Prof. Challis (//* the Thconj of the Velocity of Sound. 105 

 Q^= /'hdt-A/''pds + A{p.-,.S2-prs{). . (5.) 



Subjecting this equation to the same process as that applied in 

 the deduction of equation (4.) from equation (2.), and neglecting 

 the members which contain the factor cr, wc obtain 



Q3= - 0-305 (/i-/^) (6.) 



Calculatmg from this the numerical value of Qg for a commen- 

 cing pressure of five or ten atmospheres, we obtain 



Q3= -15-9 or =-24-5 units of heat. . . (III.) 



The value of Qg being negative, it follows that in this case 

 heat is not to be communicated, but, on the contrarj^, must be 

 withdrawn, the quantity being the same as that found by apply- 

 ing the common theory of heat. If this withdrawal up to the 

 place under consideration be not sufficiently effected, then the 

 vapour at this place will have a temperature which exceeds 100°; 

 and hence, if water be not inechanicalhj carried along with the 

 vapour, the latter must be completely dry. 



It is thus shown that the friction is not necessary to the ex- 

 planation of the fact adduced by Mr. Thomson ; the effect of this 

 friction, as already mentioned, being exactly opposite to what he 

 supposes it to be. The loss of heat arising from this cause is 

 not reckoned above. In such cases as the issuing of steam from 

 the safety-valve of a high-pressure engine, this loss is by no 

 means capable of eflFecting the consumption of the quantity of 

 heat found by equation (6.). 



LII. On the Theory of the Velocity of Sound. 

 By Professor Challis. 



To the Editors of the Philosophical Magazine and Journal. 



Gentlemen, 



A S my name has been mentioned in connexion with the dis- 

 * *• cussion now going on in your Journal respecting the theo- 

 retical N'elocity of sound, and as I have already ventured to call 

 in question the usual method of accounting for the excess of the 

 observed velocity above the Newtonian value, I beg to be allowed 

 to say a few words in explanation of my views on this subject. 



The course of reasoning which led me to a different theory of 

 the velocity of sound from that usually adopted, may be stated in 

 general terms as follows. In the treatment of hydrodynamical 

 problems according to the received ])rinciples, contradictions of 

 a peculiar nature are met with, wiiich indicate that those prin- 

 ciples are either erroneous or defective. In counnunications 

 made from time to time to the Philosophical Magazine, I have 



