Feb. 2 1, 1884] 



NATURE 



379 



results from this is not quite apparent to an outsider : it 

 is even probable that there is none, unless the unintended 

 reflex benefit, in the form of experience in book-making, 

 which the authors thereby obtain. 



Here we have two elementary booklets, one of 40 pp., 

 the other of 7.8 pp. ; and a very short examination of 

 the.n suffices to show that the writers could have spent 

 their time and energy to much better purpose, if it was 

 the public that they intended to benefit. What they have 

 written is probably not worse than what has been in use 

 for years ; but certainly it is not any better. Indeed 

 Germany has always had more really good elementary 

 expositions of the theory of determinants than any other 

 countr)', and two or three of these have passed through 

 several editions. Dr. Kaiser and " Professor " Bunkofer 

 are quite capable men for the work they have under- 

 taken : on this score little fault can be found. The latter 

 sketches his "Notes of Lessons," as young English 

 teachers would call them, with pedagogic ability and 

 skill ; the former is more wooden, and more unwisely 

 ambitious, and we cannot, unsupplicated, pardon him for 

 saying that Gauss in coining the word "determinant" 

 thereby introduced a definite new idea into analysis, but 

 he goes about his work in a sufficiently workmanlike 

 manner, and is on the whole sure of the ground he treads. 

 We only wish both authors " more power," and next time 

 a happier selection of subject. 



Prof. Mansion's " Elements " is a book of a higher type. 

 The present edition, however, is the fourth ; and therefore 

 no detailed examination can be looked for. Suffice it to 

 say that there is really no better introductory book pub- 

 lished ; the exposition and arrangement are admirable, 

 and it has, what so many Continental text-books want^ 

 small collections of suitably graduated exercises for the 

 learner. There is only one point which it seems desirable 

 that Prof. Mansion should reconsider, viz. the nomencla- 

 ture of the special forms of determinants. He employs^ 

 for example, both Sylvester's term " persymmetric " and 

 Hanker s " orthosymmetric." Should not one of these 

 immediately receive decent burial, and should not the 

 latter be that one ? It is not shorter, it is not more de- 

 scriptive, it is not more accurate in its description than 

 its rival, and its rival was by several years first in the 

 field. As for " doppelt-orthosymmetrisch," its author is 

 simply unconscionable ; it is one of those words which, 

 as Mark Twain puts it, are alphabetical processions and 

 have a perspective : we should have been glad if Prof. 

 Mansion had dealt more summarily with it. In another 

 instance, that of" skew " determinants, we have confusion 

 worse confounded. Cayley's first paper regarding them 

 appeared in Crelle (1846), and was written in French, the 

 title being " Sur quelques propridtds des determinants 

 gaiiches." The term gauche (Eng. skew, Germ, schief 

 Italian gobbo) was at once accepted and employed, as 

 well it might, by all the standard writers. Of late years, 

 however, there have been busy times with the mathe- 

 matical coiners on the Continent, and in consequence we 

 have as substitutes for " skew " — 



" symmetrale," 



"congruente" (not in Mansion), 



" pseudosymdtrique." 

 Surely it is too tiresome and quite unnecessary to wait 

 until by a process of artificial selection the fittest or un- 



fittest of these shall survive. Prof. Mansion's " Elements " 

 and the German translation of it have deservedly a large 

 circulation on the Continent, and thus have much power 

 to propagate good or evil. We would therefore earnestly 

 ask him to consider whether it would not be better to 

 recognise throughout his work only one name for each 

 special form, and to relegate all synonyms to the index. 



The last text-book on our list is Spanish. Although it 

 is the largest (200 pp.) and most pretentious of the four, 

 we regret that it is impossible to say a good word regard- 

 ing it. The authors have most manifestly no grasp of 

 the subject, and advance with a gay step and light heart 

 through inaccuracy after inaccuracy. Their model unfor- 

 tunately is Dostor, and equally unfortunately they are 

 more than faithful to him. At the very outset they show 

 their hands. The so-called "notation of Cauchy" is not 

 Cauchy's ; what is really Cauchy's is not attributed to 

 him; and the "notation of Leibnitz" is more Cauchy's 

 than Leibnitz's, but belongs to neither. Nor is this wild 

 start of Book I. redeemed by a good end. On pp. 96-98 

 five examples of skew determinants are calculated at 

 length with a complacent unconsciousness of the simple 

 property which makes all the calculation unnecessary ; 

 and pp. 99-101 are taken up with the rather epoch-making 

 definition — 



^ 



and some perfectly legitimate deductions from it. Book 

 II. deals with the so-called applications of determinants, 

 and closely follows Dostor. The most amusing part of 

 it, as is the case also with Dostor, is the chapter devoted 

 to "Applications to Trigonometry." Dostor, however, is 

 outdone on his own ground. For example, after it has 

 been proved that cos A = {U'' -\- c^ — d')libc, one whole 

 octavo page is occupied in showing, by means of deter- 

 minants, that sin |- ^ = sl(s — b)(s — c)lbc. This tour de 

 force is like that of Hudibras, telling the clock by algebra; 

 and the moral in both cases is the same. 



LETTERS TO THE EDITOR 



[ The Editor Joes not hold himself responsible for opinions expressea 

 by his correspondents. Neither can he undertake to return, 

 or to correspond with the writers of, rejected manuscripts. 

 No notice is taken of anonymous communications. 



[The Editor urgently requests correspondents to keep their letters 

 as short as possible. The pressure on his space is so great 

 that it is impossible otherwise to insure the appearance even 

 of communications containing interesting ana novel facts,'\ 



Mr. Lloyd Morgan on Instinct 

 I HAVE read with much interest Mr. Lloyd Morgan's very 

 able paper on " Instinct " in the current issue of Nature, and I 

 feel it is desirable, without following him over all the ground 

 which he has traversed, briefly to consider "hose parts of his 

 communication which have special reference to my own work. 



The broad question with which he begins — viz. : "Is there a 

 science of comparative psychology ?" — is not a question which I 

 feel specially called upon to answer, inasmuch as almost every 

 one who has hitherto written upon psychology has taken it for 

 granted that there is such a science. Nevertheless I may state 

 the justification which I am myself prepared to give of this 

 universal assumption. 



When we say that a dog is a more intelligent animal than a 

 sheep, we do not doubt that we are making as real a proposition 

 as when we say that the President of the Royal Society is a more 

 intelligent man than Dick, Tom, or Harry. Now in all cases 

 where there is a general consensus of feeling of this kind, there is 



