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Sixth Meeting, April 13, 1866.
The Rev. C. PRITCHARD, F.R.S., President, in the Chair.

Secretaries-Mr. Hodgson and Mr. STONE.
The minutes of the last meeting were read and confirmed.

Thirty-five presents were announced, and the thanks of the Society voted to the donors.

E. J. Routh, Esq., M.A.,
J. Hunt, Esq.,
C. V. de Santy, Esq., and

H. E. Western, Esq.,
were balloted for and duly elected Fellows of the Society.

The following papers were read :-
Occultation of 31 Arietis : by Mr. Talmage.

The times were given, and it was remarked that at the disappearance of the star it was distinctly seen to be projected for some seconds on the dark limb of the moon.

On a Probable Observation of Biela's Comet: by Mr. Talmage.

Pursuant to the request made at the last meeting, the author sent the approximate place of a faint cometic object seen by him, in the breaks of a cloud, on the 4th November last. No comparisons with stars could then be obtained, nor had the object been seen since; but the weather had been most unfavourable. Mr. Hind, to whom the observation had been sent, thought the object might have been the nucleus i of Biela's Comet.

Mr. Stone, while admitting that any observation of Biela's Comet would be of the greatest value, thought that this one, being unverified, could be received with little confidence. He regretted this very much, as about that time the comet would be moving rapidly, so that motion to the extent of 20 seconds would be seen in half an hour; and had the error of the Ephemeris been detected, the Greenwich observers would probably have found it.

Mr. Talmage said the observation must be taken for what it was worth. His own opinion of it was shown by his saying nothing about it for months, and only mentioning it when asked 'for information, after which he was particularly requested to record it for the

Society. It was not put forward as an authentic observation of Biela's Comet, but of an object which might be that or anything else.

On Solar Phenomena : by Mr. Waterston.
In the late President's address, allusion was made to the stability


of the semi-axis major of the earth's orbit; but the author thought this should not be assumed, as it supposed no addition was made to the sun's mass, whereas the outbreak seen by Messrs. Carrington and Hodgson on September ist, 1859, indicated the addition of large bodies. He had, therefore, calculated whether the length of the year should alter from that date, and computed that if a mass of large size had been added, the length of the year

should have increased a quarter of an hour.

Professor Adams (amidst the laughter of the meeting) said the author had forgotten one important point_namely, that the meteor which was supposed to have tumbled into the sun must have been somewhere else before-probably revolving round the sun-and that, therefore, its mass being on or near the sun, made no difference in the effect of the sun on the earth.

On the Companion of a Scorpii : by Mr. A. Cottam.

This star was well seen on two evenings by the author with a 43-inch object glass, and appeared of a green colour.

Mr. Stone wished to be allowed to ask the Astronomer Royal whether he had not lately seen the disc of the sun scattered over with particles of light; whether these portions were not smaller than he had seen them before, and whether they had not a tendency to an elongated form ?

Mr. Airy stated that some time ago [the date was afterwards ascertained to be 18th February] he was told that the sun could be seen remarkably well, and he therefore observed it with the Greenwich Equatorial. He was perfectly familiar with the mottled appearance of the solar disc, and also with the thatching of Mr. Dawes; but he now found that, besides the usual mottling, every part of the surface was broken up in a manner which was well represented as the interlacing of small luminous grain-like bodies. He felt convinced that such small elongated masses required a large telescope and excellent definition, and were, therefore, likely to be seen but rarely. They were decidedly smaller than anything he had seen before there. The power

used was not great-about 120.

Mr. De la Rue felt convinced that the Astronomer Royal had now seen the elongated small forms to which Mr. Nasmyth had first called attention.

Mr. Hodgson remarked that he was collecting evidence as to a probable outbreak of solar action on that day, and when complete he would bring it before the Society.

The President hoped that such important testimony as Mr. Airy's would not pass without some permanent record.

Mr. Stone said he had seen such bodies continuously on days of fine definition vith the Greenwich instrument, and was glad to have his observations verified by such high authority.

On a Small Star near ε Canis Majoris : by Mr. Freeman. The author had seen at Mentone a small star, at rather less distance from the large one than the Companion of Rigel, and of the 12th or 13th magnitude.

On the Companion of Sirius : by Mr. G. Knott.

This small star was seen tolerably distinct, notwithstanding some moonlight, and had its position and distance measured.

On the supposed Possible Effect of Friction in the Tides in Influencing the Apparent Acceleration of the Moon's mean motion in Longitude : by the Astronomer Royal.

This was an abstruse mathematical paper, of which Mr. Airy was only able to read a few extracts and explain the results. He commenced by observing that M. Delaunay had lately endeavoured to account for a portion of the apparent acceleration of the moon as possibly due to a real retardation of the rotation of the earth, and he conceived that such retardation might possibly arise from friction in the tidal movement of the waters. În suggesting this explanation, he assumed-first, that if the solid globe of the earth were covered with water, there would be high water under the moon (considered as the only tide-producing body); secondly, that the effect of friction would be to make the semi-diurnal tides later than they would be if there were no friction.

Mr. Airy then referred to previous investigations of the tides, all of which were necessarily imperfect from the varied boundaries and uncertain depths of the ocean. These inquiries were to be found in Newton's Principia, Laplace's Méchanique Celeste, and Airy's “Tides and Waves," in the Encyclopædia Metropolitana. Newton treated the supposition of a fluid ring equatorially surrounding the earth; Laplace, a fluid completely covering the earth, on two suppositions of depth; and Airy, a fluid equatorial ring in which the motion of the waters is either unaffected by friction, or affected by friction proportional to the velocity of motion. The results of the comparison of the theoretical inferences from these principles with M. Delaunay's assumptions are very remarkable, and in direct contradiction of these assumptions.

Newton, Laplace, and Airy agree that there will be low water under the moon. In another place Newton somewhat modifies this.

Airy shows that the effect of friction is to accelerate the time of each individual tide.

It is a result of this friction that the velocity of the earth's rotation is not affected.

It is a further result of this friction, and the consequent disturbance of the form of the waters, that the moon's motion is affected; her orbit becomes larger, and her motion in longitude is retarded.





The two last results Mr. Airy stated to be new; and the paper then became exclusively mathematical, showing the steps of an investigation of the motion of the waters in an equatorial canal of uniform depth.

The results above mentioned depend on considerations of the first order only of the disturbing force. The treatment of results to the second order is extremely difficult, embracing the solution of partial differential equations which could hardly be solved.

The Astronomer Royal had, however, pursued the subject, and at length discovered two terms which appear to exercise an influence on the rotation of the earth. One effect was clearly microscopic; and the other, although it might be palpable, still Mr. Airy thought that, looking to the imaginary state of things on which only the subject could be treated, and the difference of an equatorial canal from the real ocean with the great Continents of America and Africa running down into the waters, the result could be of very little use as a guide in the real state of the case, and would probably go for nothing.

The paper concluded with a geometrical demonstration of the startling proposition that when water moves without friction it will be low water under the moon. The fundamental points were that the rising of the water at any place does not depend on the horizontal movement of the water at that place, but on the relative value of the horizontal movement on the two sides of the place.

If the water on both sides is flowing towards the place, the water rises there. If the water on one side is flowing rapidly towards it, and the water on the other side receding slowly, the water rises there. When the surface is stationary as to height, there may still be considerable horizontal velocity; only it is clear that the water is flowing towards the place on one side just as fast as it is receding on the other. On these principles the author showed, by the aid of two diagrams—one inferring the direction of the tidal current from the changes of tidal oscillations, and the other inferring the nature of the tidal forces from the changes of the tidal currents that his proposition could be demonstrated; but without these diagrams any further explanation would be unintelligible here.

Professor Adams stated that he had followed the Astronomer Royal's address with the greatest interest, having himself independently investigated the same points. He agreed generally in the results obtained, and pointed out that it is not the whole effect of the moon, but only the different effect which it has on a particle at the earth's surface and centre, which produces the tides. This is the disturbing force, and the elevation of the water depends on this only, which is a disturbing force of the first order, but the

rotation of the earth would only be acted on by a force of the second order. M. Delaunay mentions this, and explains that Laplace went no further than the first order of disturbing force. Mr. Adams said that in a canal such as supposed, not exceeding 20 miles deep, there would be low water under the moon; if of greater depth, there would be no elevation at all; and with a still greater depth, high water under the moon. M. Delaunay makes a rough estimate that if the protuberant water be between the moon and 90° distant, there would be an action on the earth's rotation. Mr. Adams had carried the investigation further, and found that with a tide of 1 foot in height the effect would be much greater than M. Delaunay supposes. He (Mr. A.) had also considered the effect of friction on the bottom of the canal, and found that a current of small velocity follows the moon and tends to retard the motion of the earth. The retarding action on the moon is between one-half and two-thirds of the apparent acceleration. Thus a tide of 1 foot would produce an effect of 20'' in a century, but this is three times as much as the difference between observation and theory; and, therefore, although M. Delaunay is probably right in principle, it appears impossible to eliminate the effect correctly.

The President observed that we were deeply indebted to the Astronomer Royal for having come forward so promptly on this question. Laplace's work was nearly unreadable: the subject had been much simplified in the Encyclopædia Metropolitana, and now Mr. Airy had further elucidated it, and brought it within the grasp

of any person possessing a reasonable amount of mathematical knowledge.

Mr. De la Rue hoped that Professor Adams would embody his valuable remarks in a paper to accompany that of the Astronomer Royal, which Professor Adams consented to do.

Mr. Brothers, of Manchester, exhibited a repeating slide for taking a number of lunar or solar photographs very rapidly. A brass plate screwed on the telescope had an orifice through which the first picture was taken; the sensitive glass then moved several times horizontally, allowing other impressions to be obtained, after which it was raised vertically, enabling another series of pictures to be formed as it travelled back; and this process being continued, about 30 negatives could be taken before removing the plate to develop. Some of Mr. Brothers' positives were exhibited, possessing great sharpness of detail.

The meeting then adjourned.

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