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XIII . The solution of the Problem of Sound, founded on the Atomic 

 constitution of Fluids. By Professor Potter, A.M.^ 



SIR ISAAC NEWTON, investigating the expression for the 

 velocity of sound in air, found that it was represented by 

 V'^H, where ^ = force of gravity =32"19 feet, velocity per 

 second, and H is the height of the homogeneous atmosphere. 

 His method is objected to, but no other expression for the velo- 

 city of sound has hitherto been established in place of his formrda. 

 It was, however, found that the value given by the formula VgH 

 was smaller than the velocity given by experiment by about one- 

 sixth pail ; and the first who succeeded in giving an explanation 

 for this discrepancy was the illustrious mathematician Laplace, 

 who maintained that the sensible heat developed in the sudden 

 condensation of air was sufficient to account for it. Calcidatious 

 have been made to show that the amovmt of discrepancy is thus 

 completely accounted for. The explanation of Laplace has been 

 held to be untenable by many eminent mathematicians and phy- 

 sicists ; for it is correctly argued, that a wave of sound will com- 

 mence with a rarefaction as often as with a condensation, and 

 that on one side of a nodal line on a bell or vibrating plate, the 

 wave commences with a rarefaction, whilst on the other side it 

 commences with a condensation ; so that Laplace's reasoning 

 would have been equally available if the velocity of sound in air 

 had proved one-sixth less than the theoretical velocity, instead 

 of one-sixth more, by considering the cold produced by rare- 

 faction. 



In reading the history of the theoiy of sound, the scientific 

 men of future times will be astonished to find how many have 

 recorded their acquiescence in Laplace's views. 



The author of the present paper has for more than ten years 

 continually and publicly expressed his conviction, that there was 

 a fundamental error in the method of treating the hydi-odynamics 

 of clastic fluids ; because not only the theory of sound, but other 

 intei'csting pi'oblems were not capable of correct solution by 

 means of the equations as at pi'csent used. He also frequently 

 stated his belief, that the atomic theory of the constitution of 

 bodies must be introduced into hydi-odynamics before the subject 

 could be correctly treated. Having, by the publication of the 

 second part of his Treatise on Optics, now some little leisure, he 

 has undertaken the investigation of the fundamental equation of 

 the theory of sound with complete success. He may attribute 

 his success to the instructions in chemistry which he received in 

 his youth from the late Dr. Dalton, who, during that course of 



* Communicated by the Author. 



