intelligible matter. It involves the getting out the spherical co-ordinates of the moon's parallax in altitude at times assumed to be pretty near those of the beginning and ending of the eclipse. By applying these to the R.A. and declination of the moon, taken out for these times from the Nautical Almanac, it is obvious that we shall get the accurate apparent position of the moon; the sun's place can then very easily be taken out for the same times, and from their comparison we obtain the differences in R.A. and declination of their centres at those moments. If, then, the assumed times were exactly those of the contact of the limbs it is obvious that the hypothenuse of the pair of right-angled triangles now pointed out on the diagram exhibited would, each of them, exactly agree with the sum of the apparent semi-diameter at the same moment. In practice, of course, this is rarely or never the case, but the error is capable of being easily computed.
Still, this method is not rigorously exact, since the triangles are nearly spherical, and the moon's motion, which is assumed uniform and rectilinear for the interval between the first and last contacts, is really subject to appreciable variation from the assumption in both respects. A more strictly accurate method is that known as Bessel's, which is based on the true law of the cone, and takes into account every possible element of variation. But this method involves the use of a great number of logarithmic quantities, some of which, being dependent on the latitude and longitude, are constant for any particular place, and may be computed once for all for a particular station, as an Observatory. A number of others are constants for each eclipse or occultation for any part of the world, and these are all given in that fine publication, the "American Nautical Almanac." To anyone in possession of these two sets of constants, the computation, though tedious, is not difficult; but to get out all these quantities for a single eclipse would be a labour far too great to undertake, unless peculiar circumstances demanded it.
2. "The Elements of Mathematics," by J. Adams, B.A. (Transactions, p. 309.)
Mr. Heale agreed for the most part with the views expressed by Mr. Adams. It had always appeared to him that the time occupied in teaching boys the six books of Euclid was to a great extent wasted. No doubt the general method of Euclid, so elaborate and logical, was of essential service in education, but to avail oneself of this it was not necessary to wade through the whole of the propositions. On the contrary, a very small number would be sufficient. So long, however, as Euclid was retained in the Universities and examinations at home, he feared it would be premature to make any change here.
Fourth Meeting. 2nd October, 1876.
His Honour Mr. Justice Gillies, President, in the chair.
New Members.—J. Rees George, L. Lessong, Ph.D., M. Niccol, T. Niccol, Lewis Rye, F. H. Troup, A. Judd.
An animated discussion took place on Mr. Adams's paper on Euclid, read at the last meeting.
1. "On Savage and Barbaric Survivals in Marriage," by the Rev. J. Wallis, D.D. (Transactions, p. 249.)
2. "On Lime as a Manure; and its beneficial Effects when applied to the Cultivation of the Soil," by D. Hay. (Transactions, p. 206.)
