516 



NATURE 



[September 28, 1893 



the journals, and not a few private ones to ourselves. Of course 

 this copious respon-e was for the most part valueless, further 

 than to show a general belief among fanciers and breeders in the 

 facts of telegony, coupled, however, with great differences of 

 opinion touching the frequency of its occurrence. Nevertheless, 

 out of all this medley of unscientific assertion, there were a com- 

 paratively few cases where it did not appear that coincidence, 

 pre-formed ideas, mal-observation, atavism, &c., could be 

 reasonably assigned, and these served to indicate the most 

 promising varieties with which to work in future experiments. 

 The general result of our inquiry thus far has been to cor- 

 roborate the opinion with which we both started, viz. that 

 although the fact of telegony is of very much rarer occurrence 

 than is generally supposed, it nevertheless does appear to take 

 place occasionally, and especially, as Mr. Herbert Spencer has 

 recently observed, where the first offspring has been a hybrid, as 

 distinguished from a mongrel. 



On the other hand, there does not seem to be any good 

 evidence of the phenomenon in the case of mankind. For 

 although I have met with an alleged instance of a white woman 

 who, after having borne children to a negro husband, had a 

 second family to a white one, in which some negro characteristics 

 appeared, I have not been able to meet with any corroboration 

 of this instance. I have made inquiries among medical 

 men in the Southern States of America, where in the days of 

 slavery it was frequently the custom that young negresses should 

 bear their first children to their masters, and their subsequent 

 children to negro husbands ; but it never seems to have been 

 observed, according to my correspondents, that these subse- 

 quent children were other than pure negroes. Such, however, 

 was not the same case as the one above mentioned, but a recip- 

 rocal case : and this may have made a difference. 



So much, then, for the facts. As regards their interpreta- 

 tion, Mr. Herbert Spencer says, speaking on behalf of the 

 Lamarckians, '■ And now, in the presence of these facts, what 

 are we to say? Simply that they are fatal to Weismann': 

 hypothesis. They show that there is none of the alleged inde 

 pendence of the reproductive cells ; but that the two sets of cell 

 are in close communion. They prove that while the repro 

 ductive cells multiply and arrange themselves during the evolu 

 tion of the embryo, some of their germ-plasm passes into the 

 mass of somatic-cells constituting the parental body, andbecomes 

 a permanent component of it. Further, they necessitate the 

 inference that this introduced germ-plasm, everywhere diffused, 

 is some of it included in the reproductive cells, subsequently 

 formed. And if we thus get a demonstration that the some- 

 what different units of a foreign germ-plasm permeating the 

 organism, permeate also the subsequently-formed reproductive 

 cells, and affect the structures of the individuals arising from 

 them, the implication is that the like happens with those native 

 units which have been made somewhat different by modified 

 functions : there must be a tendency to inheritance of acquired 

 characters." (Contemporary Review, March.) 



On the other hand, Prof. Weismann says that, even admitting 

 the facts, they in no way militate against his theory of germ- 

 plasm. For, as he says, "such cases could be accounted for 

 from our point of view by supposing that spermatozoa had 

 reached the ovary alter the first sexual union had occurred, and 

 had penetrated into certain ova, which were still immature. 

 The immediate fertilisation of the latter is rendered inconceiv- 

 able by the fact of this immaturity ; but the sperm-cell must 

 have remained in the body of the ovum until the maturation of 

 the latter, with the nucleus of which it then united in the process 

 of amphimixis.!' (" The Germ-Plasm," pp. 385-6.) 



It seems to me that we have here, in principle, a sufficient 

 answer to the Lamarckian interpretation of the facts alleged. 

 I say "in principle," because the obvious objection that mam- 

 malian spermatozoa cannot beheld capable of delving their way 

 through the stroma of an ovary in order to reach unripe ova, 

 may be obviated by supposing that it is the " ids " and " deter- 

 minants" of disintegrated spermatozoa which do so. For, if 

 there are anysuch things as ids and determinants, it is certain 

 (from the facts of atavism) that they can survive the disintegra- 

 tion of their containing spermatozoon, and also that they can 

 then penetrate somatic tissues to any extent. 



But I have discussed the whole subject in a lengthy appendix 

 to my recently published "Examination of Weismannism," to 

 which I must refer for all details, both as regards the alleged facts 

 and their rival interpretations, My object in raising the issues 

 in these columns is to ascertain whether further light can be 



NO. 1248, VOL. 48] 



thrown upon the subject by any of your numerous readi 

 Therefore I will merely add that numerous experime 

 which during the last eighteen months I have been conduct 

 with birds, have yielded uniformly negative results. Sec 

 of purely bred ducks (white Aylesbury), and dozens 

 purely bred chickens (Polish) have been hatched ; but in no 1 

 case has there been the smallest resemblance to their telegon 

 sires. In some cases a year, and in others only a fortnight \ 

 allowed to elapse between the successive impregnations ; bal 

 all cases the broods are as purely bred as if their respect 

 mothers had not previously borne olTspring to males of wid 

 different breeds. George J. Ro.maxes 



Christ Church, Oxford, September 16. 



Quaternions and Vectors. 



In his recent letter (Nature, August 17, p. 364), whicl 

 avowedly a reply to my paper (Proc. R.,S.E., 1802-93) 

 " Recent Innovations in Vector Analysis," Prof. Gibbs di 

 not seem to me to discuss the real point at issue. 



At the end of that paper I summarised the arguments 

 favour of quaternion vector analysis under five heads. 



The first of these w.as i " The quaternion is as fundamenta 

 geometrical conception as any that Prof. Gibbs has namet 

 This argument, which was a direct criticism of Prof Gibt 

 attack on quaternions in his letter to Nature of two years ^ 

 is not even referred to in his recent letter. It may reasonal 

 be assumed that silence means consent. 



The second summarised argument was : " In every vecl 

 analysis so far developed, the versorial character of vect( 

 cannot be got rid of." Regarding this, which was a din 

 criticism of the position of Mr. Heaviside and Prof Macfarlar 

 I am glad to find that Prof. Gibbs is virtually at one with me, a 

 brings to my support the great names of Lagrange and Pois.sc 

 Now Hamilton's quaternions is admittedly the only vect 

 calculus which takes direct cognisance and makes full consiste 

 use of this principle, the logical consequences of which form t 

 subject of my third and fourth summarised arguments. Th 

 the quaternion wins all along the line. 



The fifth and last summarised argument was: "T 

 invention of new names and new notations has addi 

 nothing of importance to what we have already learned fro 

 quaternions." This, probably, has most direct connection wi 

 Prof Gibbs's recent letter, which is to a large extent an expoi 

 tion of his own system. And interesting though this may be 

 itself, it does not really make out a case against quaternioni 

 and that, be it remembered, is the point at issue. Indee 

 Prof. Gibbs himself admits that the quaternion notation has 

 certain advantage in simplicity. This is plainly so in the Cl 

 of V, of which in its quaternionic form Prof Gibbs gives a V« 

 neat application in an equation whose physical interpretation 

 the solution of an important problem. But in this very conne 

 tion, carried away by the exuberance of his humour, he seen 

 to imagine that the name Nabla is of the essence of quaternion 

 and that the quaternionist has no right to use the word potentia 



I am not aware that I anywhere expressed a dislike 1 

 the notations [<fi], ips, <f)^, which represent quantities mo 

 emphatically quaternionic, or at least Hamiltonian, in the 

 origin. What I wished to emphasise was that, in gettin 

 at the conception of the quantities <p„ <px. Fro!. Gibl: 

 makes use of the so-called indeterminate product, which is n 

 vector but is analytically the same kind of thing as the quale: 

 nion product, and that consequently his pamphlet and his fin 

 letter to Nature are hardly consistent with each other. 



I am accused of an inadvertence in the interpretation ( 

 certain integrals. I have not Prof Gibbs's pamphlet by me s 

 present, but, if I recollect aright, there is no explicit mentio 

 in it of the restriction that the operand is to be a constant vectoi 

 Nor do I see that such a restriction is necessarily implied in 

 system in which operators, whether under an integral sign 

 not, are represented symbolically apart from the operand. Th 

 operand is virtually there all the time. The equations ar 

 meaningless without it. To introduce the unexpressed operam 

 is therefore a very different thing from the act of introducing ai 

 altogether extraneous vector. With the required restriction 

 however, it appears that Professor Gibbs's integral operators ari 

 not of such general applicability as had been hoped. 



But even granting that I have been guilty of an inadvertenci 

 on this point, that in no way affects the general argument 



