500 



NATURE 



{April ^o, 1874 



Mr. Spencer distinctly refuses to identify this principle with the 

 great physical principle of the Conservation or the Persistence of 

 Energy, the firm establishment of which undoubtedly marks one 

 of the most important epochs in the history of Science. Force, 

 in Mr. Spencer's use of the term, includes numerous species of 

 which energy is but one. I feel sure that every mathematician 

 and physicist would protest against the inclusion under one term 

 of magnitudes of such different kinds as statical force and energy, 

 or the work done by such a force ; but not to dwell on this, I 

 believe that Mr. Spencer would certainly acknowledge as one of 

 his species, that which (in my view) is alone properly termed 

 Force, namely, such as can be measured in terms of tlie weight of 

 a pound or a gramme. Wliat then does Persistence of Force of 

 this kind mean ? Does it mean that the numerical sum of the 

 intensities of all the Actions and Reactions throughout the uni- 

 verse is constant ? If so, it is untrue : for, to take a simple 

 illustration, if a weight be supported, first by a single string, and 

 then by two strings not vertical, the tensions are quite different 

 in the two cases, and there is no equivalence between those 

 which disappear, and those which are introduced in passing from 

 one to the other. If not, we must take account of the directions 

 of our forces, and then, if it mean anything, it appears to be but 

 the expression of Newton's Third Law that "action and reacion 

 are equal and contrary " in this form : — " The algebraical sum of 

 all the forces throughout the universe is persistently zero." To 

 every mathematician, at any rate, this assertion and the assertion 

 that "the sum of the energies of all kinds throughout the 

 universe remains persistently of the same definite numerical 

 amount " are assertions of facts of such different orders, that to 

 class them together is rather to introduce confusion of thought 

 than to establish a grand general principle. 



I have offered the above remarks because it appears to me only 

 fair to the author of the article on Herbert Spencer in the 

 British Quartfrly Kez'irai to show that it is felt by others, who 

 have made a study of the fundamental principles of rational 

 mechanics, that his strictures on Mr. Spencer's treatment of 

 those principles are in all essential points fully justified, how- 

 ever much they may wish that the expression of those strictures 

 had been in some instances modified in its tone. 



The Park, Harrow, April 20 Robert B. Havwakd 



I THINK it is positively due, not only to the writer of the now 

 famous article in the British Quarterly Review, but to Newton's 

 memory and to Science itself, that the correspondence which 

 has been going on should not seem to terminate as a drawn 

 game, at any rate in the opinion of some bystanders, who may 

 from their antecedents be presumed competent to judge. 



That Mr. Spencer will ever be convinced is, I suppose, hope- 

 less ; I at any rate am not going to try to convince him. But I 

 can assure the British Quarterly Rrcnauer that he has my very 

 deepest sympathy in his argument with an antagonist who is at 

 once so able a ma>ter of fence as Mr. Spencer, and yet is so in- 

 tensely unmathematical, it would seem, as to pass from "exact 

 quantitative relation" to "proportionality ;" or as to talk of the 

 effect of a force, without defining how the effect is to be measured, 

 without feeling the slightest difficulty. 



Nor does it seem that Mr. Frankland, in Nature, vol. ix., 

 p. 484, is quite justified in his conclusion that the truth lies 

 between the two opposite views. And his own view is in fact 

 entirely coincident with the Reviewer's, except, perhaps, on a 

 point which is not relevant to the controversy, viz. how far the 

 experimental proof of the so-called physical axioms is eom- 

 plete. 



Will it comfort the Reviewer if I tell him some of my own 

 experience ? I, too, read Spencer after my degree ; and on the 

 first reading of the "First Principles" came to the sad conclusion 

 that I had not understood any mathematics properly ; so much 

 fresh light seemed to be thrown on them. I read it again, and 

 more critically, and doubted whether Spencer was quite correct. 

 I read it again, and concluded that he was wrong in his 

 physics and mathematics. I ought to add that I too was, 

 like the Reviewer, A Senior Wrangler 



I AGREE so fully witli the chief contents of Mr. Frankland's 

 letter (vol. ix. p. 4S4), that I wish to call his attention to one 

 point in which his letter seems to me calculated to mislead. 



He says, "the pure empiricists argue that because certain ob- 

 served results coincide with the results of calculation, therefore 

 the assumptions on which the calculation was based must be 

 true. Now without doubt the demonstrative character of this 



inference vanishes entirely under Mr. Spencer's searching 

 criticism. But it seems to me that a high probability remains." 



Now, in the name of pure empiricists, I must protest against 

 our being supposed to think that anything "must be true" in 

 any other sense tlian that there is a "high probability" of its 

 truth. I cannot refer to a better exponent of our views on this 

 point than Prof. Clifford, to whom Mr. Frankland himself 

 refers. And the idea of our having to thank Mr. Spencer for 

 showing that the inductive proofs of the laws of motion (or of 

 any other physical truths) are not demonstrative in any other 

 sense than the above is quite new to us. What Mr. Spencer 

 has done is to bring up Instances of this so-called imperfectness 

 in the demonstration as evidences that no a posteriori proof of the 

 proposition can exist, when in point of fact they are specially 

 characteristic of such a proof. 



Tliose of your readers who have examined Mr. Spencer's in- 

 genious proof of the second law of motion, contained in his last 

 letter to Nature (vol. ix. p. 461), will not ascribe mynot imme- 

 diately answering his letter to any difficulty in so doing. 



The Author of the Article in the British 

 Quarterly Review 



Lakes with two Outfalls 



In Nature, vol. ix., p. 4S5, Mr. Craig Cliristie begins a 

 letter "to correct a mistake as to a matter of fact : " " Loch-na- 

 Davie, Arran, has tivo outlets, as is correctly represented in the 

 Ordnance map ; " and he ends his letter ; " I think Colonel Green- 

 wood ought at least to have made him.self acquainted with the 

 Ordnance map." 



I take the liberty to enclose to you the new Inch Ordnance 

 map of Arran, to which my letter in vol. ix. p. 441 referred. 

 Vou will see that as " a matter of fact " the map does not give 

 two outlets, but only one. 



I need not ask for your valuable space in reference to Mr. 

 Christie's own " matters of fact," since my views with reference 

 to them are printed in the Athenc^iim of July 22, 1S65. He will 

 see there that I have not only " walked up the north stream 

 from Loch Ranza," but also by Glen Catacol and Glen Dzeven, 

 and a third time from Corrie by Glen Sannox over the water- 

 parting. Also that I have sounded the whole of this little pool 

 of bog-water by walking it, bare-legi;ed, without being over my 

 knees in the deepest part, which was at the south end, where 

 the only outlet is to Glen lorsa. 



I shall have the pleasure to communicate with Mr. Thelwall 

 ■n reference to his obliging letter. 



George Greenwood 



[The Ordnance map forwarded to us by Colonel Greenwood 

 gives only one outlet to Loch-na-Davie. — Ed.] 



As this subject appears to me to possess an interest apart from 

 the issues hitherto in question, I trust you will allow me a little 

 of your space. 



From the fact that lakes do not ordinarily occupy the crest of 

 a watershed, it would d prion appear more likely that a double 

 outfall, if it exist, should lie in or towards adjacent districts than 

 connected with opposed valley systems. The following in- 

 stance, which I observed in Norway last summer, is, in view of 

 Colonel Greenwood's letter (N.^ture, vol. ix. p. 441), worth 

 mentioning. The lake exhiljiting it lies about two miles inland 

 (N. W.) from the elevated coast which faces Trondhjem, and is 

 named Stor Lake ; its length — nearly parallel to the Trondhjem 

 fjord — is about seven miles, its greatest breadth about two. Like 

 many Norwegian lakes, it presents a faei.'s different to what we 

 are most familiar with in Britain. Instead of occupying a single 

 valley-basin, it consists of a chain of minor basins strung along 

 an axis of depression (probably a pre-existing valley), and each 

 separated from its neighbours by the subsided walls of the valley 

 of which it is the cup-like enlargement. The form of Stor Lake 

 is irregular, with long arms or creeks extended (obliquely to its 

 longer axis) into the mouths of the valleys. In such lakes it 

 might be expected now and then that the effluent waters should 

 pass out at more than one of these channels, and in Stor Lake such 

 is the case. One stream is discharged from one of the compo- 

 nent basins, nearly at right angles to the lake's greatest length, 

 the other issues along the depression on which I have said the 

 basins are "strung" — bead-like. The former opening is of 

 post-glacial date, and is superseding the original one for several 

 j reasons : — (1) it flows along the strike of a homogeneous bed of 

 j schist, whereas the other cuts across beds of various textures, 

 and (2) its volume is greater. Its rival bears evident traces of 



