office of Treasurer, Major Kater was elected in his place.
The following council was elected, to continue in office until St.
Andrew’s day, 1828.
Davies Gilbert, Esq.
Major Kater.
Dr. Roget, M.D.
Captain Sabine, R.A.
Dr. Wollaston, M.D.
Dr. Fitton, M.D.
Dr. Young, M.D.
Dr. Paris, M.D.
Dr. Prout, M.D.
Dr. Goodenough, D.D.
Dr. Buckland, D.D.
J. W. Croker, Esq.
Lord Colchester.
Sir E. Home, Bart.
Sir H. Davy, Bart.
John Pond, Esq.
Capt. F. Beaufort, R.N.
Francis Baily, Esq.
John Guillemard, Esq.
[p425]
In consequence of having been elected President _pro tempore_ by the
council, (the chair having been vacated some weeks previous to the
general election,) the duties of the office were performed by Mr.
Gilbert, on occasion of the present anniversary. After having read
over the list of members admitted, and of those deceased during the
last year, he proceeded to announce the disposal of the Royal and
Copley Medals, as awarded by the votes of the council.
Of the Royal Medals, one was awarded to Sir H. Davy, and the other to
Professor Struve. Of the Copley Medals, one was given to Dr. Prout,
and another to Lieutenant Forster. On this occasion Mr. Gilbert
pronounced an eulogium upon the respective receivers of the medals;
and, in adverting to the labours of the several individuals, he
justified the decision of the council, in bestowing upon them these
marks of distinction, in a learned and eloquent discourse.
_Proceedings of the Horticultural Society_.
_September_ 4th.
A paper by Mr. Lindley was read upon the new hardy plants which had
flowered in the Society’s garden; among them a number of new shrubs
were mentioned, which appeared likely to prove acquisitions to the
public. A thermometer was exhibited by Mr. Bregazzi, of Derby,
for ascertaining the temperature of bark-beds. It consisted of a
thermometer enclosed in a shaft of copper with a wooden handle, and
a door in its side, by which the temperature can be ascertained with
precision. It is needless to point out the superiority of this plan,
over the common mode of determining this very essential point, by
feeling of a stick previously stuck in the bed; the sensation of heat
when the stick is grasped in the hand will obviously depend in a
great degree upon the temperature of the hand itself. As usual, there
was an extensive display of all the choicest flowers and fruit of the
season. One hundred and seventy-two subjects of this description were
placed upon the table. Among the flowers, the most remarkable was
a new hardy climber from Mexico, with deep purple blossoms studded
[p426] with glittering green glands, called Maurandya Barclaiana;
among the fruit was a fine specimen, from Lord Grantham’s garden, of
the Papaw, a tropical fruit never ripened in England before.
_September_ 18th.
The exhibitions of this day were chiefly confined to a display of
Dahlias, which for magnificence exceeded any thing of the kind we
ever witnessed before. The large meeting-room was filled with masses
of the richest and most lively colours. In the whole, eight hundred
and fifty-one varieties were shown, among which the finest were from
the garden of William Wells, Esq., of Redleaf; but where all are so
excellent, it is almost invidious to particularize. The time will
be remembered by many of our readers when gardens in the autumn
contained little besides marigolds, sun-flowers, and sweet-peas; by
the aid of dahlias and chrysanthemums the autumn has now become the
liveliest season of the year, and the beauty of the flower-garden
is only destroyed by the severest of the winter frosts. Among the
grapes upon the table was a remarkably excellent yellow-berried kind,
from Portugal, from the garden of Mr. Holford, of Hampstead, which
was quite new to this country. Apples, nectarines, peaches, and
pine-apples abounded.
_October_ 2nd.
Among the flowers was a fine bunch of ranunculuses, from Mr. Groom,
of Walworth, a rare sight in October; they were obtained by having
been planted in July and carefully protected by tulip-shades when
coming into flower. The season for softer fruits being nearly over,
pears and apples formed the chief display; of these a vast number,
upwards of one hundred and eighty of the latter, were upon the
table: the Blenheim orange, or Woodstock pippin, pomme gris, scarlet
nonpareil, courtpendu plat, golden reinette, and packhorse apples;
and Chapman’s, Marie Louise, and brown beurré pears, appeared to
us to excel all their rivals. The famous gloux morceau and beurré
d’Aremberg pears were also exhibited, but were not ripe. [p427]
_October_ 16th.
The first number of a new periodical work, called the _Pomological
Magazine_, consisting of coloured figures of the fruits cultivated
in Great Britain, was placed upon the table. Among the apples were
specimens of a variety sent from England to Connecticut, in the year
1636, and reimported from America within a few years. It proved to
be a kind not known at the present day in this country, but still
cultivated in France. In the gardening books of the sixteenth and
seventeenth centuries it is mentioned under the name of the haute
bonté. The specimens exhibited served to disprove the opinion that
many of the American apples are European kinds altered by climate;
these, although the produce of trees which have been growing in
America for nearly two hundred years, differed in no respect from
French samples exhibited at a subsequent meeting of the Society.
_November_ 6th.
An excellent paper was read upon the method of cultivating horse
radish, in Denmark. The roots are cut into slips, and planted
_horizontally_, the lower end inclining a little upwards, and the
crown of the plant hanging over the alleys, by which the beds are
separated. From time to time the roots are uncovered, and all the
_lateral_ fibres are carefully removed, by which the size and length
of the roots are much increased. The place hitherto occupied by
dahlias, was now taken by Chinese chrysanthemums, of which a large
number, consisting of twenty-two different varieties, was exhibited
at the bottom of the room.
_November_ 20th.
Cuttings of the fine new Portugal grape, of which fruit was exhibited
on the 18th of September, were distributed to the members present.
A few dahlia flowers still showed themselves, notwithstanding the
unusual severity of some early frosts, and the room was crowded with
chrysanthemums. The gloux morceau and beurré d’Aremberg pears were
tasted, and found to retain the station which has been assigned to
them at the head of all known varieties. [p428]
ASTRONOMICAL AND NAUTICAL
COLLECTIONS. For Jan. 1828.
i. EPHEMERIS _of the periodical_ COMET _for its Return in 1828,
computed with the consideration of a_ RESISTING MEDIUM. _By_
Professor ENCKE.
_Elements_.
Mean anomaly 1829 Jan.9.72, mean time at Paris, = 0° 0′ 2″.83
Mean daily sidereal motion = 1069″.87572.
° ′ ″
Longitude of the perihelion = 157 17 26.2} Mean Equinox
Ascending node = 334 28 47.1} 1829 Jan.9.72.
Inclination = 13 20 47.9
Angle of the eccentricity = 57 38 25.2
_Ephemeris_.
Mean Parisian time, 1829. A. R. Decl. N. Log. Dist.
° ′ ″ ° ′ ″ ☉ ⊖
Aug. 23.3 26 50+.. 22 42+.. .34603 .19571
24.3 50... 52 .34411 .18983
25.3 49... 23 1 .34217 .18390
26.3 48... 10 .34022 .17791
27.3 46... 19 .33825 .17187
28.3 44 29 .33626 .16577
29.3 41 38 .33425 .15962
30.3 37 47 .33222 .15341
31.3 33 56 .33017 .14714
Sept. 1.3 28 24 6 .32810 .14082
2.3 22 15 .32602 .13444
3.3 16 24 .32392 .12801
4.3 9 34 .32180 .12153
5.3 1 43 .31966 .11499
6.3 25 53 52 .31749 .10839
7.3 44 25 2 .31531 .10174
8.3 34 11 .31310 .09504
9.3 23 20 .31087 .08829
10.3 11 29 .30862 .08148
11.3 24 58 38 .30635 .07462
12.3 45 47 .30406 .06771
13.3 30 56 .30174 .06075
14.3 15 26 5 .29940 .05375
15.3 23 58 14 .29704 .04670
16.3 41 23 .29465 .03961
Sept. 17.3 23 22+.. 26 32+.. .29224 .03247
18.3 2 41 .28980 .02529
19.3 22 41 49 .28733 .01806
20.3 19 58 .28484 .01080
21.3 21 56 27 6 .28232 .00350
22.3 32 14 .27978 .99617
23.3 6 22 .27721 .98881
24.3 20 39 30 .27461 .98142
25.3 10 37 .27198 .97400
26.3 19 40 45 .26933 .96656
27.3 9 52 .26665 .95910
28.3 18 37 58 .26393 .95162
29.3 3 28 5 .26118 .94413
30.3 17 27 11 .25840 .93663
October 1.3 16 50 17 .25559 .92913
2.3 16 11 22 .25275 .92164
3.3 15 31 27 .24987 .91415
4.3 14 49 32 .24696 .90668
5.3 5 36 .24402 .89923
6.3 13 20 39 .24104 .89181
7.3 12 34 42 .23803 .88442
8.3 11 45 44 .23498 .87707
9.3 10 55 46 .23189 .86976
10.3 4 47 .22876 .86251
11.3 9 10 47 .22559 .85532
12.3 8 15 46 .22238 .84820
13.3 7 19 45 .21913 .84116
14.3 6 21 43 .21584 .83421
15.3 5 21 39 .21251 .82735
16.3 4 20 35 .20913 .82059
17.3 3 18 30 .20570 .81394
18.3 2 14 24 .20223 .80741
19.3 1 9 17 .19871 .80101
20.3 0 3 9 .19515 .79474
21.3 358 56 0 .19154 .78861
22.3 357 47 27 49 .18787 .78263
23.3 356 38 38 .18415 .77681
24.3 355 28 25 .18038 .77116
25.3 354 17 11 .17656 .76568
26.3 353 5 26 56 .17268 .76037
27.3 351 53 40 .16874 .75525
28.3 350 40 22 .16475 .75031
29.3 349 27 4 .16069 .74557
30.3 348 14 25 44 .15657 .74102
31.3 347 1 23 .15239 .73668
Nov. 1.3 345 47 1 .14814 .73253
2.3 344 34 24 38 .14382 .72858
3.3 343 21+.. 24 14+.. .13943 .72483
4.3 342 9 23 49 .13497 .72128
5.3 340 56 23 .13044 .71793
6.3 339 44 22 56 .12583 .71477
7.3 338 33 29 .12114 .71180
8.3 337 23 0 .11638 .70902
9.3 336 13 21 31 .11153 .70642
10.3 335 4 1 .10660 .70399
11.3 333 56 20 31 .10158 .70172
12.3 332 48 0 .09647 .69961
13.3 331 41 19 29 .09126 .69765
14.3 330 36 18 57 .08595 .69583
15.3 329 31 25 .08055 .69415
16.3 328 27 17 52 .07505 .69258
17.3 327 23 19 .06944 .69113
18.3 326 21 16 46 .06372 .68979
19.3 325 19 12 .05788 .68854
20.3 324 18 15 39 .05193 .68738
21.3 323 18 5 .04585 .68630
22.3 322 19 14 31 .03965 .68529
23.3 321 20 13 56 .03331 .68434
24.3 320 21 22 .02684 .68345
25.3 319 23 12 47 .02022 .68261
26.3 318 26 12 .01346 .68182
27.3 317 28 11 37 .00655 .68106
28.3 316 31 2 .99948 .68034
29.3 315 34 10 26 .99225 .67964
30.3 314 37 9 50 .99484 .67897
December 1.3 313 40 9 14 N. .97726 .67833
2.3 312 43 8 37 .96949 .67772
3.3 311 45 8 0 .96153 .67713
4.3 310 48 7 23 .95336 .67657
5.3 309 49 6 45 .94499 .67605
6.3 308 50 6 6 .93640 67556
7.3 307 50 5 27 .92759 .67513
8.3 306 49 4 47 .91854 .67476
9.3 305 47 4 6 .90924 .67446
10.3 304 44 3 24 .89969 .67425
11.3 303 40 2 42 .88987 .67415
12.3 302 34 1 58 .87978 .67418
13.3 301 27 1 13 .86939 .67437
14.3 300 18 0 27 N. .85870 .67475
15.3 299 7 0 19 S. .84770 .67536
16.3 297 54 1 8 .83638 .67623
17.3 296 40 1 58 .82474 .67742
18.3 295 23 2 49 .81276 .67896
19.3 294 5 3 42 .80042 .68091
Dec. 20.3 292 45+.. 4 36+.. .78771 .68333
21.3 291 23 5 32 .77465 .68627
22.3 289 59 6 29 .76123 .68980
23.3 288 34 7 27 .74746 .69399
24.3 287 8 8 27 .73334 .69889
25.3 285 42 9 27 .71890 .70456
26.3 284 15 10 28 .70416 .71107
27.3 282 48 11 30 .68917 .71845
28.3 281 23 12 32 .67399 .72677
29.3 280 0 13 34 .65871 .73604
30.3 278 39 14 36 .64342 .74629
31.3 277 21 15 37 .62830 .75750
1830 Jan. 1.3 276 9 16 37 .61348 .76969
2.3 275 2 17 36 .59920 .78278
3.3 274 1 18 33 .58572 .79670
4.3 273 9 19 29 .57332 .81139
5.3 272 25 20 22 .56231 .82673
6.3 271 50 21 12 .55304 .84259
The opposition to the sun will be 1828, Oct. 12.34: while its light
is weak, it may be observed on or near the meridian.
On the 10th of Nov. 1828, its distance from the sun will be the same
as at the time of its discovery in 1818, and it will be considerably
nearer to the earth; and on the 21st of December, its position with
respect to the sun will be the same as at its last observation
in 1819; and with respect to earth, its situation will be more
advantageous. The 1st of January, 1829, it will set with the sun.
It follows, that the most advantageous time for seeing it will be
during the whole of November, and the first 25 days of December.
It will scarcely be seen before the end of September, as it has
heretofore never been observed more than two months before the time
of its perihelion, and even in the dark winter nights will scarcely
be visible more than 14 or 15 weeks before that period. After the
perihelion it will not be visible in these parts of the world.
ii. _Elementary View of the_ UNDULATORY _Theory of Light_. _By_ Mr.
FRESNEL.
[Continued from the last Number.]
In order to complete the explanation of the conditions necessary for
the formation of the fringes, it remains to show why a small luminous
point must be employed in experiments on diffraction, and not an
object of any considerable dimensions. If we resume the case of the
interior fringes of the shadow of [p432] a narrow body, it will be
easy to apply similar arguments to other cases of diffraction.
The middle of the central band, which is always formed by the
simultaneous arrival of rays, which depart at the same instant from
the luminous point, must be found in the plane drawn through this
point, and the line bisecting the narrow body: because, since every
thing is symmetrical on each side of this plane, the rays which unite
in it must have passed through equal routes on each side, and must
consequently arrive at the same instant, unless they have passed
through different media, which is not the case to be considered at
present. The situation of the middle stripe being determined, that
of every other stripe must also be determined accordingly. Now it
is evident that if the luminous point should change its situation a
little, and be moved to the right, for example, the plane, which has
been supposed, would incline to the left, and would carry with it all
the fringes which accompany the middle stripe. And if, instead of
supposing motion, we suppose the luminous point to become of sensible
dimensions; the integral points of which it is composed will each
produce a group of fringes, and their situations will be so much the
more remote as the luminous object is larger; and ultimately, if its
size is sufficiently increased, they will extinguish each other and
disappear. This is the reason that, when the rays cross each other at
sensible angles, as in all the phenomena of diffraction, it becomes
necessary to employ a very fine luminous point, in order to discover
their mutual influence: and the point must be so much the finer as
the angle formed by the rays is greater.
However minute the luminous point may be, it is always composed, in
reality, of an infinite number of centres of oscillations, and it is
of each of these centres that we must understand what has been said
of a luminous point. But as long as they are very near to each other
in comparison with the breadth of the fringes, it is obvious that the
different groups of fringes which they produce, instead of mixing
with each other in a confused manner, will be superposed almost
exactly, and instead of extinguishing, will co-operate with each
other. [p433]
When the two systems of waves which interfere are parallel, the
interval which separates their corresponding points must remain the
same for a great portion of the _surface of the waves_, that is to
say, in other words, the fringes will become almost infinite in
breadth, so that a very considerable displacement of the centre of
undulation will cause very little difference in the agreement or
disagreement of their vibrations. And in this case it is no longer
necessary to employ so small an object in order to perceive the
effects of their mutual influence.
If the coloured rings, which are produced by the interference of two
systems of undulations nearly parallel, exhibit, like the fringes,
and often within a very short distance, alternations of dark and
bright stripes; this circumstance depends entirely on the want of
uniformity in the thickness of the plate of air interposed between
the glasses, which causes a variation of the difference of the routes
of the rays reflected at the first and at the second surface of this
plate, of which the mutual interference produces the bright and dark
rings.
We shall readily be able, to understand why the luminous rays,
although they always exert a certain influence on each other, exhibit
it to the eye so seldom, and in cases so much limited, if we consider
that it is necessary, for such an exhibition, first, that the rays
concerned shall have been derived from a common source; secondly,
that the difference between their paths shall amount to a limited
number of undulations only, even when the light is as homogeneous
as possible; thirdly, that they shall not intersect each other at
too great an angle, because the fringes would become so small as to
be invisible even with the assistance of a strong magnifier; and
fourthly, unless the rays are nearly parallel, that the luminous
object should be of very small dimensions, and the smaller in
proportion as the inclination of the rays is greater.
It has been thought necessary to insist so much at length on the
theory of interferences, because of its numerous applications to the
calculation of the most interesting of the laws of optical phenomena.
These considerations may perhaps appear at first somewhat delicate
and difficult of comprehension, notwithstanding the minuteness of the
[p434] explanation; but with some reflection it will be found that
nothing can be simpler than the principles on which they are founded,
and their application will soon become familiar to the imagination.
In order to complete the bases of the general theory of diffraction,
it remains for us to consider the principle of Huygens, which appears
to be a rigorous consequence of the system of undulations.
The principle may be thus expressed: _The vibrations of a luminous
undulation, in each of its points, may be regarded as the result of
the elementary motions which would be transmitted to that point, at
the same instant, from all the points of the undulation, considered
separately, as they existed in any one of its earlier situations_.
It is a consequence of the principle of the co-existence of small
motions, that the vibrations, produced at any point of an elastic
fluid, by several agitations, are represented by the result of all
the velocities belonging to that point at the same instant, as
derived from the different centres of the undulations, combined
according to the laws of motion, whatever may be the number and
situation of the centres, and whatever the periods and nature of the
undulations. This general principle is applicable to every particular
case. We may suppose the agitations infinite in number, of the same
kind, simultaneous, and taking place in contiguous points of a
plane or a spherical surface: it will also be convenient to suppose
the motions of the particles to take place in the same direction,
perpendicular to the surface, their velocity being proportional to
the condensation of the medium, and none of them retrograde in their
direction. In this manner a derivative undulation will be produced by
the union of these agitations, and the principle of Huygens may be
truly applied to such a propagation. [This may be called a rigorous
consequence of the system, but it can scarcely be considered as a
proposition mathematically demonstrated: and the fundamental law of
Huygens must perhaps be assumed as an axiom or a phenomenon. TR.]
The intensity of the primitive undulation being uniform
throughout the surface, it results from this “theoretical” [p435]
consideration, as well as from other reasoning, that the uniformity
will be preserved throughout the progress of the undulation, unless
any part of it be intercepted or retarded; because the result of the
elementary motions, which have been mentioned, will be the same for
all the points. But if a portion of the undulation be intercepted
by the interposition of an opaque body, then the intensity of each
part will vary according to the distance from the margin of the
shadow, and these variations will be particularly sensible in the
neighbourhood of the tangent rays.
[Illustration]
Let C be the luminous point, AG the screen, and AME the wave, arrived
at A, and partly intercepted by the opaque body. We may suppose it
to be divided into an infinite number of small arcs, A_m′_, _m′__m_,
_m_M, M_n″_, _n″__n′_, _n′__n_, and so forth. In order to find its
intensity at the point P, belonging to any subsequent situation of
the undulation, BPD, we must find the result of all the elementary
agitations which each of these portions of the primitive undulation
would produce there if they acted separately.
The impulse, which has been given to every part of the [p436]
primitive undulation, being perpendicular to its surface, the
motions of the particles of ether in this direction must be more
considerable than in any other; and the rays depending on these
motions, if separately considered, would be so much the weaker as
they deviated the more from this direction.
The investigation of the law by which their intensity would be
governed, according to their direction, as derived from any
separate centre of agitation, would certainly be of very difficult
investigation: but happily we are not obliged to determine this law,
for it is easy to see that when the inclination to the perpendicular
is considerable, the effects of the different rays must very nearly
destroy each other: so that these rays, which sensibly affect the
quantity of light received at each point P, may safely be regarded as
being equal in intensity.
When the centre of agitation has undergone a condensation, the
expansive force tends to urge the molecules in every direction; and
if they do not perform a retrograde motion, it is only because their
initial velocities forwards destroy those which the expansion of the
condensed fluid would otherwise generate backwards: but it does not
follow from this that the agitation can only be propagated in the
direction of the initial velocities; for the expansive force in a
perpendicular direction, for example, will combine with the primitive
impulse without any diminution of its effects. It is obvious that
the intensity of the undulation thus produced may vary much at the
different points of its circumference, not only from the nature of
the initial impulse, but also because the condensations are not
subject to the same law on every side of the centre of the agitated
part[?]. But the variations of the intensity of the derivative
undulation must necessarily be subjected to a law of continuity, and
may consequently be considered as insensible in a very small angular
interval, especially in the neighbourhood of the perpendicular to the
surface of the primitive undulation; for the initial velocities of
the molecules, referred to any given direction, being proportional
to the cosines of the angles made by that direction with the
perpendicular, these results vary much [p437] more slowly than the
angles themselves, while they remain inconsiderable.
If, in fact, we consider rays sensibly inclined to each other,
such as EP, FP, IP, meeting in the point P, which we may suppose
at the distance of a great number of breadths from the undulation
EA: and if we take two arcs, EF and FI, of such a length that the
differences EP−FP and FP−IP may be equal to half an undulation: on
account of the marked obliquity of the rays, and of the smallness of
a semiundulation, in proportion to their length, these two arcs will
be almost equal, and the rays which come from them to the point P
will be nearly parallel; so that on account of the difference of a
semiundulation between the corresponding rays of the two arcs, their
effects will mutually destroy each other.