Dec. 28, 1 871] 



NATURE 



161 



LETTERS TO THE EDITOR 



[ 77/1.' Editor does not hold himself responsible for opinions expressed 

 by his correspondents. No notice is taken of anonymous 

 communications. ] 



Dr. Carpenter and Dr. Mayer 



With reference to Dr. Tyndall's communication of last week, 

 in which I most unexpectedly found a private note of my own 

 placed before your readers, 1 should be obliged by your allowing 

 me to state :— 



1. That the idea of "Correlation," as originally entertained 

 by Mr. Grove, and applied by myself to physiology more than 

 twenty years ago, most unquestionably included that of the 

 ijuantitatiLW equivalence of the convertible forces, as will appear 

 from the following passage in my memoir of 1850 (Phil. Trans, 

 p. 731) : — **The idea of correlation also involves that of a cer- 

 tain definite ratio between the two forces thus mutually inter- 

 changeable, so that the measure of force B, which is excited by 

 a certain exertion of force A, shall, in its turn, give rise to the 

 same measure of force A as that originally in operation " And 

 further I urged the precise j-clation observable between the vital 

 activity of plants and cold-blooded animals, and the amount of 

 heat they receive from external sources, as a ground for the 

 belief that heat hai the same relation to the organising force as it 

 has to electricity (pp. 747-750). 



2. In crediting Dr. Mayer therefore with the independent 

 (and in my own case the previous) enunciation of the "Correla- 

 tion " doctrine, I most certainly meant to include the notion of 

 quantitative eqinvalence. Whether the quantities be or be not 

 expressed in number seems to me a matter of secondary im- 

 portance. William B. Carpenter 



University of London, Dec. 26 



The "North British Review" and the 

 Origin of Species 



The writer of the article on the "Origin of Species," which 

 was published in the A\irth British Fevicw for June 1867, has 

 corrected in your periodical for November 30 an unimportant error 

 wliich occurs in a certain paragraph of that article. There i;, 

 however, it appears to me, a much more serious error in the 

 same paragraph, which vitiates his arithmetical calculations 

 throughout, and leads him to an erroneous conclusion. 



The paragraph in which this error occurs is quoted at length in 

 Mr. Mivart's work on "The Genesis of Species." It may there- 

 fore be worth while to point out the oversight alluded to. 



The error arises from the writer's assuming that in a race 

 which remains constant in numbers, only one individual out of 

 each family, i.e., out of the otTspringof one female, will on an 

 average survive to produce young. This assumption is not true ; 

 for since only one half of the race, namely the females, bring 

 forth young, it follows that two out of each family must, on 

 the average, survive to have offspring, namely, one male and one 

 female. Each of these will transmit its peculiarities to its 

 descendants. 



I will now quote the writer's words, putting within brackets 

 the necessary corrections. 



He says, " A million creatures ai'e born; 10,000 survive to 

 produce offspring. One of the million has twice as good a 

 chance as any other of surviving ; but the chances are 50 to i 

 against the gifted individual being one of the 10,000 survivors." 

 Further on he says, " Let us consider what will be its influence 

 on the main stock if preserved. It will breed and have a 

 progeny of, say 100 ; now this progeny will, on the whole, be 

 intermediate between the average individual and the sport. The 

 odds in favour of one of this generation of the new breed will 

 be, say, li to I, as compared with the average individual ; the 

 odds in their favour will therefore be less than that of the 

 parent, but owing to their greater number the chances are that 

 about li of them would survive [about 3 of them, for without any 

 advantage two would on an average survive.] Unless these breed 

 together, a most improbable event, their progeny would again 

 apjiroachthe average individual ; there would be 150 [300] of them, 

 and their superiority would be, say in the ratio of I J to I ; the 

 probability would now be that nearly two [6 x f , or nearly 8] of 

 them would survive, and have 200 [750] children with an eighth 

 superiority. Rather more than 2 [15] of these would survive ; but 

 the superiority would again dwindle, until after a few generations 

 it would no longer be observed, and would count for no more in 



the struggle for life than any of the hundred trifling advantages 

 which occur in the ordinary organs." 



The writer thus concludes that the advantage derived by in- 

 heritance from the sport will ultimately die out. The true con- 

 clusion is, that the advantage never dies out, but only becomes 

 distributed through the whole race ; and, moreover, that the 

 sum of the advantages of all the favoured individuals, when 

 added together, is greater than the original advantage, and 

 becomes greater and greater every successive generation, though 

 it lends to a limit at which it never actually arrives. Thus, 

 representing the original advantage by unity, the advantage in 

 the next generation is li, in the next I's, and so on. 



If now the same kind of sport arise independently, (i.e. not 

 by inlieritance from some previous sport) say once in every genera- 

 tion, and is preserved, say once in every fifty generations, the 

 advantages derived by inheritance from these sports will accumu- 

 late and become distributed throughout the whole race. Hence 

 in the course of an immense number of generations they must 

 produce a decided effect upon the character of the race. 



Thus, though any favourable sport occurring once, and never 

 again, except by inheritance, will effect scarcely any change in a 

 race, yet that sport, arising independently in different generations, 

 though never more than once in any one generation, may effect 

 a very considerable change. These conclusions are opposed to 

 those which the writer of the article is endeavouring to establish. 



Leeds Grammar School A. S. Davis 



Prof. Tait on Geological Time 

 As I have lately found, under the signature of Prof. Tait,-in 

 the well-known Rcinie Scietitifique, several statements that 

 would doubtless have been challenged had they appeared in 

 any English scientific journal, and of wh'ch the following are 

 specimens : — " Sir W. Thomson has already demonstrated, by 

 three complete and independent physical proofs, the impossi- 

 bility of admitting the existence of such periods" — " Each one 

 (of Sir W. Thomson's arguments) would suffice to upset at once 

 the pretensions of Lyell and Darwin" — "Professor Huxley's 

 attempt has completely failed ; " and .as in the new edition of 

 Juke's Geology Sir W. Thomson's demonstration is stated at 

 some length, while an adverse argument used by Jukes is omitted, 

 I venture to ask that you will allow me a few words on the 

 subject, since I treated the matter at length two years ago in 

 Scientific Opinion, and, so far as I am aware, my arguments re- 

 mained unanswered. 



1. Does not the conclusiveness of all Sir W. Thomson's argu- 

 ments depend upon the assumption of the universality of the 

 principle of dissipation of energy ? But to assume this is to 

 assume that uniformitarianism is false. The whole question is 

 therefore begged in the premisses, as must be the case in mathe- 

 matical arguments. 



2. As Mayer categorically denies the universality of the said 

 principle, by what right does Sir W. Thomson entitle it a " prin- 

 ciple of natural philosophy," and therefore state that uniformi- 

 tarians are "directly opposed to the principles of natural 

 philosophy " ? As in the opinion of tlie French Academy, and 

 of many eminent English and German savants, Mayer is one of 

 the first physicists in Europe, I think it cannot be assumed with 

 Prof Tait that, "as regards method, M.ayer and his supporters 

 are little in advance of the Middle Ages," though undou'itedly 

 Mayer is very different from Sir W. Thomson. 



3. By what process does Sir W. Thomson discover " univer- 

 sal principles?" His universal principle regarding the origin of 

 life "true through all space and all time," affords an opportune 

 answer to this question. I would simply refer to Mr. Ray Lan- 

 kester's article on that principle (Nature, No. 97, p. 36S), and ask 

 if any ona can discover a more satisfactory foundation for the uni- 

 versal principle of dissipation. From long study of Sir W. 

 Thomson's reasonings, I conclude that he will reject any evidence 

 for spontaneous generation, in consequence of the "universal 

 principle " he has assumed on that (juestion. 



4. In Section A of the last British Association, Sir W. Thom- 

 son supported his argument regarding the form of the earth (con- 

 troverted in your pages by Mr. Croll) by referring to existing 

 mountains five miles high (see .Atheniciim report). His audience 

 must have understood that these mountains are primaeval, as 

 otherwise the argument would have had no meaning. But as this is 

 the reverse of the truth, I cannot help saying that Sir W. Thom- 

 son appears to consider himself entitled, not merely to invent 

 principles, but also to invent facts. I know no conclusions of 



