154 Proceedings of Philosophical Societies. (Fes. 
opinion respecting the utility of the new edition. The Class of 
sciences heard and approved a long report in which the edition of 
M. Peyrard was examined in the greatest detail, and the conclusion 
of which is, that this edition is evidently superior to every other, 
and that the author has done every thing in his power to render it 
worthy of appearing under the auspices of the king to whom it is 
dedicated. 
Memoir of M. Puissant on the Calculation of Differences of 
Level in the Spheroid. Commissioners MM. Burkhardt and 
Delambre, reporter. 
M. Puissant employed in drawing up a complete treatise of tri- 
gonometry for the use of geodesy, has been led to treat of several 
questions already solved. He obtains all the known results by 
methods peculiar to himself. In stating the formulas which consti- 
tute the basis of the system of measures, he observes in them a 
slight error, which, however, is confined to quantities so small, 
that they are usually neglected. But it is always useful to rectify 
formulas even in their smallest details, and to point out errors 
which might be adopted with confidence by all those who occupy 
themselves rather with the practice than the theory. 
Memoir on a new Analytical Method of determining the Effects 
of Aberration in the Position of the Stars, by M. Puissant ; the 
same commissioners. 
Here, as in the preceding memoir, the author, by following 
routs with which he was well acquainted, arrives at all the known 
formulas, both for the stars, the planets, and the comets. He had 
at first demonstrated the whole by processes purely analytical; but 
afterwards making use of some ideas, of which he points out the 
source and names the author, he has been able to abridge his 
demonstrations without altering their character. 
These two memoirs, approved by the Class, will constitute a part 
of the treatise on trigonometry promised by M., Puissant. 
Determination of the true and apparent angular Distances of 
Centres of the two Stars submitted to the Influence of Paral- 
laxes, by M. Henry. Commissioners MM. Arrago and Delambre, 
reporter. 
We have seen the analytical processes substituted for the notions 
of elementary geometry in the demonstration of the most usual 
formulas of astronomy. On the contrary, we see here spherical 
trigonometry put in place of pure analysis to demonstrate the for- 
mulas by which M. Lagrange solved the problem of the eclipses of 
the sun, the stars, or planets. Ina theoretical point of view the 
method of Lagrange had obtained the suffrages both of astronomers 
and mathematicians ; but in practice it was soon perceived that 
these formulas, so beautiful and so general, were very inconvenient, 
on account of that generality itself. ‘To solve a problem so much 
above his means, the astronomer divides it into several others, 
which do not offer the same difficulty. He endeavours to multiply 
the natural data; by calculating the horary or nonagesimal angle 
