488 Mr. J. J. Waterston on the Theory of Sound. 



quired by the theory is extravagantly large. The recent ad- 

 vances in the theory of heat have, in a measure, compelled us to 

 realize the dynamic value of natural forces. To compute the 

 absolute value of the repulsive force acting between two adjacent 

 molecules of air, we have to consider that it has to support the 

 gravity of the number of rnoleciules in the height of a uniform 



p TJ -I ^ ' '\ 



atmosphere Mr- ; it-must tl^6refcn-e exceed the force of gravity 



of one molecule in this rat&. ■ Now the force of gravity in one 



second can communicate «. velocity of 32 feet per second, so that 



. the force of repulsion between two adjacent molecules of air must 



be capable in one second of communicating a velocity of 32 — 



feet. The absolute value of A,, the distance between two adjacent 

 molecules of air, we can now with great probability deduce from 

 the phaenomcna of capillarity (Phil. Mag. vol. xv. p. 1). At 

 the boiling-point of water the number of molecules of steam in a 

 cubic inch is the same as the number of molecules of air in the 

 same volume. At 86° the number of layers of aqueous mole- 

 cules in a cubic inch is 215 millions (Phil. Mag. vol. xv. p. 11). 

 Hence at ordinary temperatures the distance between two adja- 

 cent molecules of air must be about yjth of a millionth of an inch, 



and the value of ( 32 — L the velocity communicable in a second, 



is 160 thousand times the velocity of light. Can we for a mo- 

 ment believe that such a force has any real existence, that it is 

 other than a mathematical fiction ? 



3. The other physical properties are not deducible from the 

 hypothesis of a static force of repulsion. The deductive power 

 of Newton's theory is confessedly limited to Mariotte's law and 

 the velocity of sound. Laplace, by the invention of calorific 

 atmospheres, is allowed to have added to these Dalton and Gay- 

 Lussac's theory of expansion ; but it is a question whether the 

 reciprocal action between heat-atmospheres and molecules, which 

 he expresses by mathematical symbols, can be realized by the 

 mind. In judging of this, we must not forget the chapter of 

 the Mecanique Celeste, in which the author speculates upon 

 what the laws of motion would have been if force had been as 

 a function of the velocity, instead of as the simple velocity*. 

 What is to be expected from a superstructure resting upon 

 such a foundation as this reveals ? Nevertheless, granting that 



* The author of the article ' Virtual Velocities ' in the Penny Cyclopaedia 

 has the following remark ujion this chapter of the Mecanique Celeste: — 

 " We have never met with any one who could give us an intelligible account 

 of the meaning of this investigation." 



