408 INDUCTION. 



are fulfilled ; the effect is the same as if the drain had been 

 open for half an hour first,* and the stream had flowed in for 

 as long afterwards. Each agent produced the same amount 

 of effect as if it had acted separately, though the contrary 

 effect which was taking place during the same time obliterated 

 it as fast as it was produced. Here then are two causes, 

 producing by their joint operation an effect which at first 

 seems quite dissimilar to those which they produce separately, 

 but which on examination proves to be really the sum of those 

 separate effects. It will be noticed that we here enlarge the 

 idea of the sum of two effects, so as to include what is com- 

 monly called their difference, but which is in reality the result 

 of the addition of opposites ; a conception to which mankind 

 are indebted for that admirable extension of the algebraical 

 calculus, which has so vastly increased its powers as an instru- 

 ment of discovery, by introducing into its reasonings (with 

 the sign of subtraction prefixed, and under the name of 

 Negative Quantities) every description whatever of positive 

 phenomena, provided they are of such a quality in reference to 

 those previously introduced, that to add the one is equivalent 

 to subtracting an equal quantity of the other. 



There is, then, one mode of the mutual interference of laws 

 of nature, in which, even when the concurrent causes anni- 

 hilate each other's effects, each exerts its full efficacy according 

 to its own law, its law as a separate agent. But in the other 

 description of cases, the agencies which are brought together 

 cease entirely, and a totally different set of phenomena arise : 

 as in the experiment of two liquids which, when mixed in cer- 

 tain proportions, instantly become, not a larger amount of 

 liquid, but a solid mass. 



2. This difference between the case in which the joint 

 effect of causes is the sum of their separate effects, and the 



* I omit, for simplicity, to take into account the effect, in this latter case, 

 of the diminution of pressure, in diminishing the flow of water through the 

 drain ; which evidently in no way affects the truth or applicability of the 

 principle, since when the two causes act simultaneously the conditions of that 

 diminution of pressure do not arise. 



