EXAMPLES OF THE FOUR METHODS. 473 



exerted by the copper itself; and this fact, once ascertained, 

 speedily led to the knowledge of an entirely new and unex- 

 pected class of relations." This example belongs, however, 

 not to the Method of Kesidues but to the Method of Differ- 

 ence, the law being ascertained by a direct comparison of 

 the results of two experiments, which differed in nothing but 

 the presence or absence of the plate of copper. To have made 

 it exemplify the Method of Residues, the effect of the resistance 

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

 calculated a 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 phe- 

 nomena, in the course of investigations of a widely different 

 nature from those which gave rise to the inductions them- 

 selves. A very elegant example may be cited in the unex- 

 pected confirmation of the law of the development of heat in 

 elastic fluids by compression, which is afforded by the phe- 

 nomena 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 great dilemma. At length Laplace struck on 

 the happy idea, that this might arise from the heat developed 

 in the act of that condensation which necessarily takes place 

 at every vibration by which sound is conveyed. The matter 

 was subjected to exact calculation, and the result was at once 

 the complete explanation of the residual phenomenon, and a 

 striking confirmation of the general law of the development 

 of heat by compression, under circumstances beyond artificial 

 imitation." 



" Many of the new elements of chemistry have been 

 detected in the investigation of residual phenomena. Thus 

 Arfwedson discovered lithia by perceiving an excess of weight 



