29^ 



NATURE 



[Jan. 27, 1 1 



repeat, must henceforth almost inevitably be con- 

 ceived as having relations which cannot be expressed 

 in terras of matter." And again : " I claim at 

 least that any presumption which J science had esta- 

 blished against the possibility of spiritual communion is 

 now rebutted ; and that the materialist must admit that 

 it is no longer an unsupported dream, but a serious scien- 

 tific possibility, that, if any intelligences do in fact exist 

 other than those of living men, influences from those 

 intelligences may be conveyed to our own mind." 



And now, in conclusion, what shall we say of these 

 ponderous tomes.' Shall we lightly dismiss the whole 

 subject as a "pack of nonsense" ? I do not think that 

 this would be a wise or a scientific procedure. Speak- 

 ing for myself, I must confess that, in my opinion 

 Mr. Myers's views are not " on the main track " of the 

 science of to-day, whatever relation they may hereafter 

 be shown to bear to the science of the future. Speaking 

 for myself again, I am ready to accept experimental 

 thought-transference as a working hypothesis, that is to 

 say, a guide to future research on the subject. It may 

 be that any physical explanation we can at present 

 offer is no nearer the truth than was the Ptolemaic 

 hypothesis in astronomy, and yet such a working 

 hypothesis may be valuable in the existing state of 

 psychology. With regard to spontaneous telepathy, 

 notwithstanding the large amount of evidence so care- 

 fully collected and criticised, notwithstanding that I 

 have first-hand evidence more convincing (to me) than 

 anything recorded in these volumes, I prefer to credit the 

 whole to a suspense account. The physical difficulties 

 are enormous. We have to conceive the action of brain 

 on brain across a whole hemisphere. Not that this must 

 be pressed too far. There is much that is provisionally 

 accepted by science (much anent ether, and atoms, and 

 modes of molecular action) that I find it exceedingly hard 

 to conceive. And perhaps the distant action of brain on 

 brain is not harder for us to conceive than would be the 

 transmission of luminiferous waves to beings in whom the 

 visual sense was not as yet recognised, and who, hitherto 

 only acquainted with auditory vibrations transmitted by 

 the air, were called upon to believe that waves could be 

 transmitted by the ether from distant stars, and could pass 

 almost unchecked through thick masses of solid material. 

 Still, though the mass of evidence is considerable, and 

 though the physical difficulties must not be pressed too 

 far, I am not prepared fully to accept the doctrine of 

 spontaneous telepathy. At the same time, I hold that the 

 evidence adduced by earnest -workers is not to be met 

 by easy and ignorant ridicule. I do not think that science 

 is best served by those who are ever ready to throw the 

 cold water of impossibility on the light of new ideas 

 struggling into existence. 



I am, moreover, strongly of opinion that normal psycho- 

 logy has much to learn from experiments on supernormal 

 and abnormal " subjects." Beneath the threshold of con- 

 sciousness there is a vast amount of sub-conscious and 

 unconscious mental action. Of the multitudinous simul- 

 taneous neuroses only the superficial film (so to speak) 

 emerge into the light of consciousness as psychoses. The 

 study from the psychological standpoint of the underlying 

 hypopsychoses, as I have elsewhere suggested that they 

 should be termed, is as important as it is difficult. If the 



result of such work as Messrs. Gurney, Myers, and Pod- 

 more have entered upon aids in throwing light upon these 

 hidden mysteries, which are none the less realities, of the 

 human mind, their labour will, in my opinion, not have 

 been in vain. C. Lloyd Morgan 



ELEMENTARY RESULTS IN PURE 

 MA THEM A TICS 

 A Synopsis of Elementary Results in Pure Mathematics, 

 Ss^c. By G. S. Carr, M.A. Pp. xxxviii. -I-936 -j- 20 

 folding Plates of Figures. (London: Francis Hodgson, 

 1886.) 



r N our last notice of this work (vol. xxxi. p. 100) 

 *- we gave an account of Sections X., XL, and 

 XII. The complete volume contains two additional 

 sections. The first of these treats of plane co-ordinate 

 geometry, under which heading we have systems of co- 

 ordinates, analytical conies in Cartesian and trilinear co- 

 ordinates (we miss the m equations for the parabola and 

 the corresponding equations for chords, &c.). In the 

 latter division we have, amongst the particular conies 

 considered, the triplicate-ratio and seven-point circles (or, 

 as they are more usually styled, the Lemoine and Brocard 

 circles). The account is carefully drawn up from original 

 authorities, and will help to bring this latest development 

 of the geometry of the circle and triangle more into 

 notice. At present this and Dr. Casey's books are the 

 only source readily accessible to students. We are pro- 

 mised another presentment of these circles shortly, but of 

 this more anon. The concluding portion of this section 

 is devoted to the theory of plane curves. Here we have, 

 inter alia, inverse and pedal curves, roulettes, and the 

 various forms of transcendental curves. Considerable 

 space is taken up with linkages and link-works : here we 

 have accounts of Kempe's five-bar linkage, the six-bar 

 inversor, the eight-bar double inversor, the quadruplane, 

 the isoklinostat, the planimeter, and the pantograph (this 

 Mr. Carr generally calls pentograph — evidently he has not 

 consulted the " English Cyclopaedia " — and in one place 

 only, pantograph). The concluding section is mainly taken 

 up with solid co-ordinate geometry, the final articles being 

 devoted to Guldin's rules, moments and products of 

 inertia, perimeters, areas, volumes, &c. Here we have 

 the theorems which go by the names of Fagnani, Lam- 

 bert, and Griffiths (not Griffith, as the "Contents" 

 and " Index " print the name ; the text, § 6096, is 

 right). 



We have in our former notices sufficiently indicated 

 our opinion of the utility of such a book as this if tho- 

 roughly trustworthy, and have suggested that a student 

 should have this synopsis by his side when he is carefully 

 gomg through his subject, that so he may be able to spot 

 any slight inaccuracy in the text. We believe the book 

 is singularly free from errors, but it would be absurd to 

 suppose that there are not several which have escaped 

 even the notice of the author, who has imposed upon him- 

 self numerous guards for the prevention of such slips. 

 For it must be remembered that this is no hastily-pre- 

 pared work : it has occupied much of the writer's time 

 since 1 866, when the w^^i^'/'/aOT opus was commenced. The 

 author is to be heartily congratulated on the successful 



