30 Prof. Challis on Newton's 



velocity of sound thence derived is 1109*3 feet per second, 

 which exceeds by 17*5 feet the value obtained experimentally 

 by Dr. Schroder (Phil. Mag. for July 1865, p. 47). 



It will here be proper to make some remarks on methods 

 that had been previously employed for determining theoreti- 

 cally the velocity of sound. The reasoning adopted by Newton, 

 and afterwards by Laplace, fails to give the true theoretical 

 value, because it is vitiated by involving the contradiction 

 which I have indicated above. Laplace, assuming that from 

 hydrodynamical considerations no value different from the 

 quantity a was deducible, proposed to account for the differ- 

 ence between observation and theory by the effect of develop- 

 ment of heat and cold produced by the condensations and 

 rarefactions of the aerial vibrations. He accordingly sought, 

 quite logically, to establish this explanation on a theory of 

 heat. I do not suppose that any physicist now accepts that 

 theory, inasmuch as the explanation of the above-mentioned 

 difference is made to rest on some gratuitous hypothesis which 

 is not supported by any reference to an antecedent theory of 

 heat. For instance, when it is said that the acceleration of 

 the rate of propagation is due to slow dispersion of the deve- 

 loped heat and cold, no evidence is adduced to show that this 

 is a vera causa in unconfined air. From a theory of heat 

 which I have founded on Newton's a priori hypotheses, I have 

 inferred that the dispersion is so rapid as to produce little or 

 no effect on the rate of propagation ; and this result accords 

 with the value of k deduced mathematically, as said above, 

 from the properties of a fluid defined by the equation p — a 2 p. 

 (See the discussion of this question, under the head of " Ma- 

 thematical Principles of Physics," in pp. 472-474 of the before- 

 cited work.) 



After the foregoing rectification of the principles of hydro- 

 dynamics, the way is clear for proceeding from Part (I.) of 

 general physics to the consideration of Parts (11.) and (III.). 

 The former of these two parts consists of formations of equa- 

 tions applicable to the several theories of light, heat, gravita- 

 tion, electricity, galvanism, and magnetism; and the latter 

 comprises deductions from the solutions of the equations and 

 comparisons of the results with experiment. Respecting the 

 investigations belonging to these two divisions, I can only 

 refer to my own mathematico-physical productions, because, 

 as my contemporaries have in no instance adopted the New- 

 tonian hypotheses of Part (I.), they are logically debarred 

 from entering upon Parts (II.) and (III.). In a communica- 

 tion like the present it would not be possible to advert in detail 

 to the many problems I have undertaken to discuss under these 



