III. On the General Principles of which the Composition or Aggregation of 

 Forces is a consequence. By Augustus De Morgan, F.R.A.S. of Trinity 

 College, Professor of Mathematics in University College, London. 



[Read March 14, 18590 



I CALL the junction here considered aggregation, not composition. The mode in which 

 pressures or translations are put together diifers from that in which ratios are put together in 

 the manner illustrated in my last paper on logic (Vol. x. Part l). Briefly, junction of two 

 into one is aggregation when the vanishing of one does not prevent the other from producing 

 its full effect : it is composition when the vanishing of either destroys the whole effect of the 

 other also. Both are certainly compositions, if etymology have her rights; but the distinction 

 must be drawn, and it is, I think, most conveniently made, and — all subjects considered, 

 including logic — with least forcing of words, by the nomenclature I have proposed. 



The words possible and impossible have been so misused, in the mathematical and logical 

 sense, in the physical sense, and in the ambiguities arising from the double sense, that I 

 am glad to dispense with them. Bj' a result of thovght I mean any statement to which we 

 must assent, whether by consciousness alone, or by the action of the necessary laws of thought 



on postulates which consciousness must grant. Thus a + b = b + a and jx~^ dx = log x are 



equally results of thought : that the first is a pure axiom and the second an advanced theorem 

 is, so far as we can see or know, a contingency of our minds, not a law of mind. There may 

 be beings who cannot help granting the second, just as we cannot help granting the first. 

 Self-evident things may be capable of deduction from others of the same kind : of this we shall 

 see a remarkable instance. 



By a result of physics I mean any statement which, though involving results of thought 

 — which no result of physics is entirely without — also involves components which can be 

 conceived as possible to be contradicted by experience, and which therefore are only furnished 

 by experience ; that is, total want of exception to them in the past originates full belief in 

 their continuance for the future. The most deceptive phrase in our language is physical 

 impossibility. There is no such thing. Owing to the mixture of result of thought and result 

 of experience which obtains in every law of physics, it is easy to present, as a physical impos- 

 sibility, what is in truth nothing but the contradiction of a result of thought. That the 

 unusual or the unprecedented should take place during the continuance of the hitherto usual, 

 is impossible : for other than that which is to be cannot come to pass. Make then a law of 



