August 28, 1890] 



NATURE 



413 



■whole by the presence of "a ventral armour of oval 

 scales," we again have to wonder at the author's sources 

 of information. It is indeed true that many Labyrintho- 

 donts have a ventral armour of bony scutes, but these can 

 scarcely be described as oval, and in the typical Laby- 

 rinthodonts, to which some authorities restrict the term, 

 such scutes are totally wanting. The essential features 

 by which the Labyrinthodonts are characterized the 

 author carefully refrains from mentioning. A trap is set 

 for the unwary on pp. 51, 52— the shell mentioned on the 

 one page as Ainmonites bucklandi being alluded to on the 

 next as Arietites bucklandi. Equally unfortunate with 

 the author's mention of the Labyrinthodonts is his allusion 

 on p. 59 to the Mesozoic mammals, where he repeats the 

 exploded idea that Stereognathus was an Ungulate, thus 

 carefully ignoring all the recent work relating to that 

 peculiar group known as the Multituberculata, which ap- 

 pears to be allied to the Duck-mole. On the same page 

 Megalosaurus is carefully separated from the Dino- 

 saurs, to appear as a carnivorous lizard, whereas in the 

 list on p. 62 it is placed in the former group. How totally 

 out of date is the list on the page last-mentioned ought, 

 moreover, to have been known to anybody acquainted 

 with recent palaeontological literature. Page 63 is note- 

 worthy as containing at least six misprints in the spelling 

 of scientific names; but perhaps the climax of blunders is 

 attained on pp. 74, 75. Thus, on the former page we 

 are gravely told that Hyracotherium is a hog ; and if one 

 fact has been repeated over and over again almost ad 

 nauseam, it is that Hyracotherium is one of the early 

 progenitors of the horse, being, in fact, identical with the 

 American Eohippics, and we can hardly believe that the 

 author wishes the student to understand that horses are 

 descended from hogs ! On p. 75 Lingula is carefully 

 separated from the Brachiopods, while the well-known 

 Crag Polyzoan Fascicularia — one of the commonest of 

 Suffolk fossils — is stated to be a shell ! 



Finally, the glossary is an explanation of certain mine- 

 ralogical and chemical terms having for the most part no 

 sort of connection with British (or, for the matter of that, 

 with any other) fossils. What connection can possibly 

 •exist between " astrakanite — a compound of magnesium 

 sulphate and sodium sulphate deposited in winter time in 

 the salt lakes near the mouth of the Volga," and the 

 fossils of the British Islands, we are totally at a loss to 

 imagine. A similar remark will apply to eclogite, which 

 is said to be a rock consisting of red garnets and 

 hornblende ; although it really is one of the pyroxenes. 



R. L. 



OUR BOOK SHELF. 



II Teorema del Parallelogramtna delle Forze dimostrato 

 erroneo {configure) By Giuseppe Casazza. (Brescia : 

 Stabilimento Tipografico Savoldi, 1890.) 



It is curious that the mathematical paradoxer should 

 confine himself principally to the problem of "squaring 

 the circle " — that is, to the attempt to prove that tt is 

 the root of a quadratic equation with rational coefficients, 

 in algebraical language ; while other simpler questions 

 are at hand in which he might prove himself superior to 

 the conclusions of ages, by solving the problems of the 



NO. 1087, VOL. 42] 



" duplication of the cube " and the " trisection of an 

 angle." 



Some paradoxers attain their own ends by a wrong 

 result, for instance, in putting tt = /v/io— a result easily 

 tested by counting the revolutions of a railway carriage 

 wheel of given diameter, in a journey of given length ; 

 others by ignoring the rules of the game, as Napoleon is 

 reported to have played chess. 



Our author must be congratulated upon having started a 

 fresh question of controversy, which had till now been uni- 

 versally regarded as settled for about three hundred years. 



The " parallelogram of forces " must have been known 

 experimentally for thousands of years longer ; but in the 

 orthodox world, what is considered at the present time 

 the best and simplest way of proving it theoretically in a 

 strictly rigorous manner ? The proof of our youth given 

 by Duchayla is now voted cumbrous and antiquated ; and 

 only retained by veteran examiners as a searching test of 

 logical power. Nowadays we cannot afford the time to 

 linger over the elements, and it is customary to treat the 

 "parallelogram of forces" as a corollary to Newton's 

 second law of motion ; but this cannot be considered 

 perfectly satisfactory, as we are making the fundamental 

 theorem of statics depend upon a dynamical argument. 



Maxwell pointed out that, as we were concerned with a 

 statical theorem, it was better in the proof to ignore the 

 word " resultant," and to present a system of balancing 

 forces at each step ; and in this way he succeeded in 

 framing a more simple rigorous statical proof, starting 

 from the axiom that the resultant of two equal forces 

 bisects the angle between them. 



Again, by determining the conditions of equilibrium of 

 three parallel forces, instead of as usual determining the 

 resultant of two parallel forces, one figure will serve for 

 all possible cases. 



Practically it is the " triangle of forces " which we 

 always work with, and not the " parallelogram," with the 

 advantage in graphical statics of using only three hnes 

 of construction instead of five. 



To return to our author, it is difficult to make out, with 

 an imperfect knowledge of his language, whether he is 

 writing ironically or not. His dynamical language is very 

 loose ; he uses " force " and " velocity " as convertible ; 

 and throwing his remarks into the style of Galileo's 

 dialogues, he seeks to controvert all Galileo's conclusions. 

 On p. 17 he provides the critic with an appropriate and 

 characteristic quotation with which to conclude— "ho 

 pero spesso dei momenti in cui gettando all' aria i libri 

 che mi trovo sotto mano, esclamo : Ma to sono un 

 allucinato ! " A. G. G. 



LEsprit de Nos Betes. Par E. Alix. (Paris : J. B. 



Bailli^reet Fils, 1890.) 

 Les Facultes Mentales des Animaux. Par le Dr. 



Foveau de Courmelles. (Paris : J. B. Bailli^re et Fils, 



1890.) 

 The writers of these two books have very much the same 

 object in view. Their aim is to show that the mental hfe 

 of animals differs only in degree, not in kind, from that 

 of man. If anyone still thinks that animals are merely 

 machines, or that they have no higher faculties than 

 instinct, it would be well worth his while to consider 

 what either Dr. Courmelles or M. Alix has to say on the 

 subject. No impartial person could study the evidence 

 brought together by either of the two writers, and con- 

 tinue to doubt that animals display intelligence in the 

 strictest sense of the term, and that they share in varying 

 degrees many of the emotions which are often supposed to 

 be exclusively characteristic of the human race. Of the 

 two works, the one by M. Alix is the more elaborate. In 

 both books the materials are well arranged, and the 

 authors have persistently sought to present their facts 

 and ideas brightly and pleasantly. 



