78 



NA TURE 



[November 24, 1892 



as it is inconsistent with many ascertained facts which were 

 specified in my first letter, the hypothesis of "Aggressive 

 Mimicry " should surely be withdrawn. 



No speculation is needed to enhance the exceptionally inter- 

 esting facts of the Variation and the resemblances of the Volti- 

 ceUcc. If a number of people will set to work on this problem 

 in the way suggested, there is, I think, a fair chance of consider- 

 able results. It was in the hope that such effort may be made 

 that I drew attention to the matter, and I am really sorry that 

 Mr. Poulton should be hurt thereby. Nevertheless, I cannot 

 but regard his account of the matter as an example of the way 

 in which statements pass on from one writer to another, but 

 prove on inquiry to be baseless. William Bateson. 



St. John's College, Cambridge, November 14. 



Parasitism of Volucella. 



Mr. Bateson's interesting discussion of the relations between 

 Volucella and the species of Bombus (Nature, vol. xlvi. p. 

 585) suggests the following observations: — The nest of B. 

 muscorum is made without much effort at concealment on the 

 surface of the ground. If accidentally disturbed the inmates 

 set up a peevish buzzing, which, no doubt, answers the purpose 

 of warning off ordinary intruders. Yet B, muscorum is of a 

 patient and gentle disposition, and will put up with a good deal 

 of maltreatment before using its sting. Its sting, moreover, is 

 less venomous than that of either of our other common humble 

 bees. It apparently trusts to the reputation of its genus for 

 protection from annoyance. Such a creature would seem 

 marked out by Nature as the very host to be imposed on by a 

 parasite like Volucella, which, on the other hand, may need 

 all its cunning to come round an irascible being like B. lapi- 

 darius, or even like B. hnrtorum. And, in fact, as Mr. Bateson 

 points out, we find it multiplying abundantly at the expense of 

 the first named bee, and less frequent in the nests of the other 

 two. Notwithstanding this, B. viuscorum appears to be 

 certainly no less successful than either of the others in the 

 struggle for existence. W. E. Hart. 



Falmore, Carrowmena, co. Donegal. 



Optical Illusions. 



The illusion of the Gothic arch in Nature(vo1. xlvii. p. 31) is 

 too good to have a rival, but simple Norman arches occasionally 

 practise a deception of some subtlety. In certain cases they seem 

 to be of the Moorish horse-shoe form ; this happens when the 

 semicircle does not spring at once from the capitals of the Norman 

 columns, but has a short intervening vertical space of masonry. 

 Architects are familiar with the effect, and call these arches 

 stilted ; they say the stilts are commonly vertical, although 

 Norman walls have no doubt sometimes fallen away from the 

 upright course. I suppose the eye is quick enough to perceive 

 that there is more than a semicircle, while the mind is gullible 

 enough to infer that the curvature is continued. In Winchester 

 Cathedral there are some good illustrations of this appearance. 



Winchester College, November 12. W. B. Croft. 



A Strange Commensalism— Sponge and Annelid. 



A CURIOUS case of what I believe to be definite commen- 

 salism between members of these two classes came under my 

 notice the other day when collecting, and, as it is, so far as I 

 know, a new instance in this interesting inter-relationship 

 between animals, I venture to record it. 



Several large patches of crusting orange red sponge attracted 

 my attention because of the peculiarly emphatic markings of 

 what appeared to be the oscula. They were suspiciously unlike 

 anything spongiform, so I secured some good pieces of the sponge 

 for further investigation. Sections proved them to belong to the 

 Microciona plumosa of Bowerbank, but the supposed oscula — 

 which to the naked eye appeared as innumerable tiny black 

 specks, each surrounded by a grey ring — proved to be, when the 

 mass was teased out in water, in reality the ends of tubes 

 inhabited by an eyeless Leucodore {L. caeca, Qirsted). Fully 

 forty could frequently be counted in a square inch. 



The conclusion I come to after examination of a large number 

 of specimens is that actual benefit is mutually given and received 

 by each of the two messmates ; the sponge gaining considerable 

 support and extra consistency from the numerous comparatively 

 wiry upright tubes. There is also the question whether the 

 excreta of the worms is of any food value to the sponge. On 

 the part of the worm, there is little doubt that it finds a valuable 



NO. 1204, VOL. 47] 



protector in the sponge which by the way is characterized by an 

 intensely rank .smell of garlic (warning odour?). I have seen no 

 signs of this sponge being preyed upon by any animal, so we 

 may conclude its protective devices of spicules, odour or taste 

 are fairly successful. A worm whose tube is sunk completely in 

 its substance will naturally be very safely housed, and besides, 

 the friendly water- currents set in motion by the sponge cilia will 

 bring much food matter to its very mouth. 



Bowerbank in his description (" Br. Spongiadae," vol. ii. 

 p. 134) writes of a specimen as "permeated by some small 

 tubular zoophyte which it has coated with its own tissues, and 

 from these adopted columns defensive spicula are projected " — 

 evidently the same as I describe above, though he makes the 

 mistake of considering the tubes as those of zoophytes instead 

 of those of annelids. From this quotation, however, it is 

 evident that the habit is widely spread, and not merely local. 

 Here at extreme low-water the sponge grows exceedingly 

 abundant, and the commensal worm seems always present. 



James Hornell. 



Jersey Biological Laboratory, November 10. 



Induction and Deduction. 



Mr. Dixon says that there are "at least three different kinds 

 of interpretation which may be put upon the proposition, [An 

 isosceles triangle has equal angles at the base]. It may mean 

 (i) the triangle used to illustrate this proposition has equal sides, 

 therefore it has equal angles ; or (2) I have conceived a triangle 

 which has equal sides, therefore I have conceived one which has 

 equal angles ; or (3) the connotation ascribed by the adjective 

 isosceles implies the connotation ' having equal sides ' [? angles]." 



He goes on to observe that the difference between either (i) 

 or (2), and (3) is " that this latter gives us no information about 

 any real thing or concept, but only about what is implied by 

 using certain terms," that is, about the connotations of "isosceles" 

 and "having equal angles " (" equal sides " is of course a slip). 

 But if connotation refers neither to the attributes of "real 

 things" nor to "concepts" (which I suppose means ideas or 

 notions) what can it be that we "imply" by using the terms 

 isosceles, &c. ? If we do not mean things, nor attributes, of 

 things, nor ideas, do we mean anything which can convey or 

 contain information ? 



In Mr. Dixon's view the terms do convey information, but 

 information which "clearly does not require to be based upon 

 any real knowledge of things, but may be based solely on 

 definitions of words." But must not definitions of words be 

 based, in the last resort, upon knowledge either of things or of 

 concepts — definitions of current words in some current sense, 

 or even of strange words in strange senses— as e.g. if I say Abra- 

 cadabra means ixtra-mixtra, and Triangle means abracadabra, 

 and all abracadabras are four-sided, and so on? With .such 

 propositions I may certainly frame syllogisms and arrive at 

 "symbolical" conclusions, though I cannot see that I shall be 

 doing anything to convey information or to advance thought. 



And when Mr. Dixon says that the proposition "an isosceles 

 triangle has two equal sides" has "wide applicability and use- 

 fulness" because we "often find things which can fairly be 

 called isosceles triangles," it seems clear that he himself cannot 

 have taken the proposition at starting in a sense purely 

 "symbolic" (in his meaning of that word). If he did, it would 

 be little less than miraculous that an entirely arbitrary definition 

 should happen so to fit actual experience, especially when we 

 consider that other equally symbolical mathematical propositions 

 have an equal applicability. 



I think it is probably true that we often do not depend, for 

 our assent to complicated reasonings, on anything like full 

 "realization in succession of the actuality of the relations and 

 operations discussed " ; but I cannot admit that such reasonings 

 do not refer to objects of experience or of thought. Unless the 

 terms did refer to something other than themselves, we could 

 never assert S is P, ox x = y. 



I unfortunately know nothing either of Pascal's theorem or of 

 the intersections of two conies ; but I think that in the case of 

 the individual isosceles triangle, my intuition that the equality 

 of angles at the base is inseparably connected with equality of 

 sides, gives me ample ground for believing it to be " mathema- 

 tically certain" that every isosceles triangle has equal angles at 

 the base ; it is self-evident that the one characteristic cannot 

 exist without the other. That the isosceles triangle in question, 

 if put under a microscope or tested by some micrometer, might 

 turn out to be not "really" isosceles, seems to be a perfectly 



