METHOD OF DISCOVERING CAUSAL LAWS 189 



or of the total absence of impeding forces, which is its essential 

 condition, we nevertheless infer that, if this condition were ful 

 filled, the phenomenon would certainly take place. But where 

 the variations within our experience do not reveal in the one 

 phenomenon the total and indispensable cause of the other ; 

 where they do not assure us that in changed conditions no other 

 agencies could possibly interfere : then, of course, we cannot 

 infer an absolutely universal and reciprocating causal relation. 

 For instance, &quot;though solids and liquids diminish in bulk as 

 heat is withdrawn, they do not diminish at such a rate as to 

 suggest that there is a temperature at which they would vanish 

 altogether&quot;. 1 Again, in regard to gases, it is calculated that 

 &quot;they diminish in bulk, when heat is withdrawn, at such a rate 

 that they would vanish altogether at a certain very low tempera 

 ture ( absolute zero ). But before reaching that point they 

 liquefy. . . . We must not assume [therefore, without proof] 

 that a variation will continue beyond observed limits. Water, to 

 which you communicate heat, up to a certain point only gets 

 hotter; when its temperature reaches 212 [F.] it boils.&quot; 2 



Applied experimentally, the method often enables us to 

 establish &quot; laws &quot; in the sense of exact quantitative statements of 

 the proportions in which certain factors are found to contribute 

 invariably to a complex total process or phenomenon within the 

 limits of a certain range of experience (227), without at the 

 same time enabling us to explain the nature of the causal relation 

 of those factors to one another, or to some other cause whether 

 known or unknown. A good example of this use of the method 

 is furnished by the experiments devised to determine the rate of 

 the acceleration due to the force of gravity at the earth s surface. 3 



Let us now consider the method of concomitant variations 

 in its application to phenomena which we can merely observe, 

 without controlling experimentally. In the domain of physical 

 phenomena it is particularly applicable to what are called PERIODIC 

 CHANGES, i.e. certain regular changes of a phenomenon from a 

 greater to a lesser extent, or degree of intensity, and vice versa. 

 For instance, if we observe two neighbouring intermittent springs 

 acting at regular intervals, the one, say, of an hour, the other of 

 four hours, the latter discharging on each occasion about four 

 times as much water as the former ; we might infer that probably 



1 Palaestra Logica, p. 118, 361. *ibid. 



3 Cf. FOWLER, op. cit., p. 194. 



