306 INDUCTION. 



it in vibration, observed, that it came much sooner to a state of rest when 

 suspended over a plate of copper, than when no such plate was beneath it. 

 Now, in both cases there were two vercx, causae " (antecedents known to 

 exist) " why it should come it length to rest, viz., the resistance of the air, 

 which opposes, and at length destroys, all motions performed in it ; and the 

 want of perfect mobility in the silk thread. But the effect of these causes 

 being exactly known by the observation made in the absence of the cop- 

 per, and being thus allowed for and subducted, a residual phenomenon 

 appeared, in the fact that a retarding influence was exerted by the copper 

 itself; and this fact, once ascertained, speedily led to the knowledge of 

 an entii'ely new and unexpected class of relations." This example belongs, 

 however, not to the Method of Residues but to the Method of Difference, 

 the law being ascertained by a direct comparison of the results of two ex- 

 periments, 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^ivova. the laws obtained by separate and fore- 

 gone experiments. 



"Unexpected and peculiarly striking confirmations of inductive laws 

 frequently occur in the form of residual phenomena, in the course of in- 

 vestigations of a widely different nature from those which gave rise to the 

 inductions themselves. 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 phenomena of sound. The in- 

 quiry into the cause of sound had led to conclusions respecting its mode 

 of propagation, from which its velocity in the air could be precisely cal- 

 culated. The calculations were performed ; but, when compared with 

 fact, though the agreement was quite sufficient to show the general cor- 

 rectness of the cause and mode of propagation assigned, yet the whole ve- 

 locity 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 con- 

 densation 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 in the sulphate produced from a small 

 portion of what he considered as magnesia present in a mineral he had an- 

 alyzed. It is on this principle, too, that the small concentrated residues of 

 great operations in the arts are almost sure to be the lurking-places of new 

 chemical ingredients : witness iodine, brome, selenium, and the new metals 

 accompanying platina in the experiments of WoUaston and Tennant. It 

 was a happy thought of Glauber to examine what every body else threw 

 away."* 



" Almost all the greatest discoveries in Astronomy," says the same au- 

 thor,! " have resulted from the consideration of residual phenomena of a 

 quantitative or numerical kind It was thus that the grand discovery 



* Discourse, pp. 166-8, and 171. t Outlines of Astronomy, § 856. 



t 



