84 



NATURE 



[yune 4, 1874 



and Prof. Mohn, suddenly disappears. Not, however, without 

 .ndding a sentence which I am sure lie will in tlie end regret. 

 He says he has "been forced by the personal attacks in which 

 Mr. CroU has latterly thought fit thus to indulge to retort upon 

 him." Wliy, the discovery of anything "personal" in Mr. 

 CroU's writings would be as gieat a find as the true theory of 

 oceanic circulation. I do not know any papers in our contem- 

 porary scientific literature more thoroughly undeserving of such 

 a charge. Surely a man may call in question, nay, may even 

 take a little quiet fun out of another man's opinions or crotchets 

 without I.rying himself open to the stigma of being guilty of 

 "personal attacks." Besides, it seems to me that Dr. 

 Carpenter's charge is inappropriate. Mr. Croll, remarking 

 "with some reluctance" that he was "compelled to refer" 

 to Dr. Carpenter's continual quotation of eminent physicists 

 who had adopted his views, while none had shared in the objec- 

 tions to them, merely assured Dr. Carpenter that such was not 

 the case, and mide reference to one person as an illustration, 

 but without giving the person's name. The Doctor, as every- 

 body knows, has been profuse in his use of this kind of argu- 

 ment. And now the moment it is used against himself, he 

 denounces the introduction of "personal attacks ! " 



I purposely avoid entering into the merits of the question. 

 What, in common with every sincere well-wisher of Science, I 

 desire to see, is its thorough, honest and courteous discussion. 

 Dr. Carpenter's high position gives a weight to what he says 

 and does, which adds much to the regret with which his letter 

 will be perused. That this protest may be received on its own 

 merits and without reference to the pen which holds it, I with- 

 hold my name. F. R. S. 



Proportionality of Cause and Effect 



Mr. Havward now affects the air of an injured man, and 

 complains of being charged witli " confusing issues " which he 

 neither "raised nor accepted." He may be convicted out of 

 his own mouth. The following passage occurs in his last letter 

 but one (Nature, vol. .\. p. 25) : — "It should be noted that 

 my principal ' exemplification of jinconscwusly-formed pyccoiicep- 

 iions ' was of Mr. Spencer's own choosing, namely, Newton's 

 ' Second Law of Motion.' " In his last he says : — "The object 

 of my remarks w'as simply to test the truth of a definite asser- 

 tion of Mr. Spencer that ' the Second Law of Motion is an im- 

 mediate iorollary of the preconception of the exact quantitative 

 elation between cause and effect.' " 



Now let the words italicised be compared. In the first pas- 

 sage Mr. Spencer is said to hold that the Second Law of Motion 

 is a preconception. In the second he is represented as main- 

 tainmg that it is a corollary from a preconception. Is not tliis 

 " confusing issues " ? 



Mr. Ilayward has the choice of two alternatives. He may 

 admit that one of these statements is a misrepresentation of Mr. 

 Spencer's doctrine, as was alleged. Does he refuse to do this ? 

 Then he may transfix himsell on the other horn of the dilemma, 

 and Ijoldly assert that in his view a preconception and a 

 corollary from a preconception are ore and the [same thing, 

 liut until Mr. Hayward can arrive at some agreement with 

 himself as to the terms in which he shall state Mr. Spencer's 

 theory, the conclusion of impartial outsiders will probably be 

 that he is not yet in a position to pronounce authoritatively on 

 the merits of it. 



"A Senior Wrangler" is good enough to say that my 

 letter makes him feel "something like Alice behind the looking- 

 glass." After this amenity, one may be pardoned for stating the 

 position whicli his nrentai altitude leaves. A famous metapliy- 

 sician once wrote an essay to prove that the narrow discipline 

 of mathematics produces an incapacity for general reasoning. 

 Sir W. Hamilton would have found his a priori arguments con- 

 firmed if he could have read the letter of "A .Senior Wrangler." 



The "Senior Wrangler" quotes a sentence of mine to the 

 effect that " the experiences these propositions record all 

 implicate the same consciousness — the notion of proportionality 

 between force applied and result produced ; and it is out of this 

 latent consciousness that the axiom of the perfect quantilalive 

 equivalence of the relations between cause and effect is evolved," 

 He dots not quote a previous passage in which it is said : — 



" Here, as in the examples about to be given, the relation 

 between cause and effect, though numerically indefinite, is definite 

 in the icspect tliat every additional increment of cause produces 

 an additional increment of effect ; and it Is out of this and 



similar experiences that the idea of the relation of proportion- 

 ality grows and becomes organic." 



It might have been supposed that the doctrine so expressed 

 was effectually guarded against misapprehension. Are not the 

 preconceptions derived from the child's muscular experiences 

 described as nunterically indefinite (i.e. not expressible in fropor- 

 tioital mtmbers) ? Is it not said that out of them the idea of 

 the relation of proportionality ^Tt^zyj .' " In the very sentence 

 quoted by the " Senior Wrangler," is it not said that the notion 

 of proportionality \s, implicated m the child's consciousness, and 

 that the physical axiom comes from this latent consciousness? 

 And yet the " Senior Wrangler," looking down from his mathe- 

 matical heights, and catechising me as he would a schoolboy, 

 asks me whether I know " what proportionality means " ? 



But for the letter of a "Senior Wrangler," one would have 

 believed that it was made clear to everyone that the notion of 

 proportionality generated by these early experiences was vague 

 and general, not exact. How else should I have said that from 

 it " the axiom of the perfect quantitative equivalence of the rela- 

 tions between cause and effect is friVfrf/.?" After thrice reading 

 "First Principles " does not the " Senior Wrangler " know that 

 being evolved includes passing from indefiniteness to definiteness ? 

 How then can he preteni that it is meant that the child gets 

 from his experiences the knowledge that a double effort produces 

 in all cases just double the result? The argument obviously im- 

 plied is that this is the finished conception finally arrived at by the 

 adult, as holding in those cases where causes and effects are un- 

 complicated. 



Having but limited space, and assuming that the requisite 

 qualifications would be made by unbiased readers, I jiassed over 

 all those details of the child's experiences which would have been 

 required in a full exposition. Of course I was aware that in the 

 bending of a slick the visible effect does not increase in the same 

 ratio as the force applied; and hardly needed the "Senior 

 Wrangler" to tell me that the resistance .to a body moving 

 through a fiuid increases in a higher ratio than the velocity. It 

 was taken for granted that he, and those who think with him, 

 would see that out cf all these experiences, in some of which the 

 causes and effects are simple, and in otheis of which they are 

 complex, there grows the consciousness that the proportionality 

 is the more distinct the simpler the antecedents and consequents. 

 This is part of the preconception which the physicist brings with 

 him and acts upon. Perhaps it is within the "Senior Wrangler's" 

 knowdedge of physical exploration, that when the physicist finds 

 a result not bearing that ratio to its assigned cause which the two 

 were ascertained in other cases to have, he immediately assumes 

 the presence of some perturbing cause or causes, which modify 

 the ratio. There is, in fact, no physical determination made by 

 any experimenter whicli does not assume, as ana priori necessity, 

 that there cannot be a deviation from pioportion without the 

 presence of sucli additional cause. 



Returning to the general issue, perhaps the " Senior Wrangler " 

 will pay some respect to the judgment of one who was a Senior 

 Wrangler too, and a great deal more — who was distinguished 

 not only as a mathematician but as an astronomer, a physicist, 

 and also as an inquirer into the methods of Science : I mean Sir 

 John Herschel. In his '-'Discourse on the Study of Natural 

 Philosophy," he says : — 



"When %ve would lay down general rules for finding and faci- 

 litating our search, among a great mass of assembled facts, for 

 their common cause, we must have regard to the characters of 

 that relation which we intend by cause and effect." 



Of these " characters " he sets down the third and fourth in 

 the following terms : — 



" Increase or diminution of the effect, with the increased or 

 diminished intensity of the cause, in cases which admit of in- 

 crease and diminution." 



"Proportionality of the effect to its cause in all cases of direct 

 nninifided action. " 



Observe that, in Sir J. Ilerschel's view, these are " characters " 

 of the relation of cause aird effect to be accepted .is "general 

 rules for guiding and facilitating our search" among physical 

 phenomena — truths that must be taken for granted Ayivr the 

 search, not truths derived from the search. Clearly, the "pro- 

 portion.ality of the effect to its cause in all cases of direct and 

 usimpeded action " is here taken as a priori. Sir J. Herschel 

 would, therefore, have asserted, with Mr. Spencer, that the 

 Second Law of Motion is d priori ; since this is one of the cases 

 of the "proportionality of the effect to its cause." 



And now let the " Senior Wrangler " do what Sir J. Herschel 



