146 Royal Society. . 



that it pay be extended to other fluids. The demonstration of 

 Mr. Moseley, which is as follows, is remarkable for simplicity and 

 is perfectly general. Let 4>, <f>', 4>", be the effective accelerative 

 forces in the directions of the axes of coordinates, at any point 

 whose coordinates are x, y, z. By D' Alembert's Principle, 



y > -^=/((X-4))rf*+ {Y _ (p , )d y + ( z_4>")rf»), 



the integration being performed with respect to x,y, z, only; t the 

 time being constant. But when the motion is uniform, a given 

 particle in the successive instants of its motion, passes through the 

 states of the particles, which at a given instant are situated on the 

 path of its motion. Hence, if the integral above be taken in re- 

 ference to an arbitrary portion of this path, the term f(<pdx+<p'dy 

 + $''dz) may be taken in reference to the motion of a given par- 

 ticle along this portion. But in this case we know from the prin- 



cip, s of dynamics that f (<pdx + f'dy + <p" dz) = c, the 



constant c depending on the motion at the arbitrary limit. Hence 

 the proposition enunciated manifestly follows. 



It may be readily shown from this theorem, that if p = « 2 g>, 

 P = the atmospheric pressure, P' the pressure in a large vessel 

 of air maintained in a given state of compression, the velocity of 

 issuing from a small orifice into the atmosphere is determined by 



p> P— P' 



the equation v* = 2 a 2 hyp. log. -— , and not by d 2 = 2a°- — — 



as is usually supposed. M. Navierhas come to the same conclusion, 

 (Memoires de I Academie des Sciences, torn, ix.) by reasoning, how- 

 ever, upon the hypothesis of parallel sections. Mr. Moseley has not 

 neglected this application of his theorem. 



Mr. Moseley 's Treatise contains a careful statement of the prin- 

 ciples of hydrostatics and hydrodynamics, and detailed solutions 

 of a great variety of problems. There is also a chapter on hydro- 

 static machines, in which are given an account, and a theory of the 

 action, of Montgolfier's hydraulic ram. 



XXIII. Proceedings of Learned Societies. 



ROYAL SOCIETY. 



THE following are titles of papers which have been read before 

 the Royal Society during the latter part of the Session, which 

 ceased in June last. 



March 25. — Experiments to determine the difference in the num- 

 ber of vibrations made by an invariable pendulum in the Royal 

 Observatories of Greenwich and Altona. By Captain Sabine, Roy. 

 Art. Sec. R.S. 



Experiments to ascertain the correction for variations of tem- 

 perature, within the limits of the natural temperature of the climate 

 of the South of England, of the invariable pendulum recently em- 

 ployed by British observers. By the same. 



April 29. — Researches in physical astronomy. By John William 

 Lubbock, Esq. F.R.S. 



June 17. 



