m 



choice between the two suppositions, of whether the particles, 

 which are too numerous and minute for calculation, shall be sup- 

 posed to be finite or infinite. Having said thus much of the 

 nature of quantities, it remains to discuss a few points which 

 belong to the subject of proportion. 



51. Proportion may be considered, first, as it belongs fo 

 things existing separately ; and, second, as they are conjoined in 

 agency. An example of the former is, as when we compare the 

 size of two mountains, existing perhaps in different quarters of 

 the globe; an example of the latter is, as when two agents com- 

 bine to produce an effect, in that which has been called the true 

 inode of causation : my business is with the last. 



52. A small quantity appears capable of influencing the whole 

 contents of a large one: thus a single drop of sulphuric acid will 

 acidulate slightly a pint of water, containing perhaps 7,680 drops. 

 There are still more striking examples to the same purpose, but it 

 is unnecessary to enumerate them. Now as the amount of infinitely 

 divisible particles is, between these two, very disproportionate, how 

 comes it that the contents of the single drop should be capable 

 of a divisibility corresponding with that of the 7,680 drops? 



53. Supposing (as we may for the sake of the argument, though 

 it is not quite correct) that one drop of the water were equal in 

 its contents to the drop of sulphuric acid, then if each were re- 

 duced to a million parts, and were reducible no further, the oil 

 of vitriol would be capable of imparting its influence to no more 

 than the contents of one drop of the water. Nor is the conclusion 

 different, upon the supposition of an infinite divisibility belonging 

 to each; for if one half of the drop of oil of vitriol were removed, 

 or diffused, the remaining half drop, upon being divided and 

 mixed with the whole drop of the water, would riot influence the 

 whole of its contents, because the quantum of divisible particles 

 in the water would be always double those of the sulphuric acid; 

 notwithstanding which, the whole pint of water will be influenced 

 by the drop of the acid, and each drop, each particle of the 

 mixture, will appear to possess the same properties as the whole. 



54. But in this case it is necessary to infer that the propor- 

 tion of the ingredients in their division is equal to their pr0- 

 portion when aggregated ; that is, however comminuted and diffused 

 the drop of the acid might be, there will be contents of the 

 quantum of water which are not influenced by the particles of 

 the acid : if the drop of acid be infinitely divisible, so is a drop 

 of the water; if the mixture were confined to the two drops (of 

 the acid and of the water), there would be an agreement or 

 equality of proportion among the particles; but if the acid is 

 diffused among many drops of the water, then its particles can 

 apply only to combinations of particles of the water. 



55. The law therefore of proportion between conjoined 

 agents appears to be simply this, namely, that a given quantum, 

 of one agent can affect only the same quantum of another. Hence 



