Prof. Challis's 07i the Velocity of Sound. 353 



tallic silver, which gives the following for the composition of 



the salt: — 



Atomic vveiglit. Per cent. 

 Oxide of silver . 4>'3'28 1 4<-.50 30-03 



Acid .... 10-052 33*67 69-97 



The acid was not quite pure ; for when heated it softened 

 at 143°, became very soft at 149°, of the consistence of cream 

 at 150°, and quite fluid at 154°; it obviously therefore retained 

 some stearic acid, but must have consisted principally of mar- 

 garic acid, as stearic acid fuses at 167°. There is no doubt 

 that both of these oils might be advantageously employed in 

 soap-making, the supply apparently, from the statements of 

 the traders, being unlimited. 



LI I. Determination of the Velocity of Sound on the princi- 

 ples of Hydrodynamics. By the Rev. J. Challis, M.A., 

 F.R.S.y F.R.A.S., Plumian Professor of Astronomy and Ex- 

 perimental Philosophy in the University of Cambridge^. 



IN conformity with the intention expressed at the close of 

 my communication to the Number of the Philosophical 

 Magazine for last February, I propose now to exhibit collec- 

 tively the whole course of the mathematical reasoning by which 

 I obtain, entirely on hydrodynamical principles, a value of the 

 velocity of sound closely agreeing with that found by obser- 

 vation. The importance of the result, and the novelty of the 

 considerations on which it depends, will be my excuse for 

 going through the reasoning somewhat in detail, and for re- 

 peating some parts of previous communications. It may be 

 proper to state at once, that I do not regard as defensible, or 

 pertinent, all that 1 have written in the course of this difficult 

 investigation; for instance, I have found that the new hydro- 

 dynamical equation, the necessity of which I have elsewhere 

 insisted upon, is not, as I supposed, essential to the present 

 inquiry. My immediate object is to extract and put in logical 

 order what is really legitimate and essential. 



The problem to be solved is, the numerical determination 

 of the velocity of sound from the equations of hydrodynamics. 

 As this may be considered to be a case of small vibrations, 

 powers of the velocities and condensations above the first will 

 be neglected. The pressure {p) being such that J9 = a^(l +s), 

 and «, 'y, W being the resolved velocities at the point ocyz and 

 at the time /, the equations applicable are the following: — 

 « Communicated by the Author. 



Phil. Mag. S. 3. Vol. 34. No. 230. May 1 849. 2 A 



