5^4 



NATURE 



\Oct. ii, 1888 



tried by students attending the lectures at the Finsbury 

 Technical College, who, as is stated in the preface, 

 written by Prof. John Perry, have worked through them 

 and obtained "a real good working knowledge of the 

 application of the principles of mechanics and machine 

 design ; . . . their knowledge was always ready for use." 



The examples, as a rule, are thoroughly practical, and 

 may be taken as illustrating Prof. J. Perry's book on 

 " Practical Mechanics," and Prof. Unwin's book on 

 " Machine Design." 



To make the volume more complete, useful rules and 

 constants, together with tables of sines, cosines, tangents, 

 and cotangents, of angles from 1° to 45 , are added, 

 concluding with a table of the squares, cubes, square 

 roots, cube roots, and reciprocals of all numbers from 1 

 to 100, and of approximate fifth roots from 1 to 1000. 



A Text-book of Physiology. By M. Foster, F.R.S- 

 Fifth Edition. Part I. comprising Book I. (London : 

 Macmillan and Co., 1888.) 



This work was originally published in 1876, and it has be- 

 come so widely known that we need not now do much more 

 than note the appearance of the first instalment of a new 

 edition. In this edition— the fifth— considerable changes 

 and additions have been made. The changes, however, 

 do not affect the character of the book ; and Prof. Foster 

 explains that the additions, with the exception of the 

 histological paragraphs, are caused, not by any attempt to 

 add new matter or to enlarge the general scope of the work, 

 but by an effort to explain more fully and at greater length 

 what seem to him to be the most fundamental and most 

 important topics. He has introduced some histological 

 statements, not with the view of in any way relieving the 

 student from the necessity of studying distinct histological 

 treatises, but in order to bring him to the physiological 

 problem with the histological data fresh in his mind. 

 Hence in dealing with the several histological points 

 the author has confined himself to matters having a 

 physiological bearing. This first part will be followed as 

 soon as possible by the second and third parts. 



The Analysts Laboratory Companion. By Alfred E. 



Johnson. (London : J. and A. Churchill, 1888.) 

 During the past four years, Mr. Johnson has had in every- 

 day use in the laboratory a manuscript book of factors 

 and tables. The work grew by constant additions, made 

 as required ; and in the end, as he explains in the preface, 

 it became complete enough to encourage him in the belief 

 that it might prove useful to analysts generally. Accord- 

 ingly he has issued the present little volume, and no 

 doubt he is right in thinking that the large amount of 

 labour involved in the calculation of the many original 

 tables here published may be found to save much of the 

 time otherwise required by the analyst in working out the 

 results of analysis. For the convenience of students not 

 well acquainted with logarithms, of which he has made free 

 use, he has given an account of them, adding examples 

 fully worked out and chosen so as to include and 

 explain the difficulties generally felt in connection with 

 this subject. 



LETTERS TO THE EDITOR. 



[The Editor does not hold himself responsible for opinions 

 expressed by his correspondents. Neither can he under- 

 take to return, or to correspond with the writers of, 

 rejected manuscripts intended for this or any other part 

 of Nature. No notice is taken of anonymous communi- 

 cations, ,] 



Prophetic Germs. 



I regret to find that I put an erroneous interpretation upon 



the phrase "non-significant organs," as used by Prof. Ray 



Lankester. I never doubted that it meant organs or structures 



which were non-significant in respect to actual use; that, in 



short, it was his phrase for what other men have variously called 

 aborted or rudimentary organs. He now explains that " non- 

 significant," in his terminology, means any variation from 

 hereditary forms which is fortuitous — as unknown in respect to 

 its origin as it is in respect to its actual or future use. Although 

 I see no value in this phrase as descriptive of anything that 

 exists, I see great value in Prof. Ray Lankester's admission that 

 natural selection cannot act upon any structure which is not 

 already developed up to the stage of actual use. This is really 

 all I want for my previous argument, because all organs what- 

 ever do actually pass through rudimentary stages in which actual 

 use is impossible. In no possible case, therefore, can selection 

 explain the origin of any organic structure. I rejoice to find Prof. 

 Ray Lankester denouncing as "an absurdity " the idea that ' ' con- 

 genital variations are selected when they are not of any actual 

 use." It must therefore be quite according to the admitted 

 constitution and course of Nature that we should find organs 

 " on the rise, " as well as organs "on the wane." AH germs 

 must be prophetic of their future use, so long as they are in 

 germinal stages ; and, if evolution be true, the world ought 

 always to have been full of them, and ought to be full of them 

 now, unless the creative or evolutionary work has been arrested, 

 at least locally, and for a time. Argyll. 



Inveraray, Argyllshire, October 8. 



The Geometric Interpretation of Monge's Differential 

 Equation to all Conies. 



With reference to the remarks of " R. B. H." (Nature, 

 June 28, p. 197) on my interpretation of the. differential equa- 

 tion to all conies, I wish to point out that the objections he 

 seems to take do not appear to be well founded. The difficulty 

 he finds is that the geometrical interpretation given amounts to 

 the fact that " a conic is a conic." But it is easy to see that 

 there is no peculiarity in this ; it arises simply from the well- 

 known fact that all the geometrical properties of any given 

 figure are inter-dependent : one of them being given, the others 

 may be deduced as legitimate consequences from it. " R. B. H." 

 takes the proposition which constitutes my interpretation, and 

 then, coupling it with the other theorem that the osculating 

 conic of any conic is the given conic, comes to the conclusion 

 that a conic is a conic, and, apparently, he takes it to be very 

 strange ; but, as a matter of fact, given any two properties of a 

 conic (or of any other curve), we can only come to the conclusion 

 that the conic is a conic (or that the given curve is what it pro- 

 fesses to be). Take, for example, the geometric interpretation 

 of the differential equation of all right lines, which is q = o ; it 

 simply means that the curvature vanishes at every point of every 

 right line, which is equivalent to the fact that a straight line is 

 not curved, or that a straight line is a straight line. There is 

 certainly nothing strange in this : it is the legitimate effect of 

 the process employed. Would " R. B. H.," on this ground, 

 reject the geometrical interpretation of the differential equation 

 of all straight lines ? Surely the process is nothing but a piece 

 of quite unobjectionable verification. Similarly, the differential 

 equation of all circles, (1 +p''-)r- 3pq' 2 = o, means that the 

 angle of aberrancy vanishes at every point of every circle. Com- 

 bining this with the self-evident proposition that the normal and 

 the axis of aberrancy coincide in the case of a circle, we may; 

 come to the conclusion that a circle is a circle ; but I submit that; 

 this is really a verification, and surely no ground for rejecting j 

 the interpretation. Indeed, the question whether such processes 

 are to be regarded as verifications or not seems to me to be 

 much the same question whether every syllogism is a pctitio 

 principii or not. But as I have elsewhere, in the papers referred 

 to in my last letter (p. 173, ante), fully discussed what a 

 geometrical interpretation properly ought to be, I need not 

 enlarge further on this point. 



As to the difficulty which " R. B. H." feels in drawing a 

 curve at every point of which the radius of curvature vanishes, 

 I may remark that this is a "limiting case," and the matter 

 becomes clear when my interpretation is paraphrased thus : 

 "If the radius of curvature of the aberrancy curve of a given ( 

 curve vanishes at every point, that curve degenerates into a 

 conic." 



Finally, I fail to see why an interpretation is to be rejected, 

 simply because the property it enunciates happens to admit of 

 an easy verification. The conic has an infinite number of proper- 

 ties, and the chief difficulty in discovering the geometrical inter- 

 pretation of its differential equation has been to find out which 



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