COMPOSITION OR AGGREGATION OF FORCES IS A CONSEQUENCE. 301 



alone can we know that a system of pressures may undergo translation and rotation without 

 any change in the aggregate. There might have been a fixed direction, a natural polar line of 

 gravitation, such that tl^e action of particle on particle might have been a function of the 

 angle made by their joining line with the polar line, as well as of the distance between them. 



(3) The third postulate also depends upon experience. We can imagine, and express if 

 we please, a law of aggregation under which the aggregate should be one thing or another 

 according as the aggregants enter in ascending or descending order of magnitude. And we 

 can imagine the law of nature being expressed by one of these to the exclusion of the other. 



(4) The fourth postulate seems at first sight to be purely a result of thought : the whole 

 is made up of all the parts ; the weight of the whole is equal to the sum of the weights of all 

 the parts. Nor can it be denied that if the pressures were wholly unconnected, so that each 

 of them acts in the same way whether the others be more or less, present or absent, this 

 postulate would then be a result of thought. But this is only saying that if pressures be 

 assumed to act jointly by aggregation, the postulate which the notion of aggregation demands 

 must be conceded. For, as noted at the beginning of this paper, the distinction between 

 junction by aggregation and other junctions, is that the effect produced by each aggregant is 

 wholly unaffected by the magnitude of the others. Granting this, we cannot dissociate our 

 right to express a magnitude by seven from our right to say it is made up o{ four and three. 

 But it is conceivable that one pressure may receive modification from the mere presence of 

 others : and it is often actually the case. If weights be hung one under another on the same 

 string, each weight abstracts weight from those under it, and adds weight to those above it. 

 The equality of action and reaction silently makes good the position in which the speculator 

 may imagine he can call thought to witness that the weight of the whole must be equal to the 

 sum of the weights of the parts. That pressures combine by aggregation, and not by com- 

 positio7i, can be known only by experience. 



It thus appears that the proofs of the parallelogram offerees, as it is called, are not those 

 mathematical playthings which they have seemed to be when the character of the fundamental 

 assumptions is left to be decided by first appearances. There is not one of the four postulates 

 which might not be imagined false in objective nature, though all are true of notions of space 

 and time. That these postulates are so simple, so fit for the work which is to be done, that 

 they seem necessary until close consideration is applied, may only be a consequence of our 

 familiarity with their action and with their results. It may be they are evidently what they 

 ought to be only as it was evident to Dr Moore's travelling servant that blue is the proper 

 colour for the artillery. The unfeeling and immoveable rational being to whom I have ap- 

 pealed above might perhaps arrive at other conclusions, if he were consulted a priori. For 

 instance, he might doubt whether simplicity ought to characterise laws which have very com- 

 plicated work to do. 



When I say that the diagonal law of aggregation is thus founded upon results of experi- 

 ence, I mean it in the sense in which it is always said that the law of gravitation is founded 

 on experience. The observed ellipse was the first proof of the law : not the law of the ellipse. 



