The PRESIDENT opened the proceedings with the following remarks: Having now completed my year of office you will perhaps think it becoming of me to say a few words on the present occasion of our annual general meeting. I trust that during the twelve months that I have been your president the Society has had no reason to regret its choice. Beyond, however, returning my sincere thanks to the Council and all the members of the Society-but especially to the Treasurer and Secretaries-for the kindness which I have invariably received at their hands, in the discharge of my duties, I will not occupy your time by dwelling at any length on the events of the past year. What I have to say refers more to the future. First I would remark that the attendance at our meetings, though I have no reason to believe it has generally fallen below the average of the last few years, is certainly not so full as is to be desired, and is, if I mistake not, considerably smaller than it used to be in the days when I first knew the Society. It seems to me that there is a very easy explanation of this fact. In former days the customary hour of dinner in the University was much earlier than it now is; and, more than that, all or nearly all of the Colleges dined at almost the same hour. Now, as you are aware, there is a very great diversity in this respect, and this change of habits appears to me to be obviously the prime cause of the small attendance. I believe I am right in stating that those Colleges which maintain the ancient practice of dining at a comparatively early hour are now in a minority-certainly they are in a minority as regards the number of members belonging to them. I speak in the presence of those who will correct me if I am in error, but I think that the hour of the Society's meetings has more than once been changed in past time, and that we meet now at a later hour than formerly. I would therefore venture to suggest that the Society might find it advantageous to consider this subject once more; but it will be apparent, I think, to all that we cannot fix a later hour than we have at present; and that, if any change be made, it must be to one that is earlier. It will be within the knowledge of several here present that some months ago the Royal Society determined to try the experiment of holding its meetings at an earlier hour-before instead of after dinner. The experiment has, I believe, succeeded, I will not say to the full extent that some expected, but at all events partially. I understand that the attendance has improved, and that the new arrangement has been found convenient by the most constant frequenters of the Society's meetings, whether they be officials or not. I therefore cannot help throwing out the hint that we might find it expedient to try the same experiment in Cambridge, and to hold our meetings in the course of the afternoon. The next point upon which I will touch is one that is likely to be of great importance to the Society. Fellows are aware that during the past Vacation, some long-projected alterations of the building in which we are assembled have been completed, with the result of throwing into one two smaller rooms. The large chamber thus formed is at present unoccupied, but it is no secret (for the assertion was made openly in the Schools) that the intention of some of those who brought about this change was to provide a library for the accommodation of scientific books for the use of all those who use this building. The fact that such a library would sooner or later become necessary has been long foreseen, and, for myself, the time of need seems now to have arrived. This proposal has many times been discussed in private, and I believe it has been openly urged that the library of the Society should form the nucleus of the new collection. A week ago the subject was brought formally before the Council of the Society, and a Committee appointed to report thereon. It will be plain to all that the Society would be a great gainer if its books could be accommodated in a more accessible room than that which they now occupy, and members would without doubt find the large chamber on the ground floor very commodious for their purposes. But, on the other hand, there are necessarily some disadvantages, supposing that this plan was carried out. In the first place, the books thus being so much more accessible would have to be put under a much stricter supervision than at present, and this supervision could not be attained without some expense. Then, too, it has been announced that this large room will require to be used for examinations, and it is of course obvious that in that case unrestricted admission could not be at all times enjoyed even by Fellows of the Society; while we all know, from the experience of past years, the tendency of examinations to increase both in number and in duration. Fellows of the Society might therefore come to find that the projected change would involve a serious deprivation of their rights. Yet, with all this, I fully believe that the Society would on the whole benefit by the alteration, and I trust that means may be found whereby the inconvenience I have mentioned may be reduced to a minimum. More than this it is impossible for me to say at present, and of course it will be understood that the Society will have due notice given to it of any action taken by the Council, and an opportunity of expressing its opinion thereon, but I have thought it only right to take the present opportunity of announcing to the Society at this meeting what is in contemplation, and the possibility of some arrangement being entered into with the University by the Council subject to the Society's approval. There is one other matter I should like to mention to the Society. By our Bye-Laws (chap. xii.) it is laid down that "the common seal, charter and deeds of the Society shall be kept in an iron chest with two locks and two different keys, the one to be kept by the President, and the other by the Treasurer." We have the chest: the Treasurer and I hold the keys prescribed by the law, and the Society's seal and certain documents are safely kept therein but our charter is not forthcoming, and no one of the present or former officers with whom I have been able to confer can throw any light upon what is become of it. This announcement I make to the Society, not merely to exonerate myself and your present officers from responsibility, but rather in the hope that one result thereof may be the recovery of this instrument, which is interesting and valuable to us, and of no use to any one else. The following communications were made to the Society: (1) On the general motion of a liquid ellipsoid under the gravitation of its own parts; continuation of a paper on the rotation of a liquid ellipsoid (Vol. III. pp. 289–293). By A. G. GREENHILL, M.A., Fellow of Emmanuel College. The following paper contains a new method of solving the problem, by means of moving axes, which has already been attacked by Lejeune-Dirichlet and Riemann, in the Abhandlungen der Königl. Gesellschaft der Wissenschaften zu Göttingen, in the 8th and 9th volumes respectively. Suppose the ellipsoid + +. =1 to be filled with liquid, and suppose the liquid frozen, and the ellipsoid to have component angular velocities έ, n, §. Then if u, v, w denote the component velocities at xyz, parallel to the axes, u = −y$+zn, v=-z§+x}, w=-xn+y§. If the liquid now be melted, and additional angular velocities 1,,,, communicated to the ellipsoid about its axes, then and if U, V, W denote the component velocities of the liquid relative to the ellipsoid, then where w1, w,, w, are the component angular velocities of the ellipsoid about its axes, and therefore w1 = √1+5, w1 = L2+n, w1 = L2+5. 1 y 2 We see that U+V+ W = 0, and therefore a liquid particle always remains on a similar ellipsoid. If h,,h,, h, denote the components of angular momentum about the axes, If no external forces act, the dynamical equations are .(C), (D) |