586 



NATURE 



[October 20, 1892 



taining four British species (Verrall, " Cat. Brit. Dipt.," 1888) ; 

 ot these most if not all resemble various Hymenoptera. The 

 commonest and most remarkable is V. bombylans, which may 

 be seen in any English hedgerow on a sunny day in early sum- 

 mer. This fly exhibits the rare condition of existing in two dis- 

 tinct forms in both sexes. The one form is black with a red- 

 tail, in no small degree resembling a small worker of a red- 

 tailed humble-bee. such as B. lapidarius L. or B. De7-ha7neUus 

 Kirb. The other form has ayello y border to the thorax, yellow 

 hairs on the antero-lateral parts of the abdomen, and a grey tail, 

 to an equal degree resembling a small worker of one of the 

 several yellow banded humble-bees, e.g. B. hortoriim L,, 

 B. terrestris L., or B. Scrimshiranus Kirb. Both varieties 

 occur in both sexes and are about equally common. The prob- 

 lem of the evolution of these distinct forms is thus one of the 

 most complex. Some may ask. If the varieties are thus distinct, 

 how are they known to be one species ? The evidence of this 

 is (i) that no point of structure can be found to differentiate 

 them, (2) that males of the one variety have been seen coupled 

 with females of the other and vice versa (Macquart, "Suites a 

 Buff.," p. 479; Zeller, Stet. ent. Ztg., 1842, p. 66), and 

 lastly (3) that intermediate forms have been found as rarities 

 (Erichson, Siet. ent. Ztg., 1842, p. 115). This evidence 

 may not satisfy all, but as regards Mr. Poulton the identity of 

 the two as one species is not in dispute, for he admits this. 



But though the likeness of V. bombylans L. and its var. 

 mystacea L. { = phimata de Geer) to the red-tailed humble-bees 

 and to the yellow-banded humble-bees respectively, is really 

 close, neither these forms nor the less common var. Jucmorrhoid- 

 alisZi. present any special likeness to B. niuscorum L., which 

 ha.s a bright brown thorax and a grey abdomen. It is true that 

 Kiinckel has spoken of a resemblance between the var. 7nys- 

 tacea and B. niuscorum, but it is hard to see upon what ground, 

 for indeed it is much as if one were to liken a tabby cat to a 

 fox. As Kiinckel himself says, the great resemblance of the fly 

 is to the yellow-banded B. hortorum. 



To return to Mr. Poulton's statement, he says that the 

 two varieties prey upon ^'■Bovibus muscoi-utn and B. lapidarius, 

 and are respectively like these Hymenoptera." These words 

 contain an ambiguity which I cannot believe intentional. But 

 supposing for a moment that one of the varieties 7vere like B. 

 viuscorum (which it is not), the sentence must be taken to mean 

 that each variety preys upon the species of bee which it most 

 resembles, the red-tailed variety on the red-tailed bee and the 

 yellow variety on the other. This is indeed demanded by the 

 hypothesis of " Aggressive Mimicry." In this form the state- 

 ment is often made, though I never met it elsewhere in print. 

 I invite Mr. Poulton to produce observations in support of that 

 statement. If he will establish it he will do a useful work. 

 When this statement was written I must believe that Mr. Poul- 

 ton had not read the several authorities on the subject, many 

 of whom relate how both varieties have been reared from the 

 nests of each type of bee, both from the red-tailed and from 

 the yellow-banded (Kiinckel, p. 58 ; Drewsen, Stet. ent. Ztg., 

 1847, p. 211; F. Boie, Kroyer's "Naturh. Tids.," 1838, 

 p. 237). It is still possible that both varieties are born of one 

 mother, and it is possible, too, that each female does her best 

 to choose the nest of a bee like herself, but in support of this 

 hypothesis I know no evidence; and indeed Kiinckel (p. 58), 

 after considering this possibility, gives it as his opinion that 

 probably the varieties of V. bombylans lay indifferently in the 

 nests of all Botnbi. From the omission of these facts, which to 

 an appreciation of the evidence are vital, we should infer that 

 Mr. Poulton was not acquainted with Kiinckel's work, were 

 it not that he repeats Kiinckel's selection of B. muscorum as a 

 form resembled by one of the two varieties. 



But though Mr. Poulton is wrong in saying that either variety 

 specially resembles B. muscorum, he is right in saying that 

 V. bombylans preys on this bee's nests, for both varieties have 

 been bred from them, even from the same nest (Kiinckel, p. 

 58), In my rooms at this moment are several nests of B. mus- 

 corum, each containing many larvge of V. bombylans, resting 

 for the winter, to emerge in summer, as I hope. 



There is then evidence that the two varieties, though they 

 may breed together, yet remain substantially distinct ; and that 

 though they respectively resemble different species of bees, 

 they are both found together, not only in nests of bees which 

 they resemble, but also, and in my own experience, more 

 abundantly, in the nests of another bee which they do not 

 resemble. 



NO. II 99, VOL. 46] 



Mr. Poulton further omits to mention that V. pellucem, 

 though in nowise resembling the common wasp, yet lives in its 

 nests, together with V. inanis which does resemble a wasp, and 

 V. zonaria which is like a hornet (Kiinckel, pp. 54 and 55). 

 This fact also I commend to Mr. Poulton's ingenuity. 



The publication of statements like this of Mr. Poulton's, 

 omitting most salient facts— facts, besides, which, though 

 adverse to his speculations, add a ten-fold interest to the sub- 

 ject—is surely unfortunate. It may be replied that Mr. 

 Poulton's book is of a popular character and does not aim at 

 the completeness of scientific work ; but in making choice of 

 evidence, even for popular exposition, it is well to remember 

 that the value of facts is not to be measured by the ease with 

 which they may be momentarily fitted to the sustenance of a 

 facile hypothesis. William Bateson. 



St. John's College, Cambridge, October 9. 



Induction and Deduction. 



Miss Jones agitates a question that ought not to settle 

 down without having caused that discussion which its propound- 

 ing is fit to awaken. 



This discussion does not, however, relate to the mutual rela- 

 tions of Induction and Deduction — at least, not as the main topic 

 thereof. It relates to the fragmentary condition of that which 

 is usually referred to and accepted as logic. We are so apt to 

 take it for granted that our so-called logic is tolerably competent 

 and complete as an account of human reasoning in general, 

 that it is of great utility when some one — as Miss Jones does 

 now — raises a question that is adapted to direct our reflections 

 towards some one of the several, perhaps many, gaps that exist 

 in that most important, but too often not understood and mis- 

 understood, branch of science. It is with this specially in view 

 that I have ventured to write this. 



In geometry nothing is more usual than to draw a universal 

 conclusion from a case that, to all ordinary ways of apprehen- 

 sion, seems to be a single instance. Indeed, this is one of the 

 cardinal features of geometrical reasoning. Perhaps we might 

 well say that it is the most characteristic feature. It is this 

 feature that the question that Miss Jones agitates ought to call 

 into prominent notice. 



She selects for her purpose the case of the isosceles triangle, 

 and asks, How, from premising that the angles at the base of an 

 (one) isosceles triangle are equal to each other, are we logically 

 warranted in concluding that that same equality is true of all 

 isosceles triangles ? 



That we do thus conclude is known to all, as is also the truth 

 that such a conclusion is a typical one in geometry. Nor have 

 we, nor can we have, the least misgiving as to the rigorous 

 validity of such conclu>ions. 



It would be a digression for me to point out here the essential 

 characteristics of that form of reasoning which, properly speak- 

 ing, is induction. It is sufficient for my present purpose to 

 remark that true induction is utterly unable to yield us any con- 

 clusion that is more than probable and approximate. 



From these characteristics alone we may know that our 

 geometrical conclusions in view are not, as Miss Jones takes 

 them to be, inductive conclusions. 



But since our geometrical conclusions are natural and val id, 

 the question still remains, What sort of conclusions are 

 they? 



If we propose to call them deductive conclusions, then, when 

 we revert to the array of syllogisms, categorical, hypothetical, 

 disjunctive, dilemmatic, &c., we find none of them, nor any 

 combination of them, that can by any means be made applicable. 

 We have to get not merely from an apparently particular but 

 from an apparently absolutely singular proposition to a univer- 

 sal one. To do this deductively, the body of doctrines and 

 canons, that is usually called logic, confesses itself wholly 

 unable. It lays down as one of its cardinal rules, one that it 

 declares is "founded upon the Laws of Thought," that if any 

 premise is particular, then only a particular conclusion can be 

 drawn. 



Nevertheless, I am going to submit that the reasoning under 

 discussion is a true instance, not of induction, but of deduction. 

 I submit that the reasoning that we do actually follow is that 

 which may be formulated thus : — 



This isosceles triangle is any isosceles triangle. 



The angles at the base of this isosceles triangle are equal to 



