V.

Small Terms depending on Combinations of the mean anomaly and the longitude of the node.

These terms may be expressed in the following form :—

+0" 46 sin (mean anom. + long. node) —o′′·20 cos (mean anom. + long. node) — 1′′ 15 sin (mean anom.—long. node) +0′′·39 cos (mean anom.—long. node)

VI.

Correction of the Coefficient of Parallactic Equation.

The observations with the altazimuth play an important part in the determination of the correction applicable to this coefficient. The author concludes that the value of increase cannot be far from +2"6, whence the real value of the coefficient = 124"7.

VII.

Correction of the Coefficient of Variation.

The correction derived from the meridional observations =0"61; that from the altazimuth observations =+0′′.30. Adopting +0"50, the corrected coefficient will be +2370"8.

VIII.

Correction of the Coefficient of Annual Equation. The corrected value of the coefficient is found to be 670".04.

IX.

Correction of the Coefficient of Evection.

The corrected value of this coefficient is =4586"-81.

The author next investigates the corrections applicable to the elements of Ecliptic North Polar Distance.

X.

Correction of the Constant Term of Parallax.

The corrected value of this constant is found to be 57' 3"-89.

"The constant thus found," says the author, "is somewhat greater than Plana's, which is 57′ 3′′-16, or Mr. Adams', which is 57' 2"3; and a little greater than that found from the Cambridge Observations (Mem. Ast. Soc. vol. xvii. page 51), which is 57' 3" 46. It is worthy of remark that in each instance the constant derived from observation is greater than that derived from theory."

By confining his investigation to the observations subsequent to 1811, which are much more certain than those preceding that year, the author finds the corrected value of the constant to be 57' 3" 55. This brings the various numbers into better harmony.

Under this head the author has inserted the following footnote, to which he calls especial attention:

"I regret to say that in the former Memoir, vol. xvii., pages 51 and 52, I have committed a most serious error in my statement of the constant of parallax employed in the former Reductions. I have given it as 57' 3" 16, whereas it is stated explicitly in the Reductions (Introduction, pages xxi and xxii) and has been verified by reference to the manuscripts that the constant employed was 57' 1"8. I cannot account for this confusion in a research which so much engrossed my attention, and in which I was so much impressed with the difficulties of reconciling results."

The rectification of the error here referred to has enabled the author almost entirely to remove the discordances which presented themselves in the former paper between the definitive value of the constant of parallax which he arrived at by a discussion of the observations down to 1830, and the values of the same constant indicated respectively by observations made at Cambridge and Greenwich subsequently to that date.

XI.

Correction of the Inclination of the Moon's Orbit; Terms of Long Period in the Inclination of the Orbit.

The value of the inclination is found to be

18535"*55

The inequality in inclination is represented by the following terms:

-o" 73 x cos long. of node 1" 82 x sine longitude of node.

XII.

Correction of the Argument of Latitude and of the Motion of

the Argument: Terms of Long Period in the Argument. The secular motion of argument is to be diminished by 68"-6. Damoiseau's epoch is correct for 1781 nearly. inequalities in argument of latitude are found to be

The

509 x sine longitude of node.

Small Terms in the Moon's Latitude produced by the Combination of the Small Terms of Long Period, in the Inclination and in the Argument of Latitude.

Omitting two small terms of insensible value, the author obtains for the terms of ecliptic north polar distance, depending upon the argument "longitude from the first point of Aries,"

+1" 96 cosine u —- - 8" 59 sin u,

u denoting the moon's true longitude.

XIV.

Correction of the Coefficient of Evection in North Polar Distance.

The tabular coefficient 527′′.5 may be considered as sensibly

correct.

Suggestions as to the Structure of the Tails of Comets. By the Rev. T. W. Webb.

Though there seems to be no question that the dark space so frequently included in the tails of great comets is the result of a hollow structure, an attentive consideration of the appearances exhibited by the comet of Donati has led me to think it probable that some other cause may concur in its production. The ordinary laws of perspective certainly seem inadequate to its explanation, except in cases in which the darkness bears a large proportion to the brighter streams on each side of it: for unless the difference is but small between the radius of the hollow interior and that of the whole tail, the sine will not exceed the versed sine in a sufficient ratio to account for so great an increase of luminosity as is frequently witnessed. the contrary, at one period in the course of Donati's comet, at the end of September and during the first few days of October, the central darkness in the train, though very intense, occupied a comparatively small part of its whole breadth. My own estimate on September 30 gave it but one-eighth of the entire width of the tail, in which case a simple calculation will prove that the sine would exceed the versed sine only by something less than one-eighth part, and consequently the resulting difference in brightness would by no means accord with observation. The supposition of a shadow projected from the nucleus might seem at first to assist us with a supplementary amount of darkness; but it will be found unavailing when we have compared the case of the comet of 1811, in which a transparent space surrounded the nucleus alike on every side. Hence it may be thought probable that there must be some other cause for this appearance; and I have been induced to conjecture that, admitting the existence of a hollow interior, the difficulty might be met by the additional supposition of a radiated structure, in consequence of which the luminous particles, drawn out into a lengthened form, would in the apparent centre of the tail present their ends only, but on each side of it their full extent, to the observer's eye. At any rate such a conjecture would be fully in accordance with the hypothesis of a polar force of repulsive character, of which there seem to be other evident indications. May 12, 1859.

353

RECENT PUBLICATIONS.

Mr. De la Rue on Celestial Photography.

In the Photographic Journal for October 1, 1859, we find the substance of an interesting paper on Celestial Photography, read by Mr. De la Rue at the meeting of the British Association held at Aberdeen in the month of September last. We extract the following passages :—

"The mention of stellar photography one of the last applications of our art - reminds me that the image of such a heavenly body as a star being of the most simple form, it would render what I shall hereafter have to say more easily understood if I were at once to introduce to your notice what happens in applying photography to sidereal astronomy. The optical image of a fixed star, be it remembered, is an optical point, which, in consequence of the properties of light, is seen in the telescope as a very minute disk surrounded by certain rings, which become fainter and fainter as they enlarge; these rings are always more or less broken up, according to the state of the atmosphere. The photographic image, on the other hand, is a mere speck, difficult to find among other specks present in the most perfect collodion film, when viewed with a high magnifying power.

"Let us now suppose we have a suitable telescope turned upon a Lyra, which is conveniently situated, from its great altitude on the meridian, for photography, and is moreover sufficiently brilliant to give an instantaneous picture. If the telescope be steadily supported at rest, the star will, in consequence of the earth's rotation, course along the field of the telescope in a line parallel to the earth's equator; and as it produces an instantaneous picture, the image obtained is a line indicating the path of the star. We should be led to expect, à priori, that the line, for the short distance it is made, would appear straight; but so far from this being the case, the line is much broken up and disturbed, and consists of an immense number of points, crowded in some places and scattered in others. This arises from disturbances in our own atmosphere, which cause the optical image to flit before the eye, which nevertheless can make out the proper figure of the image, although it dances before it several times in a second, and the mind is able to select and remember only the states of most perfect definition. The photographic plate, however, remembers and records all the disturbances, and hence presents, as a result, a number of positions of the point of light, and consequently a less beautiful picture than we see optically.

"In the foregoing remarks it was supposed that the telescope was at rest; but now let us suppose that the telescope is mounted on an axis parallel with the earth's axis, and provided with a driving apparatus, capable of carrying the telescope

B

round in the direction of the star's apparent path, so equally that, if viewed by a micrometer eyepiece, the star would remain in contact with one of the wires of the eyepiece. The photographic image of a star obtained by a telescope under these conditions, after some seconds' exposure, is not one clear disk or point, but a conglomeration of points, extending over a greater or less surface, according as the atmosphere produces a greater or less flickering.

"A photographic image of a star, after an exposure of some seconds, is consequently a disk of comparatively large dimensions in comparison with the true image, and can be really seen on the plate. It will readily be seen, that as a single point like a fixed star acquires comparatively large dimensions on a sensitised plate exposed for some seconds to its action, so must every optical point in an image of other celestial objects from the same cause occupy a space of greater or less dimensions; hence the photographic image will never be so perfect as the optical image given by the same telescope until we can produce pictures of all objects instantaneously, and we are a long way from this desirable end at present.

"Notwithstanding, however, the disadvantages under which the photographer labours, I have obtained pictures of celèstial objects, showing details which occupy a space less than two seconds in each dimension-I might, I think, say even one second. Now two seconds = gth of an inch on the collodion plate, and a second on the lunar surface at the moon's mean distance, is about one mile. The lunar picture in the focus of my telescope is about 15th inch diameter, but this varies, of course, with the distance of our satellite from the earth. It will be conceded that much valuable work has already been done, and that if the photographs are taken for a number of years, selenological disturbances will not escape detection if they take place.

"With regard to the size of focus stated, it might be suggested that it would be better to enlarge the image; but this would prolong the time, and allow greater disturbance to take place. Thus the result would not be so good. It is by magnifying the photographs afterwards that we get good positive copies. One of these on the table is about eight inches diameter; that is to say, it is magnified about seven and a half times.

"Occasionally I take photographs of the fixed stars, and have made pictures of the double star, Castor, and others, but, as a general rule, I devote my attention chiefly to the moon.

"As in the production of the lunar pictures some few seconds of exposure are required, it is essential to have a clockwork driver to the telescope, capable of adjustment to lunar time, which differs from sidereal time. In my own telescope this is at present effected by altering the length of the conical pendulum or friction governor, thus altering the time of its rotation (or double beat). And this plan, or some modification