September 5, 19 18] 



NATURE 



Vstem of teaching- mathematics, not only in col- 

 leges, but also in schools, where antiquated 

 methods are still too prevalent. 



There is one omission in the book which is 

 regrettable ; the authors do not discuss the theory 

 of dimensions. This is a much more important 

 matter than it might be thought, especially when 

 the student works geometrical exercises with 

 numerical coefficients, so that the dimensions are 

 partly latent. Far too often even an honours 

 student fails to note that his answer must be 

 wrong, because it does not satisfy the test of j 

 •dimensions; and it is needless to emphasise the 

 value of the theory in physics. 



Typographically the book is all that could be ( 

 desired, except that we should have preferred old- 

 face figures in the tables. The diagrams are I 

 numerous, attractive, and well printed. 



(2) The new edition of Dr. Askwith's elegant 

 work differs from its predecessor mainly in defining 

 the conic sections in the Greek way as sections of 

 a cone. The earlier chapters (i.-viii.) on the tri- 

 angle, circle, cross-ratios, etc., make this method 

 easy, with one notable exception ; unless we dis- 

 cuss complex points and lines by a purely geo- 

 metrical method (such as that of v. Staudt), we 

 are not justified in treating every figure consisting 

 of a conic and a line as being projectively equi- 

 valent to a figure consisting of a circle and a 

 line. This is the weak point of Dr. Askwith's 

 book; it is not clear whether he is appealing, in 

 the last resort, to algebra, or relying upon the 

 •exploded "principle of continuity." In other 

 respects the treatise fully deserves the favourable 

 reception which it has obtained. 



G. B. M. 



OUR BOOKSHELF. 

 Association: A Story of Man for Boys and Girls. 

 Bv Edward B. Cumberland. Pp. 32. (Published 

 by the author at " Le Chalet," Penn, Bucks., 

 1918.) Price 25. 

 For nearly thirty years Mr. Cumberland 

 has been headmaster of William Ellis School 

 at Gospel Oak, and in convinced obedience 

 to the founder's testament has been (since 1889) 

 teaching " social science " to boys of ages from 

 eight to eighteen — a remarkable record of 

 pioneer work on lines which are sure to be 

 widely followed in the near future. In other ways, 

 too, with its early physics laboratory (1890) and its 

 specially built geography room, the school has 

 been in the front line, and we would heartily con- 

 gratulate Mr. Cumberland on what he has 

 achieved in spite of conditions often far from 

 encouraging. He has expressed some of his 

 ideals in an interesting little book which he calls 

 "Association." The title, refers to the author's 

 reasoned belief that one of the factors of human 

 progress has been association, co-ordination, the 

 multiplying of inter-relations. He illustrates this 

 in a retrospect of the ascent of man, and by show- 

 ing how the individual finds himself and realises 

 NO. 2549, VOL. I02] 



himself, both in body and mind, as an active 

 social person. 



The booklet seems to us better suited for adults 

 than for boys and girls, for it is very tersely 

 written. "We cannot even refer to the many wise 

 things that are said about home and school, work 

 and play, town and country, civics and Nature- 

 study; but the two dominant ideas are: (1) that 

 "knowledge of Earth and its story helps to make 

 man fitter for life on it, and also to raise him above 

 it " ; and (2) that the open secret of progress is 

 to enter into more and more complex associations 

 for noble ends, rising from school and family to 

 community and city, and from nation to humanity. 

 The booklet is an intensely personal document, 

 revealing a fine purpose. There is a tiny fly in 

 the ointment in the suggestion (on page 9) that 

 "creatures that crawl" should be regarded with 

 disgust. 



\femoir of John Miehell, M.A.. B.D., F.R.S. By 

 Sir Archibald Geikie. Pp. 107. (Cambridge : 

 At the University Press, 1918.) 

 Sir Archibald Geikie has done a further service 

 to British science in reviving the memory of John 

 Miehell, and in directing attention to his work in 

 various fields. Geologists are familiar with 

 Michell's name in connection with Jurassic strata, 

 and especially with the " Lyas " that he traced 

 from Somerset to Lincolnshire. It is unfortunate 

 that this ancient quarryman's term should suggest, 

 in its modern form, a pseudo-classical origin. 

 Miehell, after his retirement from the rectory of 

 St. Botolph's, Cambridge, and from his_ brief 

 tenure of the Woodwardian professorship of 

 geology, continued, as rector of Thornhill, "those 

 important investigations in physics and astronomy 

 with which his name will always be associated." 

 He died in 1793, before the experiment that he 

 had designed for determining the earth's density 

 could be carried out; but his apparatus came, 

 through Wollaston, into the hands of his friend 

 and correspondent Cavendish, who improved it 

 in detail, and ungrudgingly acknowledged 

 Miehell as its originator. A long and interesting 

 letter from Miehell to Cavendish on the strata 

 near Grantham is here published for the first time. 

 In his frequent journeys from Thornhill to London 

 he made observations at his halting-places, such 

 as Greetham on the old North Road, and one 

 feels that he would have hailed the work of his 

 successor, William Smith, as confirming much 

 that he had seen. In 1760, while still at Cam- 

 bridge, fie contributed a paper on earthquakes to 

 the Royal Society, in which he urged that the 

 initial shock is propagated by wave-motion 

 through the earth. 



This admirably printed and attractive work 

 raises pleasant memories of the times when the 

 "learned leisure " of our country clergy was often 

 , lev.. ted to scientific culture. The divorce of 

 clerical duties from collegiate fellowships, how- 

 ever desirable on both sides, has undoubtedly re- 

 duced the endowments of research. G. A. J. C. 



