LAW, CAUSE 371 



relations may be indicated in another way. As Bacon, Mill, 

 and most other writers on causality have indicated, a causal 

 connection can be assured only when some sort of concomi- 

 tant variation has been noted with reference to the cause 

 and effect. This is tested by introducing a variation in the 

 intensity of the cause and noting whether there is also a 

 variation in the intensity of the effect. If this variation 

 can be noted, and if it is of a comparatively direct sort, the 

 causal correlation may be presumed to be a genuine one. 

 For example, if as the cause increases the effect increases 

 at the same rate, the situation is judged to be truly causal. 

 In fact, even if the cause increases more rapidly than the 

 effect, or the effect more rapidly than the cause, there is 

 still a reasonable ground for concluding that a causal con- 

 nection exists. These would be considered direct variations. 

 But as the variation in the values of cause and effect, re- 

 spectively, becomes less and less direct, the conclusion to a 

 causal connection becomes more and more conjectural. If, 

 for example, a succession of changes in the cause in some 

 interval produces no changes in the effect, the conclusion as 

 to a causal correlation becomes relatively precarious. 



Now if this feature of direct and concomitant variation 

 in cause and effect may be presumed to characterize the 

 causal situation definitively, there can no longer be any 

 objection to the reduction of causal correlations to mathe- 

 matical functions. For the series of proportionate values 

 can be expressed through the method of approximation as a 

 simple function, e = f (c). In the well-tested cases e must 

 be a single-valued function of c; otherwise a variation in e 

 could occur without a variation in c. Now this looks very 

 much like a causal law in the sense that it asserts a depend- 

 ence of e upon c. But the distinction between dependent 

 and independent variables in a functional relation is purely 

 relative; consequently the law can also be represented in 

 the form, c = f (e), in which c is also a single- valued func- 

 tion of e. However, this no longer looks like a causal law, 

 for it presumably expresses a dependence of c upon e. 



