The First Meeting of the new Session, March 8th, 1878. The minutes of the preceding meeting were read and confirmed. Rev. Frederic John Hall, Haileybury College, Hertford. William Hobson, Esq., Park View, Whalley Range, Manchester. Lieut. Robert Hoggan, R.N., H.M. Dockyard, Sheerness. William Curtis Otter, Esq., 60, Grosvenor Park, Camberwell. F. H. Stevens, Esq., B.A., Clifton College, Bristol, were balloted for and duly elected Fellows of the Society. Mr. Glaisher announced that 84 presents had been received since the last meeting. Mr. Chambers said: Before we pass to the ordinary business, I want to throw out a suggestion as to whether some arrangement cannot be made for expediting the publication of the Monthly Notices. It strikes me as inconvenient that we should not receive the Monthly Notices until the day of the following meeting. I know that on a former occasion when complaint was made at Somerset House, the defence put forth by the Editor was that gentlemen did not return the "proofs " in time. Now, supposing that to be the cause of the delay, I think those gentlemen ought to be fined to the extent of having their communications post VOL. XVI. poned, rather than that the general convenience of the whole body of members should be sacrificed to the dawdling propensities of two or three members. Mr. Ranyard: This number contains the annual report, and it is no doubt rather exceptionally late owing to the difficulty in getting some of the "lives" completed, but during the last few months the numbers of the Monthly Notices have been published much earlier than they formerly were. Capt. Noble: I can heartily endorse all my friend Mr. Chambers has said. I have asked Mr. Cayley on several occasions at the Council why the number has not been sent out earlier, and I think the fault has generally been laid upon the printers rather than upon the gentlemen who will not correct the proofs. The last two or three numbers have been a long time in reaching me. I have usually to read them coming up to town in the train. If there is anything in the Notices which would involve discussion at our meetings we ought to have at least 24 hours to consider it. I do not know whether a hint to that effect will have any good result. There are reporters in the room, and perhaps if the fact goes forth that the Fellows would be better satisfied with more expedition, it may wake somebody up-but I will not say whom. (Laughter.) Mr. Lynn: I think we must allow that the case is rather exceptional this time, considering the great length and value of the report. Mr. Chambers: Unless my memory fails me, certainly during three out of the last five months my Notices have not reached me till the Friday morning of the meeting day, and I have only been able to read them coming up in the train on the morning of the day. The President: We will now pass to the ordinary business of the Society. Mr. Neison explained the substance of a paper On Hansen's terms of long period in the lunar theory. It would be remembered, he said, that about three years ago the Astronomer-Royal, in a paper read before the Society, announced that a certain term of long period in the motion of the moon, discovered by Hansen, ought to be omitted for the future from the lunar theory, upon the ground that the later investigations by Delaunay and Prof. Newcomb had shown that its value was insensible. A short time back Prof. Newcomb published a paper in the American Journal of Science, in which he made an elaborate investigation of the corrections of Hansen's tables of the moon, and showed that though Hansen was able, by certain artifices to make his tables represent the motion of the moon for the period between 1750 and 1850, yet for periods anterior and subsequent to this time Hansen's tables gave places which deviated from the true position of the moon. It was very difficult on any hypothesis to explain these discordances, and of late years Hansen's tables were far from truly representing the place of the moon. While making some researches upon certain points of the lunar theory, Mr. Neison said that he was led to examine Delaunay's investigation, and found that, though it was perfectly correct so far as it went, yet he had entirely omitted certain classes of terms from his equations, which might yield a sensible result, although he had fully considered what would be the effect of the action of the planet Venus on the motion of the moon, Delaunay had failed to consider how the action of the sun would be modified in accelerating or retarding the moon in its altered orbit. He has shown that the action of Venus will cause the moon to move in a somewhat larger orbit for the space of about 50 years, and then in a smaller orbit for a similar period. It would be evident that, when the moon was moving in the larger orbit, the earth would have less effect upon it, and consequently the perturbing influence of the sun upon the motion of the moon would be greater. Delaunay, in considering the perturbing influences of the sun upon the motion of the moon had omitted to take into account the variations of the moon's orbit caused by the action of Venus, and had assumed that the effects would destroy each other. Mr. Neison's paper was intended to show that it was possible that the action of the sun upon the alternately larger and smaller orbit of the moon, might be sufficient to account for the term of long period for which Delaunay had been unable to find any explanation, when he considered the moon as moving in a fixed orbit, and neglected the effect of Venus. Mr. Drach: May I ask Mr. Neison how much the orbit is enlarged? Mr. Neison: I am afraid I cannot say off-hand. Mr. Drach: I mean how much would the major axis of the moon's orbit be enlarged by the action of Venus? Mr. Neison: The increase would be very small, perhaps not amounting to th of a second of time for the year, but it goes on for 50 years, and at the end of that time it may be two seconds of time. The President: I will ask you to return your thanks to Mr. Neison for his paper. Mr. Proctor was called upon to read a paper On the determination of the axial position of Mars with respect to the earth at any epoch. He said that he had intended to make use of the observations of Mr. Green to prepare a new chart of Mars to submit to the meeting, but that he had found that the work would be greater than he had expected, and he had therefore been obliged to defer the chart till another occasion. It seemed to him that Mr. Dawes, though one of the most acute of observers, was not very skilful in delineating upon paper what he saw. There was a great amount of work in going over and correcting a chart of Mars, and the paper that he was about to explain was intended to show that one might form projections of Mars by making use of the right ascension and declination of the planet given in the Nautical Almanac, in cases where tabulated results, like those on which Mr. Marth had expended so much labour, were not available. a From Mr. Proctor gave the following construction for drawing the polar axis and equator of Mars from the known right ascension and declination & at any epoch, I. (about 39°) being the inclination of the equator of Mars to the terrestrial equator, and N. (about 47°) the right ascension of the rising node of the former plane on the latter. Let P O P', E' O E be diameters intersecting at right angles of the circle P E P', take arc P p = I., and draw the chord p c n perp. to P P' cutting it in c. p take arc pl of circle p l n about c as centre = a — N., and draw y perpendicular to p n cutting circle P E in d and produce lq to meet E E' in L. About L as centre strike arc dh h' cutting pn in h, and on this arc measure from harc h D equal to 8. Then Dr perpendicular to d q L gives r the end of polar axis of Mars. Regarding P E P' as disc of Mars, and P P' as the meridian, while the minor semi-axis of the Martian equator at epoch is equal to Dr. The part of this construction up to the point where the arc I is taken equal to (a N.) is common to all cases, and the construction from that point takes less time than is required for writing the description of it. p Mr. Proctor said he had another paper which was in fact an answer to a short paper by Mr. Stone on the question of the intrinsic brightness of objects seen with the telescope. It would perhaps be more interesting to the Fellows than the paper he had just read. The subject of intrinsic lustre was often misunderstood. The point which he had dwelt upon was this: if you have any surface whatever the surface of a nebula for example, or part of the sun or a planet, or any object subtending a sensible angle and you form an image of this surface, whether magnified or not, it will always be of less intrinsic brightness than the real surface itself, or under very favourable conditions, of equal brightness, but it can never be of greater brightness. Mr. Stone said that this was demonstrated by Sir George Airy, but so far as he could judge from Mr. Stone's remarks, the original paper only referred to refraction, and proved that a refracting medium could not cause a surface to appear brighter than itself. My paper pointed out that reflection also could not produce an increase of brightness. Mr. Stone went on to say (if I have not misunderstood him) that in star clusters the atmospheres of the suns might overlap. I concluded that he meant optically overlapping, not physical overlapping. In this I misunderstood him. But in return Mr. Stone has misunderstood me, because he seems to think that I had imagined that one could not, by telescopic power, increase the quantity of light got from an object. Mr. Stone asked, if that cannot be done, how is it that the satellites of Mars are visible with a telescope of 26 inches and not with a telescope of 4 inches. In reality the point I raised related only to surfaces. In the case of the satellites of Mars we do not see a surface, and in regard to the quantity of light received by the eye the aperture is all-important; but when it is a question of surface, although the visibility of an object may be greatly increased by the use of a telescope, the brightness of the surface cannot be so increased. I may mention (though it is not in the paper), the following illustration of the mistake people often make on this point. In the dusk of evening you take up a piece of printed paper, you find you can hardly read it, but when you look at it through a magnifying glass you can read it distinctly now, many think that it must be a great deal brighter when the letters are thus seen; but look at both surfaces together and you will find the magnified surface is a great deal duller, though, being magnified, you can read it more easily. Mr. Neison said he thought that Mr. Proctor had not fully caught the meaning of Mr. Stone. He thought that Mr. Stone intended to say that there was an additional reason for seeing small points of light with a large aperture over and above the mere increase in light collected by the object-glass, for with a large aperture you would have the light of the star collected into a smaller stellar disc, while with a smaller aperture it would be diffused over a larger disc, which would not be so easily seen in contrast with the illumination of the atmosphere. With regard to Sir George Airy's paper, Mr. Neison believed that Sir George showed that under no circumstances could you, as Mr. Proctor said, make any given illuminated area, either by transmitted light or reflected light, brighter than it really was. Mr. Proctor: Does he actually state that general case? In that case he has thoroughly anticipated what I have said. Mr. Neison I do not know whether he included reflection explicitly, by he includes it implicitly when he deals with the question of light falling from the moon being reflected on the earth; but I must say that Mr. Proctor was the first to show me |