214 THE PRINCIPLES OF SCIENCE. 



atmosphere at the earth's surface would be 968 feet per 

 second, and very rude experiments made by him in the 

 cloisters of Trinity College seemed to show that this wa&. 

 not far from the truth. Subsequently it was ascertained by 

 other experimentalists that the velocity of sound was 

 more nearly 1142 feet, and the discrepancy being no 

 less than one sixth part of the whole was far too much 

 to attribute to casual errors in the numerical data. 

 Newton attempted to explain away this discrepancy by 

 hypotheses as to the relations of the molecules of air, 

 but without success. 



Many new investigations having been made from time 

 to time concerning the velocity of sound, both as observed 

 experimentally and as calculated from theory, it was found 

 that each of Newton's results was inaccurate, the theo- 

 retical velocity being 916 feet per second, and the real 

 velocity about 1090 feet. The discrepancy therefore re- 

 mained as serious as ever, and it was not until the year 

 1816 that Laplace showed it to be due to the heat 

 developed by the sudden compression of the air in the 

 passage of the wave, this heat having the effect of in- 

 creasing the elasticity of the air and accelerating the 

 motion of the impulse. It is now perceived that this 

 discrepancy really involved the whole doctrine of the 

 equivalence of heat and energy, and the discrepancy was 

 applied by Mayer, at least by implication, to give an 

 estimate of the mechanical equivalent of heat. The esti- 

 mate thus derived agrees satisfactorily with independent 

 and more direct determinations by Dr. Joule and other 

 physicists, so that the explanation of the residual dis- 

 crepancy which so exercised Newton's ingenuity is now 

 complete. 



As Sir John Herschel observed, almost all the great 

 astronomical discoveries have been first disclosed in the 

 form of residual differences. It is the practice at well- 



