62 



NA TURE 



[May 28, 1874 



do me the favour of reading my original note again, he will find 

 that the object of my remarks was simply to test the trutli of a 

 definite assertion by i\Ir. Spencer that " the Second Law of 

 Motion is an immediate corollary of the preconception of the 

 exact quantitative relation between cause and effect." It was 

 entirely beside my purpose to discuss the general psychological 

 question of the formation of conceptions or preconceptions 

 farther than as it is involved in the truth or otherwise of this 

 particular assertion. Mr. Collier's note is therefore, as far as 

 regards my remarks, entirely irrelevant and needs no other reply 

 than to invite him, as Mr. Spencer declines to do so, to answer 

 the simple and definite questions proposed by me as difficulties 

 which Mr. Spencer is boimd to answer, unless he is prepared to 

 admit that he was wrong in the assertion on which I com- 

 mented. 



I have assumed throughout that Mr. Spencer means to assert 

 that tlie Second Law of Motion is involved in, not merely that it 

 invok'ts, a particular preconception. And yet this latter is all 

 that Mr. Collier asserts in the summing up of Mr. Spencer's 

 argument, with which he concludes his note. If Mr. Collier 

 truly represents Mr. Spencer, I can only say that, while the 

 assertion may be admitted to be true, it certainly appears to me 

 to be so trite as to be hardly worth formulating. The whole 

 question turns on the distinction between "involving" and 

 "being involved in," which I suppose Mr. Spencer and Mr. 

 Collier would regard as an important one, though it is difficult 

 in some cases to make out distinctly from their language and 

 their line of argument whicli they mean to imply. 



Passing in conclusion beyond the particular issue to which I 

 have hitherto confined myself, I would remark that to my mind 

 all that Mr. Spencer's and Mr. Collier's illustrations prove is 

 that, while unconscious experiences (whether individual or inhe- 

 rited) may give rise to certain general, but (except in the very 

 simplest cases) vague, preconceptions, it is only when these pre- 

 conceptions are wedded to consciously-made observation or ex- 

 periment that they cease to be barren generalities and give birth 

 to the fruitful laws of Physical Science. To a mathematician, at 

 any rate, it is almost ridiculous to observe how little either Mr. 

 Spencer or Mr. Collier seem to realise the great gap between the 

 indefinite observation that two things always increase and 

 decrease simultaneously, and the definite conclusion that they are 

 proportional to one another. For example, it is hardly a parody 

 of Mr. Collier's remarks to say; — "A child discovers that the 

 greater the angle between his legs the greater the distance 

 between his feet, an experience which implicates the notion of 

 proportionality between the angle of a triangle and its opposite 

 side ; " a preconception, as it appears to me, with just as good a 

 basis as that whose formation Mr. Collier illustrates, but one 

 which, as I need hardly add, is soon corrected by a conscious 

 study of geometry or by actual measurement. 



Harrow, May 25 ROBT. B. H.WWARD 



Mr. Collier's letter, Nature, vol. x. p. 43, is even more 

 astonishing than anything that Mr. Spencer has written. A 

 mathematician who reads it feels something like Alice behind 

 the looking-glass ; and perhaps behind the looking-glass it may 

 be " a question pertaining to the psychological basis of inductive 

 logic," with which mathematicians, as such, have nothing to do. 

 But in this wor;d, this side the looking-glass, in which forces are 

 measured and effects are measured, Mr. Collier's letter is very 

 perplexing. 



For example, after giving several inst.ances in which a greater 

 force produces a greater effect, Mr. Collier proceeds: "The 

 experiences these propositions record all implicate the same 

 consciousness — the notionof proportionality between force applied 

 and result produced : and it is out of this latent consciousness 

 that the axiom of the perfect quantitative equivalence of the 

 relations between cause and effect is evolved." 



Does Mr. Collier know what proportionality means? Does 

 any one of the experiments indicated prove that where effort is 

 doubled the result is doubled 1 The child pulls his boat by a 

 string through the water; if he pulls twice as hard does he pull 

 it lioice as fast ? 



It seems to me that the people on the other side of the looking- 

 glass think perfect quantitative equivalence (however measured) 

 means the same as proportionality ; and are willing to raise first 

 the general result of experience, that greater forces produce 

 greater effects, into an axiom of exact quantitative equivalence 

 (without troul^ling themselves to consider how quantity is to be 

 estimated), and then to accept Newton's Second Law as an in- 

 stance of this quantitative equivalence, without showing any 



connection between quantitative equivalence and direct propor- 

 tionality in that instance or in any other. 



A Senior Wrangler 



Ocean Circulation 



Mr. Croll will doubtless be of opinion that as my"theorie3" 

 show such an utter ignorance of " even the elements of physics 

 and mechanics," I can employ my time much better in acquiring 

 some knowledge of those sciences, than in continuing to discuss 

 the subject with him. 



I shall be glad to be allowed to state to the readers of Nature, 

 as I have to those of the Pliilosopliical Magazine (May), other 

 grounds on which I must decline to prolong this discussion. 



1. Mr. Croll has charged me (Phil. Mag. for March, p. 177, 

 note) with a serious misstatement in regard to the mean annual 

 rate of the Gulf Stream, which he affirms to be nearly double 

 what I have represented it. Now my statement was avowedly 

 based on the average of the -oliole year's observed ratts ; whilst 

 Mr. Croll has taken as the basis of his the arithmetical mean 

 between the maximum and the minimum. It has been said 

 in disparagement of statistics that "anything can be proved 

 by figures ;" and Mr. Croll, who is nothing if not a statistician, 

 seems to me to justify the imputation, for the adoption of his 

 method would make the average number of children of a mar- 

 riage to be at least ten I 



2. Mr. Croll, in asserting that I have left out of consideration 

 " the fact that the sea is Salter in intertropical than in polar re- 

 gions, and that this circumstance, so far as it goe?, must tend to 

 neutralise the difference of temperature," has only exhibited his 

 own ignorance of a very important fact of Ocean Physics — the 

 low salinity of equatorial surface-water ; which was ascertained 

 in Kotzebue's voyage fifty years ago, has been confirmed by 

 many later series of observations, has been repeatedly cited in 

 text-books, and has been adduced by myself as an indication 

 that polar water is continually ascending from the bottom to the 

 surface under the equator. But further, not only has this fact 

 been confirmed by the Challenger observations, but so remark- 

 able an accordance has been shown by them to exist between 

 the low specific gravity of equatorial surface-\s3Xitx and that of 

 equatorial liotloiu-waXer, as strongly to indicate that, as the latter 

 is certainly polar, the former is so also. It suited Mr. CroU's 

 purpose, however, with these observations before him, com- 

 pletely to ignore them, and to state as fact what is the precise 

 contrary of facts. 



3. According to Mr. Croll and his anonymous authority, the 

 Astronomer Royal must be unfamiliar with even "the elements of 

 physics and mechanics ; " for, speaking from the chairof the Royal 

 Society in 1S72, he explicitly expressed his acceptance of the 

 doctrine I advocate, as "certain in theory and supported by 

 observation." The eminent meteorologist. Prof. Mohn, of 

 Christiania, also, who expressed to me in writing last year his ac- 

 ceptance of it, must be equally ill-informed ; as, too, must be Dr. 

 Meyer of Kiel, who has been engaged for four or five years past 

 in the investigation of the physics of the Baltic, the North Sea, 

 and their connecting channels, and who has satisfied himself so 

 completely of the power of small differences of specific gravity 

 to put large bodies of water in motion. I have noiohere said that 

 no eminent physicist shares Mr. CroU's objections ; though I 

 have not myself met with such a one. 



I regret to have been forced, by the personal attacks in which 

 Mr. Croll has latterly thought fit to indulge, thus to retort upon 

 him. Henceforth I shall not consider myself called upon to 

 take any notice of asserdons and argumenls which I do not find 

 to exert the least influence on the opinions of the eminent 

 scientific men with whom it is my privilege to associate. 



William B. Carpenter 



Glacial Period 



In answering Mr. Bonney's letter in Nature, vol. x, p. 44, 

 I shall confine myself to the consideration of his second objec- 

 tion to my theory, as the precise southern limit of the glacial 

 action is not of present importance, and the height of the Scan- 

 dinavian sea-beaches is irrelevant to the inquiry. 



Mr. Tiddemann, in an admirable p.aper On the glaciation of 

 North Lancashire (Quirt. Journ. Geol. Soc, vol. .xxviii. p. 471), 

 has mapped out the course of the ice as shown by scratched 

 rocks, lines of transported boulders, carriage southwards of local 



