diameters, angular displacements in the direction of

the telescope are ultimately read off with a microscope by means of a

screw with divided head, termed a _micrometer_, placed tangentially to

the divided circle; or by a series of lines placed at equal distances

apart in front of an eye-piece or within a microscope; but in the

ordinary portable instruments, or those that a surveyor can personally

carry about the country, the ultimate subdivisions of the circle are

still generally made by a vernier scale only, which will presently be

described, although the smaller modern micrometer reading instruments

are slowly but surely coming into favour for all high class work.

305.--_Centesimal Division._--Ten to fifteen years ago on the Continent

generally, and in America occasionally, the division of the circle into

400-grades and ½-grades, and the subdivision of these decimally to

centigrades, appeared to be coming more and more into use, particularly

with the more extended use of the tacheometer. Under this system it

will be seen that the right angle subtends 100 grades. This division,

with its centesimal parts, was found to blend conveniently with

logarithmetical calculation and to permit the free use of the slide

rule with great saving of time over ordinary calculation, but it is now

very little used.

The decimal division of the ordinary degree of 90 to the quadrant

greatly facilitates the calculation compared with what is necessary

with the sexagesimal division into minutes and seconds, and the reading

of the verniers is much simpler and less liable to errors; moreover,

the mental conversion of the sexagesimal division into decimals of the

same degrees is much simpler than the conversion into the centesimal

degrees of 100 to the quadrant.

306.--=Dividing Engine.=--This important tool is used for cutting the

graduations on all surveying instruments. If possible a position should

be secured for it on a ground floor at a mile or more distance from

any railway, and at a good distance from roads upon which there is

heavy traffic, as small vibrations are sufficient to cause unpleasant

working and some error in the division of large instruments. For very

accurate work some makers divide at night for the sake of stillness.

The principles of construction of this machine, as at present in

general use, were invented by Jesse Ramsden, of which an account was

printed by the Board of Longitude in 1777. Refinements of detail have

been added to the invention, and the steady action of steam or electric

power has been applied in place of the foot, but otherwise the machine

remains practically the same. Therefore a brief description of this

machine as originally invented will be sufficient for the purposes of

this work, which is not intended to fully describe the tools used in

the manufacture of instruments.

307.--_Ramsden's Engine_ consists of a circular brass surface plate,

made generally of 36 inches diameter. This plate is supported from

below upon a hollow vertical axis, which moves in an adjustable collar

placed at its upper end and in a conical point or pivot at its base.

The pivot rests in a cup of oil and supports the weight of the plate

and axis, so that this part rotates with little friction. The outer

edge of the surface plate is cut with 2160 teeth or threads, into which

an endless or tangent screw works, so that the plate can be revolved

any desired quantity by means of the screw. Six turns of the _tangent_

screw moves the plate 1°. The head of the tangent screw is divided

as a micrometer into 60 parts; therefore the movement of one of the

divisions of this head revolves the plate 10″ of an arc. A ratchet

wheel of 60 teeth is attached to the tangent screw, and so arranged

that by reciprocating motion applied to a rack which works into it the

circle can be advanced any multiple of 10″. Motion is given to the

tangent screw by a catgut over a pulley worked by the foot. The work is

centred and clamped down upon the surface plate. While the divisions

are being cut this surface plate remains for the time quite stationary.

308.--The dividing knife is attached to a swinging frame having a

reciprocating motion. The forward extent of its swing is regulated by a

detent wheel with teeth of varied heights, which, as they are brought

by the mechanism consecutively forward, stop the knife at a definite

position; so that the cuts upon the circle--technically the limb--are

regulated for lengths to represent 10 degrees, 5 degrees, degrees and

parts. In the use of this dividing machine the divider who worked it

had alternately to press his foot upon a treadle and then pull a cord

attached to the dividing knife frame. These motions are now performed

by self-acting mechanism. For full particulars and details of the

dividing engine see Troughton's Memoir, _Phil. Trans._, 1809: _Memoirs

of the Royal Astronomical Soc._, vol. v. p. 325; vol. viii. p. 141;

vol. ix. pp. 17 and 35. For various plans that have been tried see

_Holtzapffel's Turning and Mechanical Manipulation_, pp. 651-955.

309.--_The Material_ upon which the _limb_ or circle of an instrument

is divided is almost uniformly of silver, except for mining survey

instruments, which need a very strong cut. Silver being dense and

of extremely fine crystallisation, or _grain_, as it is technically

termed, bears a uniform smooth cut with sharp outline. Occasionally

circles or arcs are divided on platinum, certainly the best metal,

as it keeps constantly clean; but it is expensive. The verniers are

then made either of this metal or of gold. The silver of the circle,

when this metal is employed, is rolled down from a surfaced cast plate

of about ·25 inch in thickness to about ·045 inch, by means of which

it becomes uniformly dense and fine grained. In all cases possible,

that is, upon all flat internal surfaces, the silver is placed in an

undercut groove and planished down to fill the groove without any other

fixing being necessary. This plan of insertion is employed for all

vertical circles--the horizontal circle of Everest's theodolite, limbs

of sextants, box sextants, etc. In Fig. 117 the silver is shown at

_A_, in the section to which it is drawn by a plate after it is cut in

slips. It is shown placed in its groove _B_ ready for planishing down.

By this method certainty of dense surface is obtained for the future

division.

310.--Upon bevelled edges and outer surfaces the rolled silver is

planished to form, and then soldered to the metal of the part of the

instrument to be divided. The surface, after being made as dense as

possible by planishing or otherwise is turned to form and stoned to

surface ready for the dividing knife.

[Illustration: Fig. 117.--_Insertion of silver in circle._]

311.--=Graduating.=--The object aimed at by the skilful divider is to

obtain as deep a sharp-edged cut as possible, which shall be at the

same time as fine as it can be read clearly by the microscope with

which it is to be used. This matter is most important to the possessor

of the instrument afterwards for use, as in the atmosphere the silver

soon forms an oxide and a sulphuret upon its surface which has to

be cleaned off; and at every cleaning a portion of the silver is

necessarily removed, so that in old or badly divided instruments the

divisions become dull or lost from this reason.

[Illustration: Fig. 118.--_Piece of charcoal._]

312.--After the instrument is divided it is engraved with figures and

stoned off with fine blue-stone, and finally finished with willow or

pearwood charcoal, which has just sufficient cut in it to leave a hard

edge to the division lines.

313.--It may be useful to the surveyor, far from aid of the optician,

to know that divisions on silver which are much oxidised may be brought

up to sharp lines by the use of a piece of fine-grained charcoal,

sharpened by a clean file to a chisel point. This should be frequently

dipped in water, and rubbed lightly with the flat of its end surface,

Fig. 118, keeping the motion of the hand in the direction of the

circumference of the circle. The piece of charcoal before being used

should be first tried upon a piece of plain, smooth metal--an old coin

which is worn smooth will do--to see that it is not _scratchy_. No

kind of polishing powder should in any case be used for cleaning limbs

or verniers, as _this_ is sure to rub down the edges of the cuts and

thereby ruin the divisions of the instrument.

314.--It must be understood that the above directions are not intended

for the ordinary cleaning of the circle for an instrument in general

use, as such would be injurious to it. In the ordinary daily use of

the circle, if it is not in any case touched by the hand, and is kept

carefully brushed with a large, soft camel-hair brush when taken from

the case, and the same when returned to it, it will keep a long time in

an excellent state. If the circle is slightly tarnished, this tarnish

may be removed by a piece of quite clean wash leather; but the brush is

always the safest if sufficient. If the vernier gets _grubby_ against

the circle, a piece of clean thin writing-paper may be passed between

these parts, which will clear out any dirt or grit there may be between

sufficiently.

315.--=The Vernier Reading Index.=--This is one of the most important

inventions ever applied to instruments of precision for measuring

upon the circumference of the circle. It was invented or brought into

practical use by Pierre Vernier, a native of Ornans, near Besançon, in

Burgundy. The first publication of the invention appears in a pamphlet

published in Brussels in 1631, _Construction, Usage, et Proprietes

du Quadrant Nouveau de Mathematique_. This invention was possibly

foreshadowed, as it is mentioned by Cristopher Clavius in his _Opera

Mathematica_, 1612, vol. ii. p. 5, and vol. iii. p. 10; but he did not

propose to attach it permanently to read into an arc, that is, to place

it in its practical form.

316.--The value of the vernier as a means of reading small quantities

depends upon the fact that the _eye_ cannot separate lines, drawn at

equal distance apart, of above a certain degree of closeness, there

being a point for all vision where such lines appear to mix with

the ground upon which they are drawn and form a tint; therefore, an

index reading into such close lines would be, unless under extreme

magnification, most indefinite; whereas the eye can see a single

separate line clearly and detect any break in it. The vernier for

reading subdivisions depends upon the functions of the eye having power

to detect any break in an otherwise straight line, so that a line that

appears without a break may be taken as the index of reading from

among others that appear broken or separated. It is found in practice

that a line as fine as it can be clearly seen will appear broken in

its continuity with another equally fine line, if at the meeting the

rectilinear displacement is as much as ·25 to ·2 part of the width of

the line. It therefore follows that we may read closer by displacement

of parts of a single line than by any possible series of lines that

can be drawn in spaces apart upon a surface; so that if we can arrange

lines in such a manner that they open out or separate into distinct

lines to admit of this principle, we obtain the full value of the

unbroken single line reading, and this is the principal aim of the

vernier.

317.--On the same principle that we can find the straight or most

direct line of a series of lines to take as our index, we can also

estimate the amount of the displacement of our selected line, if this

does not read perfectly straight from the vernier division to the

circle division. This small difference is detected in practice by many

experienced surveyors, so that a vernier reading nominally to minutes

only is recorded _n_′ + 15″, 30″ or 45″, that is to 15″. There is

no doubt that this will be approximate, but it may be much nearer than

the even minutes, say to the 30″ on a 5-inch, or the 15″ on a 6-inch

sharply divided circle.

[Illustration: Fig. 119.--_Origin of vernier scale._]

318.--_The Vernier Scale_, as employed by Vernier, was divided to

read minutes upon a circle or limb divided to half degrees, by taking

thirty-one divisions of the scale and dividing these in thirty equal

parts for a separate scale to read against it. This plan is now termed

an _inverse reading_, the reading being the reverse to the direction

of that of the arc. In modern practice the vernier to read minutes is

divided to the length of 29 half degrees, and this length is subdivided

into thirty equal parts: consequently, where the vernier and scale

are placed edge to edge or reading to reading, every division of the

vernier _advances_ consecutively on the scale one-thirtieth of the half

degree, that is = 1′ of arc on the scale divided to half degrees. In

the above diagram, Fig. 119 represents the scale and vernier at the

position from which the description is taken, wherein the vernier is

shown to cover 29 half degrees or 14° 30′, and this length is divided

into thirty parts. The consecutive advance of the vernier on the scale

is shown + 1′ for each half degree. In this position of the vernier,

or at a similar position in relation to any other half degree of the

circle the arrow placed at the zero of the vernier reads direct into

the degree or half degree, so that this reading must be _n_° or _n_°

30′ at any equivalent position in relation to any line on the limb.

[Illustration: Fig. 120.--_Vernier scale, reading 23° 12′._]

319.--In Fig. 120 the arrow upon the vernier scale is shown reading

at a position beyond 23°, which we then know must be 23° _n′_. Now,

if we look along the vernier, the lines of this and the scale appear

coincident at the twelfth division of the vernier; consequently, the

_n′_ is 12′, and the reading is altogether 23° 12′.

320.--Learning the reading of the vernier is very similar to that of

the clock, wherein a child at first gets confused by the difference of

value of the minute hand and the hour hand. In the case of the vernier

we have only to get clearly in our minds that the degree reading and

the vernier reading are quite distinct processes, in which the vernier

reads _minutes_ only, and this _by coincidence of lines only_, and that

it has nothing to do with degrees, which are indicated by the arrow

_only_. The arrow may be assumed to be placed on the vernier scale to

save an unnecessary line of division; but this practically might just

as well be placed quite outside of it, as it has nothing whatever to do

with the vernier reading.

[Illustration: Fig. 121.--_Vernier scale, reading, 23° 47′._]

321.--It is important to make this matter of reading the vernier clear;

therefore in Fig. 121 the index arrow and vernier are shown reading

past a half degree. At this position the arrow reads 23·30 on the limb

+ the vernier, or 23° 30′ + _n′_ of the vernier reading. We find the

coincident line of the vernier with the limb is at 17, therefore the

reading is 23° 30′ + 17′ or 23° 47′.

322.--The principle of the vernier, upon which it takes its reading

from the coincidence of lines, as just stated, points out that

the figuring of values of points of coincidence may be varied at

discretion, and the zero index may be in any convenient position. The

above described is the common reading to the theodolite and many other

instruments. In mining dials and some other instruments the zero is

placed in the centre. We may, for example, take a central reading with

a vernier reading to 3′, wherein the circle being divided into degrees;

the vernier is then, necessarily, in the direct method, divided into

twenty divisions (20 × 3 = 60) which correspond with nineteen degree

marks of the circle. With a central reading the vernier in this case is

figured 30, 45, 0, 15, 30. This is rather a simple reading, as the zero

to which an arrow is attached gives the true bearing, and it is readily

seen to which degree it refers.

[Illustration: Fig. 122.--_Vernier reading centrally to 3′._]

[Illustration: Fig. 123.]

In Fig. 122 the 45 of the vernier is coincident with a line of the

limb, this must, therefore be 45′; and as the index arrow is past 44°,

it is 44° 45′. If the vernier had read the division next past the 45,

the division being to 3′, this reading would have been 44° + 45′ + 3′ =

44° 48′. The same principles may be applied to any subdivision. Circles

are commonly divided by the vernier in various ways to give readings

from 5′ to 5″.

Theodolites reading to 30 seconds are usually divided degrees and

thirds of degrees on the circle and minutes and halves on the vernier,

as illustrated (Fig. 123), the reading in this case being 153 degrees

40 minutes on the circle and 8 minutes 30 seconds on the vernier,

giving a total reading of 153° 48′ 30″.

A 20 second reading usually has divisions of 20 minutes on the circles

and these are subdivided into minutes and thirds by means of the

vernier.

[Illustration: Fig. 124.]

Fig. 124 is an illustration of this, showing a reading of 28 degrees 40

minutes on the circle and 12 minutes 20 seconds on the vernier, giving

a total of 28° 52′ 20″.

A 10 second reading is designed in the same manner as the above, but

each division of the circle is 10 minutes instead of 20 minutes, with

minutes and sixths on the vernier. Fig. 125 is an illustration of this,

showing a reading of 7° 16′ 30″.

[Illustration: Fig. 125.]

323.--_For Centesimal Division_ the vernier to read minutes is

generally divided 50 into 49 for the half grades, for small circles 4

inches to 5 inches. For larger circles, 6 inches to 8 inches, verniers

are cut 25 to 24. The circle is then divided to ·25. Where there is

space for five divisions to the grade, ·20, the third decimal place,

may be estimated or read exactly to ·005 by a vernier 40 to 39, or

more closely if desired by a micrometer, to be described presently.

[Illustration: Figs. 126, 127.--_Sections of scales and vernier for

circular readings._]

[Illustration: Figs. 128, 129.--_Sections of scales and vernier for

circular readings._]

324.--=Surfaces of Limb and Vernier.=--To get a perfect reading of

a vernier the scale and vernier should be brought into contact upon

a plane. This, for many reasons, is impossible in a great number of

cases upon an instrument, from the conditions of its construction,

convenience of vision, and in some cases for want of means of ensuring

durability of the edges which work together. Therefore verniers and

scales are more commonly constructed upon the methods shown in section

Figs. 126, 127, where _VV_ are verniers, _LL_ limbs. The plan shown

in section Fig. 128 gives a nice reading on a new instrument; but the

part of the edge not covered by the vernier is open to accident, or if

nearly covered by a part of the instrument, open to the introduction

of gritty dust, which wears the meeting line open, and thereby causes

loss of edge to edge reading. Fig. 129 shows a section we find on some

French instruments. This plan was introduced by the late Colonel A.

Strange for the section of the limb reading of theodolites for India,

but it was found in practice awkward to use upon this instrument, as it

required unpleasant stooping to read it. It is, nevertheless, one of

the best permanent vernier readings, as the division remains constant

under the amount of wear occasioned by the sliding of the vernier upon

its circle.

325.--With the reading planes shown in section Fig. 126 we require

great care to bring the eye, whether open or through the microscope,

directly radial with the centre of the circle at the line into which

the vernier cuts. If we read the line in the slightest degree one-sided

it is quite possible to make a difference of a minute on a 5-inch or

6-inch circle. This is the section of the general reading plane of

theodolites, where, from the necessary height of the telescope, the

limb has to be placed much lower than the eye. With this section the

circle comes fairly square to a comfortable position for reading. It

will be noticed that there is a slight lap shown to the vernier over

the limb at _a_, Fig. 126, which is always found in new instruments of

this section. It gives an allowance for wear between the vernier and

the limb caused by the fretting of the metals together, as also by the

intrusion of grit, which is always present in instruments used in the

open air. The lap should not be great, and it should be nearly equal

along the edge of the vernier, although it is a difficult matter for

the maker to get it perfectly so.

Fig. 127 is a section of the reading planes common to sextants and

parts of many instruments. This plan requires the same care to obtain a

truly perpendicular reading to the division as that described above for

Fig. 126.

326.--In the very best of work there is at all times a certain amount

of error, both between the divisions themselves, and in the place of

the axis in relation to the centre of the divided circle, and of the

position of the vernier in relation to both these. It therefore becomes

necessary, where exactness is required, to place at least two verniers

to read opposite sides of the circle. These bisect every reading

through the axis of the instrument, and detect very small errors in

the work, as well as personal errors of the observer, of which the

mean reading of the minutes or seconds only may be taken and used for

correction to mean position. Where very great precision is aimed at,

three or even five verniers are sometimes placed round the circle,

and the mean reading is taken of the small differences in minutes or

seconds, after calculation for correction, to find the direct position

of the axis of the telescope required for the record of the observation.

327.--=Reading Microscope.=--The microscope usual for reading the

vernier is either a simple plano-convex lens of short focus or a

Ramsden eye-piece of the kind described for observing lines on

the diaphragm of a telescope, art. 82. Frequently the microscope,

technically called the _reader_, is made of a compound form, sometimes

with a diagonal prism or mirror. It is uniformly mounted in such a

manner that it may move concentrically to the divided circle into which

it reads. In English instruments it is placed normal to the surface of

the vernier, so that following its curvature it may read opposite any

line upon it. In French instruments the reader is frequently placed

obliquely, so as to look along the line of the limb into that of the

vernier, which is said to be advantageous in certain lights.

328.--In theodolites for reading the horizontal circle, the reader is

sometimes mounted to slide in an undercut groove near the circumference

of the limb to follow its curvature. This motion is not pleasant; it

is better in this and all cases of vernier reading, if possible, to

mount the reader on frame-work proceeding directly from and moving

upon the axis. Where it is practicable, it is much better to have two

readers where there are two verniers, and in all cases to have one

to each vernier, than to shift one reader about after the instrument

is placed in position, which is liable to disturb it. With opposite

readers mounted on a pair of arms formed of one piece of metal, where

these bisect the circle working through its axis, by the setting of

one reader truly normal to the coincident division of the vernier the

opposite reader will be set also; so that this does not only save time,

but the instrument need not be touched for reading the second vernier.

The same principle should be applied to any greater number than two

verniers as nearly as it may be practical.

329.--Instruments that have to be packed in cases for conveyance should

always have readers removable from the instrument, with proper fittings

in the case provided for them, or they should be hinged to turn up to

a secure position, the latter being a more expensive but a much better

way. It is better also, if possible, to remove the light frame with

the reader if this does not turn up, so that it cannot be injured in

replacing the instrument in its case.

[Illustration: Fig. 130.--_Reader fixed normal to surface._]

[Illustration: Fig. 131.--_Jointed reader to set to any angle._]

330.--Fig. 130 shows a good rigid form of reader for an oblique

plane of division:--_V_ vernier, _L_ limb. This reader is placed on

an arm radial from the centre of the instrument, more generally in

pair with an opposite reader. The connection with the arm is commonly

made for portability with a dovetail slide fitting to the reader,

sprung by a saw-cut down it to ensure constant contact after wear,

as shown in section Fig. 132; _N_ arm of reader, _O_ fitting to arm.

The better form is shown in Fig. 131. In this the arm is jointed,

so that the reader out of use is turned up into the central part of

the instrument. This plan admits of adjustment of the reader for

reflection of light from the division, or for reading _down the lines_

if preferred. The magnifying power of either of these microscopes is

generally two to three diameters. The adjustment of the glasses should

be such as will produce a flat field (Ramsden's principle, p. 41), so

that several divisions of the vernier and limb may be read sharply when

it is in focus, although the central division only is taken for the

reading.

[Illustration: Fig. 132.--_Section of movable arm fitting to reader._]

331.--=Surface Reflection to Reader.=--In reading with the microscope

the silver surface, from its brightness in certain lights, gives

unpleasant reflections which render the reading difficult. In practice

the hand or a piece of white paper is used to shade the open vernier in

such cases. In large instruments a piece of ground glass is fixed in a

frame over the vernier, which throws a soft light, producing the effect

of a dead surface upon the silver, or the light is reflected from a

cardboard or ivory surface. Fig. 133 shows a common form of microscope

for reading a vertical circle, by which the light is reflected from a

white surface surrounding the field-glass end of the reader.

[Illustration: Fig. 133.--_Reflecting surface reader._]

332.--=Shades for Vernier.=--It is very general on the Continent to

place the divided reading of the circle and its vernier on a plane

perpendicular to the axis, Fig. 128, and to place the reader at a fixed

angle for down-the-line reading, the object-glass of the reader being

constructed to focus parallel rays. In this way the division of the

circle is followed into its vernier or _vice versa_. In this case the

silver may be shaded by ground glass, which gives a soft, pleasant

reading in most lights. The general arrangement is shown, Fig. 134; _L_

limb, _V_ vernier, _S_ shade of ground glass, _M_ reader. Objection

is made to glass shades by civil engineers as being too delicate and

liable to fracture, with risk of the particles of glass getting into

the working parts of the instrument. To obviate this the author has

made the shade of a piece of thin horn or transparent ivory, which

appears to answer very well and to save this risk.

[Illustration: Fig. 134.--_Oblique reading microscope with shade,

French plan._]

333.--For ordinary instruments with no provision for shading, a piece

of transparent horn about 2¼ inches by 1¼ inches may be carried

in the waistcoat pocket, and will be found a great comfort if held

over the vernier when the lines appear glary, or the horn may be

placed in a pocket frame with the case containing reflector for bubble

reading, Fig. 52. In large theodolites, used for geodetic surveys, the

object-glass of the micrometer microscope is sometimes surrounded by

a thin belt of turned ivory. This throws a very soft light upon the

divisions.

334.--=Micrometer Microscope=, _for Reading Subdivisions_.--Where

more exact reading is required than is possible with the vernier, as

in the case of the reading of circles 10 inches or more to seconds, a

micrometrical microscope is employed, which gives means of measuring

the distance from line to line of the division upon the limb by the

displacement of a web, point, or line moved by a fine screw with a

divided head.

The great demand of late years for reducing the size and increasing

the accuracy of theodolites has induced the highest class makers

to introduce micrometer reading instruments of six, five, and even

four-inch circles, and their accuracy is far greater than is possible

with any instrument of the same size that reads by verniers. Of course

the workmanship in these instruments has to be of a higher order,

and the reviser estimates the accuracy of the micrometer through

magnification and the necessary refined workmanship to be at least four

times as great as the vernier reading, with the advantage that the

micrometer is much more certain and easier to read.

335.--The construction of the reading micrometer as originally designed

by Troughton has not been materially modified in those in general use.

Certain refinements have been introduced for astronomical work: these

are sometimes expensive and often cumbersome, so that they need not be

considered in relation to surveying instruments.

336.--In all cases where micrometers are used, the structure of the

framework of the instrument which carries them should be made extremely

rigid, as very minute deflections or vibrations render the reading

to seconds of arc impossible. The number of micrometers applied to a

circle is generally 2, 3, or 5.

337.--If a circle is to be read by micrometers, the vernier is

generally dispensed with. The circle is usually divided to read in

5′. The first approximate reading used to be taken by a single index

line with the aid of the ordinary reader, Fig. 130. From the index

line the degrees or minutes were taken to the last 5′ line indicated.

Since the introduction of high-class engraving machinery the figuring

is made at each degree and is clearly read in the microscope, so that

the index reader is unnecessary. This engraving is quite a nice piece

of work, as to figure from 0 to 360 means nearly a thousand figures,

and on a 5-inch circle these have to be less than 1/100th of an inch

high. Only the highest class makers are able to do this work. When a

microscope is adjusted to one line it should be observed that all the

other microscopes upon the same circle should also read exactly to a

line that should be true from microscope to microscope to the arc they

subtend between each other.

[Illustration: Fig. 135.--_Side elevation of Troughton's micrometer._]

[Illustration: Fig. 136.--_Section of micrometer._]

[Illustration: Fig. 137.--_Micrometer slide._]

338.--=The Micrometer=, as it is now technically termed to include the

whole piece of apparatus, is a compound microscope consisting of three

lenses, with measuring apparatus at the mutual foci of the field-glass

and of the two lenses which form the eye-piece. The field-glass,

which is placed nearest the divided arc, is generally an achromatic

microscopic lens of an inch or more in focus. The eye-piece is of the

Ramsden form, Fig. 16. By the construction of the compound microscopic

arrangement the eye of the observer may be placed at any convenient

distance from the limb, and any desired magnification may be obtained

to assure micrometric nicety of measurement. The engravings represent

the micrometer, Fig. 135 in side elevation, Fig. 136 longitudinal

section, and Fig. 137 the micrometrical slide, which is shown partly

in section for demonstration in all the figures; _a_ the micrometer,

_q_ microscope body tube. This has a male screw outside at _b′_, upon

which there are two collars _dd′_ with capstan heads. These collars

hold the microscope upon the reading frame _b_ at any required distance

from the limb to secure proper focal adjustment. _g_ objective tube.

This screws into the body tube and permits adjustment of the objective

to the division of the limb and the micrometer index web by the milled

head _s_. This tube has a locking nut _i_ to secure it from after

movement when it is once properly adjusted. _h_ an achromatic object

glass of half an inch or over in focus. _e_ the casing that receives

the eye-piece which screws into the outer plate of the micrometer.

_f_ the eye-piece, generally made about one inch long. This slides by

friction in its cell to produce distinct vision of the spider lines in

the micrometer.

339.--The micrometer frame, Fig. 137, _a_ has a fixed scale or _comb_,

with five or more points or teeth formed upon it, and a movable sliding

frame, upon which a spider web or webs are inserted and cemented in

finely engraved lines to form an index, brought as nearly as possible

to the mutual focal plane of the object-glass and the eye-piece. The

index web frame has a fine screw of about a hundred threads to the inch

tapped into it. The micrometer screw, divided drum, and milled head are

now generally constructed as shown in Fig. 137. Two springs press upon

the index frame and the outer frame, and thus keep the drum up to its

collar. The drum _r_ is divided upon its edge into sixty equal parts,

to read seconds of arc generally to a single line index. The screw is

moved by the milled head beyond the drum, so that the divided surface

of the drum need not be touched.

340.--The portion of the arc measured being generally 5′, the distance

of it, as it appears at the magnified image of the arc at the position

of the index of the micrometer, is made to correspond with five turns

of the micrometer screw, the head of which divides each turn into 60.

By this means the 5′ is divided into 300, that is, to single seconds,

and by approximation of the interspaces on the micrometer head, as

far as the reading is concerned, to fractions of a second. The fixed

scale, or _comb_, as it is termed, is commonly placed in the focus of

the eye-piece with five webs upon it, fixed to agree with five turns

of the screw or a rack with points at the bottom. These webs or rack

divide the 5′ of arc in minutes, and indicate the number of revolutions

of the screw, as shown by the displacement of its index line. A pair of

lines or webs are commonly placed in modern instruments at 1′ part, to

ensure certainty of reading by the mean of two observations.

341.--The magnitude of 5′ of arc depends necessarily upon the radius

of the divided circle; therefore the microscope of the micrometer has

to be made to suit the division it is required to subdivide--that

is, using the same micrometer, the smaller the circle the higher the

magnifying power is required to be to take register by the same screw.

Within a wide range the micrometer is perfectly adjustable, to ensure

exactness upon this point, by varying the distance of the object-glass

from the limb, for which purpose the microscope is made adjustable by

the pair of screws _dd′_ which clamp it to its standard as already

mentioned. The principle of this adjustment is easily seen, for if

we place the object lens at a distance equal to its solar focus from

the limb, the image will emerge in parallel lines; but as we cause

it to recede from the limb, the image may be brought to any position

within the tube greater than the solar focus of the objective of the

microscope. The image is therefore brought to a position where it may

be picked up conveniently by the eye-piece. In this manner we have only

to make the adjustment of the object-glass from the limb such as the

space of any pair of divisions of the limb may be magnified up equal to

the displacement of five turns of the screw for seconds measurement.

342.--The two points where the divisions and their images are situated

are termed the _conjugate foci_ of the lens, and the magnifying power

is proportional to these distances; thus, if we call the distance

of the object, that is the limb, from the object lens _f_, and the

distance of the focal plane of its image within the tube _F_, the image

will exceed that of the object in the ratio of _Ff_, or _F_/_f_ will

represent the magnified image. By this method it will be seen that the

expression _F_/_f_ will have an increased value, if we either increase

_F_ or diminish _f_, which we have to consider in the construction of

the microscope to bring it to the conditions under which it will adjust

to bring the micrometer screw exactly to its required reading.

[Illustration: Fig. 138.--_Grubb's plan of securing micrometer screw._]

343.--It is very general in instruments at the present time to tap the

micrometer screw directly into the micrometer frame, and to make the

drum and milled head a part of the screw. In this case a very soft

motion may be given to the screw by dividing its nut longitudinally and

bringing the parts together with a certain amount of spring. Sir Howard

Grubb, of Dublin, has placed a spring ball fitting, as shown Fig. 138

at _EE′_, over the screw upon his astronomical instruments, which gives

a very soft motion to the screw. These refinements are very important,

as it is not desirable that any undue pressure should be put upon a

delicate instrument which under all conditions must be made rigid

enough to resist it, and the greater the pressure required to bring the

instrument to bearing the stronger it must be made.

[Illustration: Fig. 139.--_Stanley's micrometer slide._]

344.--=Stanley's Micrometer.=--The author has made an arrangement in

which the screw has a long, double tubular sliding stem, Fig. 139. The

inner stem which carries the milled head has a groove cut down it,

into which a stud from the inside of its covering tube slides. This

arrangement permits the milled head to be pressed inwards or outwards

in turning it without any pressure coming upon the micrometer greater

than the friction upon the sliding tube, and that of a weak spring

which keeps the stem nearly extended in its tube. A simple Hook's joint

_H_ is formed at the head of the screw, so that no part of the weight

of the hand comes upon the screw. A tubular guard-piece _T_ prevents

the milled head hanging down too far when out of use. When the screw

is used it is lifted to about the centre of the guard tube. With

this arrangement, as no practical weight or pressure comes upon the

micrometer from handling it, the supporting frame-work may be made much

lighter than is necessary with any other form of micrometer.

345.--The author prefers to form the micrometer scale and the index

of fine lines engraved upon parallel worked glass for surveying

instruments. This avoids the risk of breaking webs, and, what is much

more important, he finds that with engraved lines on glass he is able

to bring the scale and index exactly and permanently into the plane

of mutual foci of the object-glass and eye-piece by placing the lines

upon the same faces of glass, thus avoiding the great difficulty of

focussing to guess-work of an intermediate position between two sets of

webs at different distances.

The strip of glass _A_ is fixed by a clamp and two screws to the side

of the micrometer box. The slip _B_ is ground and polished to fit _A_.

_B_ is carried by the micrometer frame _F_, which holds it in a clamp

by two screws. A spring, not shown, presses _B_ against _A_, so that

any displacement of the micrometer lines may be made by the milled

head. The lines upon _A_ are adjusted to the position of the circle

they are intended to read at exactly 5′ or other quantity.

For the smaller instruments which will be much more frequently used by

the surveyor a simpler form of reading is used, and as the reviser is

convinced that in future this form of reading will gradually replace

the vernier for all high-class work, a full description of this very

simple reading is here given. The reviser is confident, after many

years of practice for the most accurate form of index, that a point

certainly stands first, a pair of webs or lines on glass, between which

the division is seen, second; and a single web or line on glass placed

over the division, third. The comb mentioned in art. 339 is done away

with, and one revolution of the micrometer screw made to carry the

index over one division of the limb. For clearness the engravings show

only a 10″ reading; for a 5″ reading the divisions on the limb are

to 5′ instead of 10′, and the micrometer head is divided and figured

accordingly.

[Illustration: Fig. 140.--_Stanley's micrometer reading._]

Fig. 140 shows at _C_ a portion of the theodolite circle as seen

through the micrometer microscope. _P_ is the movable pointer, _M_ the

micrometer head, and _I_ the index or reading line.

To use the micrometer the first steps are to carefully focus the

pointer _P_ by means of the eye-piece until it appears clear and

perfectly sharp, and set the reflector at the bottom of the microscope

so that it reflects sufficient light to illuminate the divisions on

the circle. Then, by turning the micrometer head _M_, set the pointer

_P_ to the centre of its travel, so that it covers the _V_ cut in the

bottom of the slide, and leave the _0_ of the micrometer head exactly

opposite the index line _I_. Now proceed in the same manner with the

other microscope. After setting the microscopes as described above,

lightly clamp the lower clamp screw of the instrument and release

the upper one. Now revolve the upper part of the theodolite until 360

degrees on the circle appears exactly under the pointer of one of the

microscopes. The other will then be pointing to 180 degrees, and the

instrument is set ready for measuring the first angle.

[Illustration: Fig. 141.]

We will presume now that a bearing has been taken by the telescope

and it is required to read the angle, and that on inspection of the

micrometer it is seen to be in the position illustrated at Fig. 141,

viz., between 227 and 228 degrees. Now as the degree is subdivided into

6 parts, each of these subdivisions must represent 10 minutes of arc,

therefore the pointer is situate between 227° 30′ and 227° 40′. It is

now necessary to measure exactly the distance of the pointer from the

division 227° 30′, which is done in the following manner, by means of

the micrometer head _M_.

[Illustration: Fig. 142.]

This micrometer head is so constructed that one complete revolution of

it causes the pointer to exactly travel over the space of one division

on the circle.

The head itself is divided into 10 primary parts, which indicate single

minutes, and these are subdivided into 6 parts of 10 seconds each,

therefore in order to measure the exact position of the pointer in Fig.

141 it is only necessary to turn the head _M_ until the pointer is

exactly over the previous division of the circle (as shown in Fig. 142)

and read the distance on the micrometer head _M_. In this case the head

has been turned through six main divisions of 1 minute = 6 minutes and

two subdivisions of 10 seconds = 20 seconds, giving a total reading of

6′ 20″, this, added to the circle reading of 227° 30′, gives 227° 36′

20″, which is the correct reading of the angle.

It will be seen that this method is very much simpler and a great deal

more accurate than any form of vernier reading, and also that its

greater accuracy permits the use of smaller instruments. Thus a 5-inch

micrometer reading theodolite is more accurate than a 6-inch one with

verniers.

Six-inch micrometer theodolites are usually divided to read to 5

seconds of arc. The method of reading is the same as described above,

but in this case the circle is divided to spaces of 5 minutes each and

the micrometer head to 5 main divisions of 1 minute, each of these

having 12 subdivisions of 5 seconds, which it is possible to again

subdivide by estimation and so measure angles to 2½ seconds.

Another feature in favour of micrometer reading instruments is the

ease with which they can be adjusted. With verniers, should they get

out of adjustment through damage, the instrument must be returned to

a maker; with micrometers, if through rough usage or accident, it is

found that after bringing the pointers to the centre of their _V_'s and

setting the micrometer heads to _0_ they are not exactly opposite one

another (180 degrees apart), then their setting has become disturbed

and must be readjusted in the following manner:--First bring the _V_

of one micrometer to the 360° on the circle, then see if the _V_ of

the opposite micrometer is exactly at 180°, if not this can be easily

set to it by means of the small adjusting screw which will be found at

the left end of the micrometer box, that is, the opposite end to the

divided head. Having examined the _V_'s and adjusted them if necessary,

the next step is to set the pointers _P_ exactly to 360° and 180°

respectively, in which position the divided heads should both read

_0_; if they do not do so reset them as follows: Take a screw-driver

and slacken the small screw which is in the centre of the divided

head; this will free the divided rim so that it can be turned without

shifting the position of the pointer. Turn the divided rims until they

read exactly _0_ at the index line and retighten the screws. This

completes the adjustment.

[Illustration: Fig. 143, 144.--_Sections of clamp and tangent in two

directions._]

346.--=Clamp and Tangent Adjustment.=--The vernier reading to the

circle, when this was adjusted by the hand, was scarcely practicable

at nearly its full value until the discovery of the _clamp and tangent

screw motion_ was made. This useful invention is due to Helvetius,

the celebrated astronomer of Danzig (about 1650). By this mechanical

arrangement the circle or arc is left quite free to move about its axis

until the clamp is screwed down, which then fixes it firmly. The fixing

arrangement of the clamp is attached to a solid part of the instrument,

but is so constructed that when it is clamped it may yet be moved

without unclamping, in relation to the fixed part of the instrument,

by the tangent screw which, as its name indicates, is placed in a

direction tangential to the circle or arc. This arrangement may take

many forms in detail, two of which, the most general and especially

adapted to surveying instruments, will be described.

[Illustration: Fig. 145.--_Elevation and part section of clamp and

tangent._]

347.--The above illustrations, Figs. 143, 144, represent a clamp and

tangent motion in two sections at right angles to each other. This form

is common to vertical circles and arcs generally, of a theodolite,

arc of sextant, circles upon some mining-dials, protractors, and many

other instruments. Fig. 145 is partly a front elevation of the same,

but with part of the clamp screw _A_ cut off. The stem of the tangent

screw is shown in section at _E_. In all the figures _L_ is the limb

of the circle or arc. This has a groove at its under side at _G_, into

which a fillet of the clamping piece _C_ is inserted to make the clamp

slide freely about the periphery of the circle when the clamping screw

_A_ is loose. A spring is sometimes inserted to open the clamp between

the sliding piece _K_ and the clamp _C_. _FF_, Figs. 143, 144 is the

tangent nut to _E_. This nut is sawn down and has a cross screw to keep

sufficient tightness to prevent loss of time, and yet to allow the

tangent screw to work pleasantly at the same time that it holds the

circle and vernier quite dead to the position to which it is adjusted

by the screw. The tangent nut _F_ has to move to the direction

horizontal to the plane of the tangent screw; therefore it has an axis

vertical to the plane of the clamp. This is shown at _K_. The axis is

held down firmly by a nut and a washer fitted with a square hole, to

prevent the nut unscrewing. The tangent screw has a collar fitting or

shank at the tangent boss _B_, which is turned down from the full-sized

metal of the screw. The fellow collar on the outer side of the boss is

formed by the shank of the milled head of the tangent screw _D_. The

hole through the milled head is made square, so that it can be adjusted

up to the boss without risk of after unscrewing by friction by the

screw _E_. This is tightened up by means of a screw-driver applied at

_E_. The boss _B_ has a vertical axis _N_, similar to the tangent nut,

and is attached to a solid part of the instrument by the washer and nut

shown at _0_.

348.--The above construction is solid and good, and will bear

considerable wear; but there is a little delicacy of touch required to

adjust the collars to the boss and to give pleasant tightness to the

screw; a better plan is to dispense with the split in the tangent nut

and the inner collar turned on the tangent screw, and place a spiral

spring over the tangent screw which follows the adjustment, or in

some cases a long bow spring may be conveniently used in place of the

spiral. These plans answer very well: one of them will be presently

described for axis clamping. In place of the groove at _G_ the clamp

is sometimes constructed to move on an arm direct from the axis of the

circle. This is on the average a pleasanter motion, but in complex

instruments it would often interfere with the motion of other necessary

parts.

349.--=Axis Clamp and Tangent.=--This is generally used to bring the

horizontal axis of an instrument to bearing, and is made independent of

the circle and vernier. The ordinary form, which is very effective when

properly constructed, is shown Fig. 146. This form is used for clamping

the vertical axis of a theodolite, mining-dial, Y-level, and some

other instruments. The clamp _C_ surrounds the axis as a collar, from

which two _lugs_ in the same casting are projected at _a_. These are

brought tight upon the outer axis socket _B_ by means of the screw _W_,

which has a _wing-nut_ head to give good purchase. In the construction

of this form of clamp the collar should be fitted and ground to its

bearings with the lug in the solid, and the cut at _a_ be sawn through

afterwards.

[Illustration: Fig. 146.--_Clamp and tangent to a vertical axis._]

350.--The tangent screw adjustment is shown at _T_, moved by the milled

head _M_, the boss _E_ being fixed to the instrument. This part of the

arrangement is just the same as that described above for a vernier

tangent. Objection has sometimes been made to this form of clamp, that

it tends to become weak after a time from the constant clamping and

releasing, which causes loss of elasticity in the metal. When this

occurs it is no doubt due to the metal of the clamp not being good

gun-metal; or, if brass, not thoroughly pressed or hammered before the

piece is made up. A plan, in not uncommon use in Germany, of avoiding

this supposed source of weakness is to bring up a _tumbling piece_

direct on the axis by a screw. This is shown in Fig 147, screw _W_;

tumbling piece _A_. This produces a direct clamp upon the axis socket

_B′_. The clamp ring _CC′_ is made loose on its socket.

351.--In practice it is found impossible to clamp the axis of a

theodolite without disturbing the centre more or less. In some

experiments the author made he found the direct or tumbling piece clamp

Fig. 147, although it holds firmly, disturbs the centre much more than

the clasping clamp Fig. 146. Therefore when the former is used the

clamp should be upon a strong flange. This increases weight, and it can

scarcely be so well for a portable instrument. In all cases, in the

construction of the instrument, clamps should be fitted and screwed

down before the centre is ground and finished. This ensures the centre

being made correct in its clamped position, in which it will afterwards

be used.

[Illustration: Fig. 147.--_Clamp and tangent to vertical axis, German

plan--Hunäus._]

The arrangement Fig. 147 shows also a spring S falling upon a stud

at _E_, fixed upon a part of the instrument upon which it acts as a

fulcrum. The spring should be of hard rolled German silver. In this

case the tangent screw needs no split or other adjustment to make it

tight, as all loss of time is taken up by the spring.[14] The plan is

found practically to answer fairly; but unless this is very carefully

made there is a want of solidity in the movement which a well-fitted,

direct-acting tangent screw possesses.

352.--The French generally in all their superior instruments clamp upon

a flange carried out from the lower rim of the socket, with the screw

placed longitudinally to the axis. When this plan is very carefully

carried out, so that the clamping has neither tendency to raise or

lower the socket-piece, it is no doubt very good. In large instruments,

where weight is no object and the flange may be made large, it is

certainly the best plan. In such cases the clamp may be released as

a free fitting to prevent the possibility of strain. Fig. 148 shows

the French plan attached to a tribrach: _S_ socket, _F_ flange, _C_

clamping screw, _T_ tangent screw. The tangent in this arrangement acts

against a spiral spring contained in a tube _A_, which gives a very

steady motion to the instrument.

[Illustration: Fig. 148.--_French axis clamp and tangent._]

353.--Some particulars of the care required in the manufacture of the

tangent screw were given, art. 22. The test for the equality of this

screw, which is important when it moves a vernier, is to loosen its

clamp and to see whether it works equally, firmly, and smoothly at

all parts when it is turned down from end to end. The test for its

straightness is to screw down the clamp, then to notice any little

mark on the milled head of the tangent screw, or make a slight mark

upon it, and to place this mark uppermost, and then to take a reading

with the vernier, then to turn the milled head a quarter turn and take

another reading, and again another quarter, and so on consecutively.

By comparing the rates of reading of the vernier at the quarter turns,

if we find these equal the screw is straight. A little allowance is

necessary for imperfect work. If the work is very bad at some quarter

turns there will be an advance at the opposite quarter of nearly double

the proper mean quantity.

354.--=For Testing and Adjusting the Fitting of the Tangent

Screw.=--The clamp should be tightened down and the ball _B_, Fig. 144,

held tightly between the thumb and forefinger; then, by using a gentle

reciprocating motion in the direction of the tangent just sufficient

to move the circle, if there is any looseness in the screw or the ball

fitting _B_ it will be felt as a jar, or technically, a slight _loss

of time_. If this be in the ball _B_ it can be taken up by the screw

_E_ at its end. If it be in the screw it can be taken up by the cross

clamp screw. If it be in neither of these, it may be in one or both

of the axes _N_ and _K_. In this last case it will need refitting. It

appears a somewhat simpler test with a theodolite to lightly press

the telescope on one side of the eye-piece and take a reading of the

vernier, and then to press the other side and again take a reading.

This, possibly, indicates loss of time in the clamp and tangent if

there is found any difference in these readings; but this would not

be with any certainty, as the fault might be in some other part of

the instrument. It, nevertheless, is a simple plan to test the whole

instrument, including the clamp and tangent, although this does not

localise any defect there may be in any special part of it.

355.--=Use and Wear of the Clamp.=--The common fault of a novice when

he commences to use an instrument is that he applies too much violence

to all clamping parts. Thus we find the lower parallel plate of an

instrument soon becomes deeply indented, and the clamp of the tangent

screw often strained, or its screw worn loose by extreme clamping.

The best rule to avoid this with a clamp is to make a personal test

of how little force is required to produce sufficient hold for the

action of the tangent screw, and when this is found out to try to clamp

_only slightly in excess of this_. A novice scarcely recognises the

power of a screw. It is, perhaps, a fault of some makers of giving

much too large heads to clamp screws which to a certain extent permits

this overstraining from clamping. In discussing this matter with a

scientific civil engineer upon an instrument which had been very

much strained, to which small clamping screw heads were suggested,

this gentleman replied that he looked to the optician to "supply

instruments, not _brains_," and made the user responsible; but, really,

a young surveyor is generally so intent on the object of his work that

he cannot consider the mechanical details of his instrument, to which

his attention possibly has never been properly directed; so that there

is a policy in cutting off possibility of injury to the instrument

where this can be conveniently done.

356.--_Use and Wear of the Tangent Screw._--Seeing that the axis of

an instrument is quite free to the extent of the loss of time on the

tangent screw which holds it, and that this freedom, by any slight

touch of the telescope, may cause a difference of reading--in some

cases of several minutes of arc--it becomes important to observe that

the tangent screw is in good order. This matter considered at its full

value, we may wonder, perhaps, what kind of work may have been done

with the tangent screw loose and worn down in its central part, as we

find it in many old instruments sent for repair. A great amount of the

common defects we find in worn tangent screws might have been prevented

by using certain precautions; and even the much-worn tangent screws

would sometimes go on fairly by a different method of use from that to

which they have evidently been submitted. The wear of a tangent screw

is due principally to the fact that this screw is necessarily oiled

to make it work freely, and that the oiled part being exposed to dust,

this dust attaches itself and works into the thread with the oil so as

to cut both the screw and the nut. Precaution is necessary that this

should be obviated as far as possible. One precaution may be taken,

that when the screw is oiled, say once in three months, the parts

outside the nut should be cleaned off quite dry with a few strands of

thread. The oil left in the nut, if the screw has been turned through

it, will be quite sufficient to lubricate the screw. Another better

precaution is to use only one part of the screw for a period, say one

month. The screw may be divided mentally into three parts--_near part,

middle part_, and _end part_. If one part only be used for a period,

and the vernier be set in using the instrument so that not more than

about 1° of motion is required of the screw, no grit can be carried far

into the centre of the nut; and if the precaution of cleaning the screw

with thread be taken every time the instrument is returned to its case

after a day's work, the screw being left at about the same place on the

screw and nut, it will keep true with little wear. When another part

of the screw is taken into use, this part should be first cleaned with

thread and then oiled with watch oil, after which the former position

of the nut should be cleaned quite dry with thread. Treated in this

manner a tangent screw will last, in constant wear, for ten years or

so, keeping in fairly good order. Where a spring is used to take up

loss of time there is less risk, and the only precaution necessary is

to be sure the spring continues to act properly. There is generally,

however, a little more wear with a spring than with a free thread.

357.--If the instrument be not touched after the tangent is set, and

there is no wind to cause vibration, the instrument will read correctly

although the tangent may be out of order. But after the adjustment

by the tangent screw, which may cause a disturbance, it is always

necessary to set the microscope to the vernier. This is one important

reason why the microscope should move as softly as possible, and that

it is advisable to centre it upon the axis. Where any doubt of the

quality of the tangent exists, the telescope should be reobserved for

verification of its position after reading, which is also undoubtedly

the safest in all cases.

358.--Some contrivances have been applied to tangent screws to prevent

wear from dust, and also to take up the nut after wear. A very good

plan, common in American instruments, is to insert the end part of

the screw beyond the nut in a closed tube. This entirely prevents

dust from resting on this part; and if the precaution be taken to

clean the exposed part of the screw after use it is very effective

for preservation. This plan the author has combined with a spring

arrangement, which appears to render it very safe from loss of time

and much wear. This arrangement is, however, a little expensive to

make, therefore can only be applied to high-class instruments. Fig.

149, _C_ nut, through which tangent screw passes; _B_ tangent boss, A

milled-head, _H_ covering tube to the point of the screw, _GG′_ _EE′_

pair of telescopic tubes which cover the screw. A German silver or

platinum spring works inside these tubes, keeping a constant separating

pressure between _C_ and _B_ to take up any loss of time in the screw.

[Illustration: Fig. 149.--_Protected tangent screw with helical

spring._]

359--=Free Tangent Screw.=--There is always a risk of a tangent screw

of any fixed kind producing a certain amount of strain upon the

instrument, therefore, where practicable, it should be made free. The

illustration, Fig. 150, shows the form of free tangent the author now

applies to many instruments. The centre stud is clamped to the lower

part of the instrument by the screw shown in dotted lines. To the left

hand a piston containing a spiral spring carries a pressing-rod against

which the screw to the right hand works.

[Illustration: Fig. 150.--_Free tangent adjustment._]

360.--=Loss of Time by Wear= of the nut is variously taken up when no

spring is used. One plan was shown of splitting it up. A plan common in

Germany is to make the nut in two pieces, which are brought up by two

screws. This is a very effective plan. The author has found a tumbling

piece arrangement also effective. Fig. 151, _S_ section of tangent

screw, _T_ tumbling piece moved by the adjusting screw, shown above,

for wear of the tangent screw. This adjusting screw _A_ should be

tapped tight without oil, and put together dry to prevent its receding

by pressure.

[Illustration: Fig. 151.--_Tumbling piece adjustment for wear of

tangent screw._]

361.--=Hypotenuse and Base.=--Other trigonometrical values besides

the division of the circle into equal parts are occasionally placed

on instruments for special purposes. The most common of these is the

scale of difference of hypotenuse and base, which is generally placed

upon the back of the vertical arc of a theodolite and upon some dials

and clinometers. The division for this purpose is generally done by

hand. The scale gives a percentage difference for certain angles. Thus

when used with chain measurement, it gives the number of links of the

chain to be deducted per chain of 100 links for the inclination of land

that the theodolite or other instrument indicates in following the

surface contour.

362.--=A Horizontal Scale of Tangents= was placed upon the surveying

theodolites by Ramsden. This was divided upon a scale carried by the

vernier plate, which read to the zero line (0°) of the limb. It is

found in practice more accurate to take the tangent to any curve from a

scale of tangents, as, for instance, that in Molesworth's pocket-book,

and set this off upon the limb by means of the vernier.

363.--=Gradient Scale.=--Civil engineers engaged on railway work

occasionally have a scale of gradients upon the back of the vertical

arc 1 to 100, 150, 200, etc. These are better read from the circle with

vernier from a table of gradient arcs.

FOOTNOTES:

[14] The illustration is taken from _Die geometrischen Instrumente_,

Dr. G. Chr. K. Hunäus. Hanover, 1864.

CHAPTER VII.

THEODOLITES--CONSTRUCTIVE DETAILS OF 5-INCH AND 6-INCH TRANSITS--

SPECIAL ADDITIONAL PARTS--PLUMMETS WITH SCREW ADJUSTMENTS OF

IMPROVED FORM--STRIDING LEVEL--LAMP--ADJUSTMENT OF AXIS OVER A

POINT--SOLAR ATTACHMENT--PHOTOGRAPHIC ATTACHMENT.

364.--=The Theodolite= is the most perfect instrument for measuring

both horizontal and vertical angles by the aid of a telescope and

graduated circles. For the purpose of surveying, the theodolite is

mostly employed to take a system of triangles upon the horizontal plane

of the surface of the land, and of objects at any position in which

they may be placed. When altitude angles are taken separately these

are generally applied to give corrections to chain or other actual

measurements upon the surface by calculation of the difference of

hypotenuse and base.

365.--The theodolite in all its essential features, as differentiated

from sighted compasses for taking angles, mentioned by Digges,[15] was

the invention of Jonathan Sisson, a celebrated mathematical instrument

maker of the beginning of the 18th century.[16] Great improvements

were afterwards made in this instrument by Ramsden, who brought it up

nearly to its modern efficiency by the introduction of the transit

principle.[17] Later improvements in portable instruments consist

in the application of the _transit_ principle to the telescope,

which was formerly applied to astronomical and the larger geodetic

instruments only. Other improvements have been made more recently in

constructive details.

366.--Theodolites were commonly made of two distinct types, which

were originally distinguished as _plain_ theodolites and _transit_

theodolites. In the plain theodolite the telescope moves through an

arc of about 45° upwards or downwards from the horizontal plane, but

very few of these are now made compared with the number of transit

theodolites in which the telescope may take a complete revolution upon

its horizontal axis, so that a back and fore sight may be taken by a

half revolution. This difference of construction entails a difference

in the manner of mounting the telescope to correct its adjustments. In

the transit the accuracy of centring and reading is easily discovered

by taking a back and fore sight at a distance as equivalent to an arc

of 180°, which may be read on any part of the limb by transitting the

telescope, wherein the correspondence of this arc to the reading of

the limb to right and left hands will detect error. With the plain

theodolite the equivalent method of examination is effected by placing

the telescope in Y's, as previously discussed for the Y-level, and

turning it end for end on its bearings, a process liable to disturb

the direction of the telescope unless special care be taken. In the

following description of the details of construction of a theodolite it

will be convenient to take the transit form of instrument, as this is

more comprehensive, the original pattern being selected, as this may

be constructed with the limited amount of tools generally found in a

surveying instrument workshop.

[Illustration: Fig. 152.--_5-inch transit theodolite (old form)._]

367.--The size of a theodolite is fixed technically by the diameter of

the line of division upon the horizontal circle. A 5-inch or 6-inch

theodolite is the largest size that may be carried comfortably in a

single case; and no great advantage is gained by having an instrument

beyond this size if the work is that of the ordinary surveyor on town

and county surveys. The verniers of 4- and 5-inch instruments read

sharply to single minutes of arc, which is as nearly as can be plotted

with any degree of certainty with an ordinary protractor reading

by vernier also to minutes only; 6-inch instruments read to 30 but

generally to 20 seconds. Occasionally 4-inch theodolites are selected

for lightness at a sacrifice of capability and of distinct and exact

reading. The following table gives the average weight of the transit

theodolite illustrated on the last page:--

Instrument. Case. Overcase. Tripod.

4-inch Transit. 11 lbs. 8 lbs. 4 lbs. 8 lbs.

5-inch " 13½ " 9 " 5 " 9 "

6-inch " 19 " 10 " 6 " 11 "

8-inch " 36 " 20 " 10 " 18 "

If with lamp extra about ¾ lb. If with striding level extra

about ¾ lb.

It will be seen that the 5-inch instrument of this class with cases

and tripod, say altogether 36 lbs., is really of quite as much weight

as a fairly strong man can carry through a hard day's work. The 5-inch

instrument is therefore becoming more and more popular with practical

civil engineers, and its performance, if of good modern work, is quite

equal to the 6-inch of less than half a century ago.

368.--By giving a description in detail of a transit theodolite, the

general principles of a great number of other instruments, particularly

those of larger dimensions, will be included, except for certain

details that the specialities of the particular instruments demand.

The most convenient plan to follow in this description will be to take

the structure of a 6-inch transit theodolite of common construction,

as it is built up from its base, piece by piece, according to the rule

of ordinary structure; where more modern theodolites vary mostly from

this is in having many parts shaped out of the solid, which are screwed

together in the form illustrated.

369.--_The Tripod Stand_ of a theodolite of 6 inches and under is

generally made identical with that of a level, a common form being that

described for a dumpy, art. 216. The arrangement of one turn-up leg,

as shown Fig. 63, is very advantageous for the theodolite if it is to

be used on mountainous or even very hilly ground. For instruments

exceeding 6 inches a framed stand, which will be described further on,

is better. Some makers use a framed stand for a 6-inch instrument. The

rigidity of the stand ought to be quite equal to that of the work in

the theodolite, or a little in excess, and when this is attained it is

sufficient. Where the stands of theodolites so often fail is from the

defective construction of the tripod head, not at all from deficiency

of timber in the tripod itself; and overloading this, in adding weight

without attention to scientific construction, is worse than useless.

370.--In the following description of the transit theodolite the

parallel plate setting-up arrangement is taken, as this is at the

present time (1914) still in use in this country and in America. There

is nevertheless great probability that it will not long continue

to be so, as year by year the tribrach system, described art. 233,

for levels is coming more forward, both for levels and theodolites.

This tribrach system the author holds to be much more scientific,

and when thoroughly understood, more simple and expeditious to work

with. It is also to be recommended, as there is no possible risk of

strain upon the general work of the instrument, nor risk of error

from distortion of the vertical axis from strain in setting it up to

adjustment. A constructive drawing of a common transit theodolite with

parallel plates is shown Fig. 153, of which the following is a detailed

description.

[Illustration: Fig. 153.--_6-inch transit theodolite--back view, with

sections._]

371.--_The Lower Parallel Plate N._--This has a large boss-piece taken

up from its central part, which forms a dome of a hollow globular

section, technically termed the _socket_, shown at _X_. In the interior

of the lower part _N_ a coarse female screw is cut, of about fourteen

threads to the inch, which is used to attach the instrument to its

tripod.

372.--_The Upper Parallel Plate_ is constructed as a flange from a

solid _boss L_. This piece is generally made in gun-metal of a form

as solid as possible, to resist the straining action of the parallel

plate screws. The boss is prolonged downwards by a _stem-piece_, upon

the lowest part of which a _ball collar_ of globular section is firmly

screwed. The screw is turned by means of two opposite holes, into which

a powerful forked screw-driver is inserted, until it is jambed up too

tightly against its shoulder to ever become loose by the ordinary use

of the instrument. The ball collar fits into the socket carried up

from the lower parallel plate. The whole of this globular arrangement

is termed the _ball and socket_. The boss _L_ of the upper parallel

plate, with its stem, has a hollow conical hole through its axis, into

which the _body-piece_, to be described, fits accurately. Upon its

outer upper part an inset collar is formed which acts as a guide to the

clamp _K_. At the outer edge of the parallel plate _M′_ four vertical,

conical holes are made, which take _socket-pieces_, which are tapped as

_nuts_ to the parallel plate screws _M_. These socket-pieces are jambed

into their holes tight home to their shoulders. The socket-pieces are

made separate, both to give a greater length of female screws than the

thickness of the plates, and that they may be easily restored at any

time if worn loose in the threads by the action of the plate screws.

373.--_The Parallel Plate Screws._--One in elevation is shown at _M_,

with its point dotted, and one in section at _M′_. The four parallel

plate screws are in opposite pairs, placed exactly at right angles

to each other in a line passing through the vertical axis of the

instrument. These are made of gun-metal about 3/8 inch in diameter,

with a deep thread of about thirty-two to the inch. They require

cutting on a nice steady screw-cutting lathe. The lower points of the

screws are slightly domed, sufficiently only for the amount of rocking

they have to take, so as to impress the lower parallel plate as little

as possible. The milled heads _M_ are placed between the parallel

plates, not above, as previously described for levels. There being

a constant strain upon these screws in use and by intrusion of grit

from flying dust they soon become worn. After wear the threads may

be recut deeper, and new socket-pieces fitted to the upper parallel

plate. To prevent wear the upper parts of these screws are sometimes

encased in tubes--a plan very generally adopted in America. At the

foot of one of the parallel plate screws a _stay-piece_ is fixed to

the lower parallel plate, which forms a kind of ring round the screw.

This prevents the parallel plates from shifting upon the axis at the

ball and socket. The parallel plate screws should be without any shake

or what is technically termed _loss of time_. They should move firmly

but softly. They should _support_ the instrument against the ball and

socket upon which the whole rocks to position by their aid, but not be

screwed down too tightly, as this has a tendency to disturb the axis

of the instrument however solidly it may be made. Makers often have

instruments in their hands for repairs in which the parallel plate

screws have been deeply indented into the lower parallel plate, with

the centre of the instrument permanently strained more or less.

374.--_The Body-piece._--The only outward part seen in elevation of

this is shown at _T_: it is shown in section _T′_. This piece carries

the _limb_ of the instrument _SS′_ by a centred collar to which it is

attached by screws. About the centre of the body-piece an inset collar

is formed to take the clamp _KK_ which bites upon it. The lower outer

part of the body-piece forms a conical fitting in the boss of the

upper parallel plate _L_. The interior is a hollow conical axis. The

body-piece is generally made of hard gun-metal. The greatest possible

care is required in its manufacture, art. 21. The interior and exterior

should be perfectly concentric at every part. Much of the value of the

instrument depends upon the perfection of the work in this piece.

375.--_Axis Collar Clamp K_ has been already described, art. 349, and

is illustrated in Fig. 146, which is taken from a theodolite, so that

only specialities in relation to the instrument Fig. 153 need be noted.

This clamp surrounds the body-piece and clamps it by means of the screw

_K_ shown on the left hand. The clamp is connected with the upper

parallel plate through the _tangent screw_, the head of which is shown

at _P_, so that when the screw _K_ is tightened the parts _L_ and _T_

are fixed together, except that a slow motion can be given to these

parts by the tangent screw _P_. By this clamp and tangent arrangement

the whole of the upper part of the instrument is rendered free to

revolve, to bring the instrument to bearing when the clamp is loosened,

the final adjustment being secured after clamping by the tangent screw.

It is this part of the instrument which is used after setting it up

to bring the magnetic needle true to magnetic north, or otherwise to

direct the telescope to any established distant mark, object, or star

that may be fixed for the zero or other index point of the horizontal

circle, to which all readings from its position are referred.

376.--_The Central Vertical Axis_ is shown only in half section at

_Z_. This is made uniformly of bell-metal, in the form of a truncated

cone, extending from the horizontal circle plate S to the interior

of the socket _N_. Its fitting surfaces are at the two ends of the

cone, extending about half an inch, the central part being chambered

back. At the upper part a _pin-piece_ centres the _vernier plate_, to

which it is attached by a wide collar with three or four screws. A

square shoulder rests with weight only just sufficient to support the

instrument upon the body-piece. This part has to be so adjusted that

the axis perfectly fits and yet moves freely. A square-hole collar

and screw are fixed on the lower end of the axis, just to touch the

socket of the body-piece, so as to secure the axis in its position when

the instrument is lifted. An eye or a hook is fixed into the screw

at the lower end to take the cord of the plummet used for fixing the

instrument over a definite point on the ground. This is not shown in

the engraving.

377.--The axis of an ordinary theodolite is made the weakest part. It

is generally considered in the trade right for it to be so, as in case

of accident no other part of the vertical axis system is likely to be

deranged; and this is the easiest part to replace, being, as it were,

independent of other fittings. Whether this should be taken _cum grano

salis_ is a question; at any rate with the axis weak it is not policy

to load the upper part of the instrument with metal--which in places

at least, is generally made ten times as strong as the axis--when the

instrument has to be carried about by a person over his shoulder. Some

suggestions will be made on this point hereafter.

378.--_The Horizontal or Lower Plate or Limb._--Sometimes the whole

of the piece _SS′_ is termed the _limb_, but more generally this word

is applied to the divided part only. This plate is of brass, and is

attached to the body-piece by screws. The outer rim, which is somewhat

triangular section, is undercut upon the inner side of its lower

surface to support the _clamp-piece_, the outer edge being turned to a

fillet to take the clamp which is rebated to fit it. The upper surface

of the rim, or the limb proper, is turned to the frustum of a cone of

about 45°. This part is covered with silver, which is beaten out to the

conical form and soldered down upon it, and afterwards turned to true

form. The dividing has been discussed in the last chapter.

The 6-inch instrument is generally divided to 20′, but sometimes to

30′, and the vernier reads to 20″ or 30″. The figuring is from 0 to

360, right to left, taken facing the instrument.

379.--_The Vernier Plate_ is shown in section under _P′_. The vernier

from which it is named is shown at _VV′_, Fig. 155. The vernier plate

is carried from the central axis and forms the foundation for all the

superstructure. The upper and lower plates are left very free where

they are brought together, the verniers being generally sprung down

just to gently touch the limb. The vernier surface is let down some

distance into its plate for protection. The reading of the vernier has

been discussed in the last chapter.

380.--It may be particularly noted, as already stated, that the

central axis and the body-piece are attached to the vernier and

horizontal plates by _screws_. This plan might strike one as being

unsound: it is not really so, the reason for this construction being

that these axes are, or should be, of bell-metal, and that this metal

being very hard and brittle it would not be so easily worked, or so

serviceable as brass for the limb and vernier plate, neither would

there be means of correcting errors which generally occur both in the

workmanship and in the dividing of this delicate part. The adjustment

for fixing the limb and vernier plate, technically called _centring_,

in particular requires considerable technical skill. It is generally

performed by the divider, who is a specially intelligent artisan. In

the author's improved theodolite, to be described further on, the axis

is in one casting with the standard; but in this case the construction

is different, the axis being made larger and the whole body being in a

special gun-metal which approaches bell-metal in hardness.

381.--The vernier plate carries the ball nut of the tangent screw,

shown at Fig. 153_J_. The general arrangement may be seen by the

section, but is more fully described art. 347. One thing is important

in this screw, viz., that it should range without strain quite parallel

with the plates, so as not to give the slightest tendency to elevate or

depress the edge upon which it is placed during motion in any part of

its thread. The clamp is sometimes placed between the plates.

Surveying and Levelling Instruments, Theoretically and Practically Described. For construction, qualities, selection, preservation, adjustments, and uses; with other apparatus and appliances used by civil engineers and surveyors in the field. · 第 21 / 26 章

LEVELLING STAVES--CONSTRUCTION--VARIOUS READINGS DISCUSSED--