Nov. 23, 1 871 ] 



NATURE 



63 



to ivhich I have no r/ply to make, except that if they thought as we do, 

 they must have ait immortal soul as we have, which is not likely, 

 as we should apply the argument to all animals, such as spongesi 

 oysters," &c. I am sure these ideas are not unfrequently repeated 

 in his correspondence, as for example, in one of his replies to 

 Morus(vol. i. No. 67 of the 4to edition, in Cousin's Edition, x. 

 p. 204 ct set/.). He there even talks of two souls, an ame corpo- 

 relle which is the cause of passions and affections, and an incor- 

 poreal principle of thought, which he elsewhere says was infused 

 by the Deity into man at the first moment of his existence. He 

 also observes, I tliink logically enough, that as no boundary line 

 can be drawn elsewhere, we have no choice between conceding a 

 soul to oysters or refusing it to all animals save man. I am not 

 however concerned to defend the validity of his reasons, but rather 

 to contribute this information as an historical point of interest. 



Trin. Coll., Dublin, Nov. 11 



J. P. Mahaffy 



Plane-Direction 



I THINK " plane-direction " is the best of the competing 

 names. The planes of cleavage in a crystal are the "plane* 

 directions" in which it is most easily split. They cannot 

 be called either "aspects" or "positions." The opposite 

 faces of a cube certainly cannot be said to have the same 

 "aspect." 



If a rigid body receives a movement of translation, it retains 

 something unchanged. What is this something to be called ? 

 It might be called "lie" or "set," but both names are equi- 

 vocal. Two equal and similar figures possessing this something 

 in common might be very well described as " similarly laid," 

 "similarly set," or "similarly placed." We may say that they 

 have " similar positions," but we can scarcely say that they have 

 "the same position ;" for change of position is commooly held to 

 include movements of translation as well as of rotation, and a 

 point is usually defined as having position but not magnitude. I 

 think it is worth while to consider whether "position" cannot 

 be restricted to the more limited sense, "place " being employed 

 in the wider sense. 



I wonder that no one has yet raised a murmur against the 

 proposition itself, which your correspondents are so anxious to 

 render literally into English. It appears to me that the plain 

 English form in which Mr. Wilson first stated it is clearer and 

 more precise than the German abridgement. In the strictest 

 sense of "determine," one "Richtung" determines one " Stel- 

 lung" and one "Stellung" determines one "Richtung," inas- 

 much as to one plane-direction there corresponds one normal 

 direction. 



In a special sense it is true that two " Richtungs " determine 

 a third (tjerpendicular to them both), and that two " Stellungs " 

 determine a third (also perpendicular to both) ; just as two points 

 may be said to determine one plane (bisecting their joining line 

 at right angles). In all these instances the fact is that not one 

 only but many are "determined," but all except one come 

 out in pairs or multiples of two. It is this one, which has no 

 fellow, that is in a special sense "determined." 



I think it is paradoxical and misleading to state, without quali- 

 fying words, that two linean directions determine one plane- 

 direction ; inasmuch as two linean directions really serve to define 

 as many different pairs or multiple pairs of plane-directions as 

 we please, and if we are permitted to distmguish the two linean 

 directions by dtfferent names, tluee plane directions can be sepa- 

 rately defined by them without any ambiguity. Similar remarks, 

 of course, apply to the other half of the proposition. 



J. D. Everett 

 Rushmere, Malone Road, Belfast, Nov. 1 1 



" Wormell's Mechanics " 



Will you do me the favour of inserting a brief reply to the 

 few remarks made concerning the above text-book in last week's 

 Nature? 



I. On page 8 of the book occurs an explanation of what is 

 usually termed the transmissibility of force, and a statement of the 

 axiomatic principle that we may imagine a force to be applied at 

 any pomt in the line of its direction, pm'uled this point be 

 rigidly connected with the first point of application. On page 

 14 a deduction from this principle is made and employed to prove 



the rule for finding the directions of the resultant of two forces 

 acting on a point. The reviewer says that this deduction, "if 

 true, would assert that the attraction of the sun and the earth upon 

 the moon might be transferred to any heavenly body in space 

 which happened to be in the line of direction of tlie resultant of 

 the forces." If the restriction laid down with emphasis in the 

 book, and printed in italics as quoted above, be not ignored, this 

 is a legitimate inference, and if the point to which the forces are 

 transferred parallel to themselves be rigidly connected with the 

 moon, any conclusion having reference to the magnitude or 

 direction of the resultant action on the moon derived as a con- 

 sequence of the imaginary transposition of the pomt of applica- 

 tion of the forces will be correct. 



2. In finding the direction of the resultant of two parallel 

 forces, the same transposition of the point of application is 

 employed, and, of course, it is understood with the same proviso. 

 This proof your reviewer qualifies as "meaningless," whereas I 

 feel sure that, taken in connection with the original axiom and 

 the deduction above referred to, it would be accepted by any 

 mathematician as both intelligible and correct. 



3. The next statement is that the definition of a rigid body is 

 given as a property of forces. This is not so, but the whole 

 theory of statics, when developed independently of dynamics, 

 rests on the properties of a force and the properties of a rifid 

 body jointly. '^ 



4. The reviewer next dwells upon a curious error which un- 

 fortunately escaped my notice until it was pointed out but a short 

 time ago by a schoolboy, and which forms one of three corrections 

 on a slip of errata. Any student would, however, have been 

 able to make the correction for himself by the help of the pre- 

 ceding pages and the applications to the following exercises, a 

 circumstance which I think an unprejudiced critic should not have 

 overlooked. 



5. Your reviewer next remarks that a student who tries an 

 experiment with a block and tackle would naturally be sur- 

 prised at finding that the result of experiment does not agree 

 with that of the theory, and adds, "nor can we find a single 

 word in the book whicli would enlighten his difficidty. " The 

 reviewer cannot have read section 71. 



6. The subjects mcludedin the book are such as comprise the 

 course described in the curriculum and examination papers of the 

 University of London, and if occasionally the discussion of un- 

 practical arrangements of mechanical powers is required, I am 

 not answerable. Indeed, I hope to see the day when a reform of 

 this part of the curriculum will necessitate my rewriting the work 

 on an entirely different plan, namely, one according to which 

 kinematics forms the first part, kinetics the second, and statics 

 the third, the propositions of the third part being special cases 

 of those of the second. But that at present it answers the pur- 

 pose for which it is intended, is proved by the fact that all the 

 questions set this year can be answered from it. 



So far as most of the facts and illustrations are concerned, "I 

 am but a gatherer and disposer of other men's stuff, " and a writer 

 of an elementary text-book to suit the requirements of a particu- 

 lar examination could not easily be more. 



The tone of depreciation with which the \vTiter of the article 

 has been pleased to refer to the work, so directly opposed to a 

 previous notice of the same book in the same journal, seemed 

 to me to call for some reply, and I should wish to describe more 

 fully the objects I have aimed at in compiling the work, but that 

 I know I have already taken up enough of your valuable space. 

 Richard Wormell 



ONE OF THE GREATEST DIFFICULTIES OF 

 THE DARWINIAN THEORY 



CIR JOHN LUBBOCK has done good service to 

 "^ science in directing attention to the metamorphoses 

 of insects, by admitting freely the great difficulty in con- 

 ceiving " by what natural process an insect with a suctorial 

 mouth, like that of a gnat or butterfly, could be developed 

 from a powerful mandibulate type like the Orthoptera, or 

 even from that of the Neuroptera " (Nature for Nov. 

 9, page 28). Such " difficulties " have struck many from 

 the first, and it is in no small degree encouraging to those 

 who love the hberty of science, to find that the time is ap- 



