March 13, 1890] 



NATURE 



439 



place at which he does invoke the assistance of reversed selec- 

 tion is exactly the place at which reversed selection must neces- 

 sarily have ceased to act. This place, as already explained, is 

 where an obsolescent organ has become rudimentary, or, as 

 above supposed, reduced to 5 per cent, of its original size ; and 

 the reason why he invokes the aid of reversed selection at this 

 place is in order to save his doctrine of "the stability of germ- 

 plasm." That the force of heredity should finally become ex- 

 hausted if no longer maintained by the presence of selection, is 

 what Darwin's theory of perishable gemmules would expect to 

 be the case, while such a fact would be fatal to Weismann's 

 theory of an imperishable germ-plasm. Therefore he seeks to 

 explain the eventual failure of heredity (which is certainly a fact) 

 by supposing that after the point at which the cessation of selec- 

 tion alone can no longer act (and which his first oversight has 

 placed some 70 per cent, too low), the reversal of selection will 

 begin to act directly against the force of heredity as regards the 

 diminishing organ, until such direct action of reversed selection 

 will have removed the organ altogether. Or, in his own words, 

 "The complete disappearance of a rudimentary organ can only 

 take place by the operation of natural selection ; this principle 

 will lead to its diminution, inasmuch as the disappearing struc- 

 ture takes the place and the nutriment of other useful and im- 

 portant organs." That is to say, the rudimentary organ finally 

 disappears, not because the force of heredity is finally exhausted, 

 but because natural selection has begun to utilize this force 

 against the continuance of the organ — always picking out those 

 congenital variations of the organ which are of smallest size, 

 and thus, by its now reversed action, reversing the force of 

 heredity as regards the organ. 



Now, the oversight here is that the smaller the disappearing 

 structure becomes, the less hold must "this principle" of 

 reversed selection retain upon it. As above observed, during the 

 earlier stages of reduction (or while co-operaling with the 

 cessation of selection) the reversal of selection will be at its 

 maximum of efficiency ; but, as the process of diminution con- 

 tinues, a point must eventually be reached at which the reversal of 

 selection can no longer act. Take the original mass of a now 

 obsolescent organ in relation to that of the entire organism of 

 which it then formed a part to be represented by the ratio 

 I : ICXD. For the sake of argument we may assume that the mass 

 of the organism has throughout remained constant, and that by 

 " mass " in both cases is meant capacity for absorbing nutriment, 

 causing weight, occupying space, and so forth. Now, we may 

 further assume that when the mass of the organ stood to that of 

 its organism in the ratio of I : too, natural selection was strongly 

 reversed with respect to the organ. But when this ratio fell 

 to I : icxx), the activity of such reversal must have become 

 enormously diminished, even if it still continued to exercise any 

 influence at all. For we must remember, on the one hand, that 

 the rever.-al of selection can only act so long as the presence of a 

 ■diminishing organ continues to be so injurious that variations in 

 its size are matters of life and death in the struggle for existence ; 

 and, on the other hand, that natural selection in the case of the 

 diminishing organ does not have reference to the presence and 

 the absence of the organ, but only to such variations in its mass 

 as any given generation may supply. Now, .the process of re- 

 duction does not end even at l : 1000. It goes on to i : 10,000, 

 and eventually i : cc. Consequently, however great our faith in 

 natural selection maybe, a point must eventually come for all of 

 us at which we can no longer believe that the reduction of an 

 obsolescent organ is due to this cause. And I cannot doubt 

 that if Prof. Weismann had sufficiently considered the matter, 

 he would not have committed himself to the statement that 

 "the complete disappearance of a rudimentary organ can only 

 take place by the operation of natural selection." 



According to my view of the matter, the complete disappear- 

 ance of a rudimentary organ can only take place by the cessation 

 of natural selection, which permits the eventual exhaustion of 

 heredity, when heredity is thus simply left to itself. During all 

 the earlier stages of reduction, the cessation of positive selection 

 ■was assisted in its work by the activity of negative or reversed 

 selection ; but when the rudiment became too small for buch 

 assistance any longer to be supplied, the rudiment persisted in 

 that greatly reduced condition until the force of heredity with 

 regard to it was eventually woin out. This appears to me, as 

 it appeared to me in 1874, the only reasonable conclusion that 

 can be drawn from the facts. And it is because this conclusion 

 is fatal to Prof. Weismann's doctrine of the permanent "sta- 

 bility " of germ-plasm, while quite in accordance with all 



theories which belong to the family of pangenesis, that I deem 

 the facts of degeneration of great importance as tests between 

 these rival interpretations of the facts of heredity. It is on this 

 account that I have occupied so much space with the foregoing 

 discussion ; and I shall be glad to ascertain whether any of the 

 followers of Prof. Weismann are able to controvert the view.s 

 which I have thus re-published. 

 London, February 4. George J, Romanes, 



P.S. — Since the above article was sent in. Prof. Weismann 

 has published in these columns (February 6) his reply to a 

 criticism by Prof. Vines (October 24, 1889). In this reply he 

 appears to have considerably modified his views on the theory 

 of degeneration ; for while in his essays he says (as in the pas- 

 sage above quoted) that " the complete disappearance of a rudi- 

 mentary organ can only take place by the operation of natural 

 selection " — i.e. only by the reversal of selection, — in his reply 

 to Prof. Vines he says, "I believe that I have proved that 

 organs no longer in use become rudimentarj', and must finally 

 disappear, solely by 'panmixia' ; not through the direct action 

 of disuse, but because natural selection no longer sustains their 

 standard structure" — i.e. solely by the cessation of selection. 

 Obviously, there is here a flat contradiction. If Prof. Weis- 

 mann now believes that a rudimentary organ " must finally dis- 

 appear solely " through the zvithdrawal of selection, he has 

 abandoned his previous belief that "the complete disappear- 

 ance of a rudimentary organ can only take place by the operation 

 of selection. " And this change of belief on his part is a matter of 

 the highest importance to his system of theories as a whole, since 

 it betokens a surrender of his doctrine of the "stability "of germ- 

 plasm — or of the virtually everlasting persistence of the force of 

 heredity, and the consequent necessity for a reversal of this force 

 itself (by natural selection placing its premium on minus instead 

 of on plus variations) in order that a rudimentary organ should 

 finally disappear. In other words, it now seems he no longer 

 believes that the force of heredity in one direction (that of sus- 

 taining a rudimentary organ) can only be abolished by the active 

 influence of natural selection determining this force in the oppo- 

 site direction (that of removing a rudimentary organ). It seems 

 he now believes that the force of heredity, if merely left to itself 

 by the withdrawal of natural selection altogether, will sooner or 

 later become exhausted through the mere lapse of time. This, of 

 course, is in all respects my own theory of the matter as origin- 

 ally published in these columns ; but I do not see how it is to 

 be reconciled with Prof. Weismann's doctrine of so high a degree 

 of stability on the part of germ-plasm, that we must look to the 

 Protozoa and the Protophyta for the original source of congenital 

 variations as now exhibited by the Metazoa and Metaphyta. 

 Nevertheless, and so far as the philosophy of degeneration is 

 concerned, I shall be very glad if (as it now appears) Prof. 

 Weismann's more recent contemplation has brought his prin- 

 ciple of panmixia into exact coincidence with that of my cessa- 

 tion of selection. — G. J. R, 



Newton in Perspective, 



The interesting modern science termed by the Germans Geo- 

 metrie der Lage, and by the French and other Latin peoples 

 giometrie de position, may be traced in germ to that part of 

 Newton's "Principia" which deals with the construction of 

 curves of the second order, and to what has survived in tradi- 

 tion of Pascal's lost manuscript entitled " Trait e complet des 

 Coniques." The more recent developments of this important 

 subject cast much new light upon Newton's propositions, many 

 of which we are now enabled to solve by easier and more direct 

 methods. A noteworthy example is here fully worked out, in 

 order to show how problems which Newton solved by indirect 

 and circuitous processes may be solved more simply by the aid 

 of modern graphics. 



Problem. — Given the four tangents EA, AB, BC, C'D (Fig. 

 l), as well as a point of contact ; to construct the conic. — First 

 it will be necessary to give some faint idea of Newton's solution 

 of this problem, without entering upon details which can be 

 found in the Latin edition of the "Principia" edited by Sir 

 William Thomson and Prof. H. Blackburn. Having expounded 

 at great length a general theorem for the transformation of 

 curves, Newton transforms the quadrilateral figure formed by 

 the four tangents into a parallelogram. Then he joins the given 

 point of contact y, transformed according to the same principle 

 as the given four tangents, to the centre O of the parallelogram 



