6 Frof. J. Le Conte on the Discrepancy betiveen the Computed 



In the animated and instructive discussions which followed 

 the enunciation of this objection, it was first satisfactorily shown 

 by Prof. Airy, and subsequently by Rankine, Stokes, Haughton, 

 and Bravais, that the whole difficulty grew out of a glaring mis- 

 conception of the physical basis of Laplace's reasoning*. Thus, 

 the Astronomer Royal shows that " the velocity does not depend 

 on the absolute pressure of the air in its normal state of density, 

 but upon the proportion of the change of pressure to the change 

 of density. This is increased by the suddenness of condensation 

 in one part, which, when the elastic force is great, makes it still 

 greater — and by the suddenness of rarefaction in another part, 

 which, when the elastic force is small, makes it still smaller, — thus 

 in both ways inweasing the change of pressure." In like manner, 

 Prof. Rankine clearly shows that Laplace's " investigation starts 

 from the principle, known to be a fact, that when the density of 

 a gas is changed, whether by compression or dilatation, its tem- 

 perature changes also, and it does not assume a pressure propor- 

 tional to the new density until it has had time to recover its ori- 

 ginal temperature. . . . The momentary variation of temperature 

 being in the same direction with the variation of density, the 

 momentary variation of pressure, whether positive or negative, is 

 larger, as compared with the original pressure, than the variation 

 of density as compared with the original density. . . . -Now the 

 velocity with which a disturbance of density is propagated is pro- 

 portional to the square root, not of the total pressure divided by 

 the total density, but of the variation of pressure divided by the 

 variation of density. ... It is therefore greater than the result 

 of Newton's calculation, — and this, whether the disturbance is a 

 condensation or a dilatation, or compounded of both." This 

 physical reasoning obviously demonstrates, to use the language 

 of Prof. Stokes, " that the development of cold by sudden rarefac- 

 tion is as much an essential part of Laplace's explanation of the 

 increase in the velocity of sound, as the development of heat by 

 sudden condensation." It seems to me that a candid review of 

 this discussion must convince every impartial physicist that this 

 objection has its origin in a total misconception of the funda- 

 mental principles of Laplace's explanation, and that the views 

 of this illustrious geometer, so far from having been in the slight- 

 est degree invalidated, have emerged from the controversy with 

 greater distinctness of features in relation to the reality and truth 

 of their general physical outlines. 



2. The difficulties and uncertainties embraced under the 



* Airy, in Phil. Mag. S. 3. vol. xxxii. p. 343 (1848). Rankine, ibid. 

 S. 4. vol. i. p. 226. Stokes and Haughton, ibid. vol. i. pp. 305 and 332 

 (1851). Bravais, in Ann. de Chim. et de Phys. 3 ser. vol. xxxiv. p. 82 

 (1852). 



