EXAMPLES OF THE FOUR METHODS. 503 



of the air and that of the rigidity of the silk should 

 have been calculated & priori, from the laws obtained 

 by separate and foregone experiments. 



" Unexpected and peculiarly striking confirmations 

 of inductive laws frequently occur in the form of 

 residual phenomena, in the course of investigations of 

 a widely different nature from those which gave rise 

 to the inductions themselves. A very elegant example 

 may be cited in the unexpected confirmation of the 

 law of the developement of heat in elastic fluids by 

 compression, which is afforded by the phenomena of 

 sound. The inquiry into the cause of sound had led 

 to conclusions respecting its mode of propagation, 

 from which its velocity in the air could be precisely 

 calculated. The calculations were performed; but, 

 when compared with fact, though the agreement was 

 quite sufficient to show the general correctness of the 

 cause and mode of propagation assigned, yet the whole 

 velocity could not be shown to arise from this theory. 

 There was still a residual velocity to be accounted for, 

 which placed dynamical philosophers for a long time 

 in a great dilemma. At length Laplace struck on the 

 happy idea, that this might arise from the heat deve- 

 loped in the act of that condensation which necessarily 

 takes place at every vibration by which sound is 

 conveyed. The matter was subjected to exact calcu- 

 lation, and the result was at once the complete expla- 

 nation of the residual phenomenon, and a striking 

 confirmation of the general law of the developement 

 of heat by compression, under circumstances beyond 

 artificial imitation." 



" Many of the new elements of chemistry have 

 been detected in the investigation of residual pheno- 

 mena. Thus Arfwedson discovered lithia by perceiv- 

 ing an excess of weight in the sulphate produced from 



