November lo, 1923] 



NA TURE 



685 



Real Mathematics : Intended Mainly for Practical En- 

 gineers, as an Aid to the Study and Comprehension of 

 Mat/ieiii'itirs. By E. G. Beck. (Oxford Technical 

 Publications.) Pp. ix + 306. (London: Henry 

 Frowde and Hodder and Stoughton, 1922.) 155. net. 



Ark t'li-iinLTs as bad as they pretend to be, or, at any 

 rate, as .Mr. IScck wishes us to believe ? His desire is 

 " to bring ah nit n change of attitude towards mathe- 

 matics," " to show the thing as an actual, tangible 

 rcaiit\ . instead of as a collection of rigid and unrelated 

 rules and formulae." He asserts that " tlie physical 

 realities of mathematics haw hKoiia' >\vathed about 

 with wrappings of mystcrv and suggestions of the 

 supernatural." No doubt there is still room for 

 improvement in mathematical text-books ; but Mr. 

 Beck must be singularly ignorant of modern text-books 

 if he imagines that these sentcnics are anything but a 

 lilx-1 on them. 



In any case, if modern mathematical text-books are 

 at fault, their improvement will not be secured by 

 Mr. Beck's methods. At hoitom tliere seems to be 

 nothing in his explanations that is not contained 

 in most of the decent school books — only Mr. Beck 

 talks ' * In addition he says some absurd things. 

 Tlu iking example is perhaps the discovery 



that y' - 



Mr. Be< , . on mathematical teaching are best 



understood from the following self-revelation : " The 

 ability to solve a dififerential equation is, of itself, net 

 worth five seconds of effort to acquire ; but if such 

 ability enable a man to design niarhines or structures 

 more economically, or if it svvw liim as a ki v to the 

 recorded experience of others, its \aliic would clearly 

 be so enormous as to lie beyond th* si (ij)r of ordinary 

 means for estimation." In other words, the only 

 justification of inatlicinatich is the creation ol (hx'iiU'nds ! 



The Social and Political Ideas of some (ireat Mediceval 

 Thinkers : a Series of Lectures delivered at King's 

 College, Vniversity of London. Edited by Prof. 

 I*". J. C. IIea^;l■,!la\^ . V\). 22-\. (Loiiduii, Calcutta 

 and SmIiiiv : G. G. liarraj) and Co., Ltd., 1923.) 



I 



Tm 



in ' 



>iiin;n I diitaiiH ei'_:ht studies <i|" politieal thought 



Mi'Mle Aji^ \\lii'ii, \sitli t \vi I exeeptidiis, appear 



' iiiti.dU' ill liie torrn in whii h tiiev Were delivered 



our>e fif puliiie lei tures in Kind's College, London. 



duriiii: the autumn of i(;22. Se\-cn ol thr lei ti: 



with iii<!i\ iileal t Iiiii!.:'ix. I H-iniiiie' witki 



•!i|i'i-.ilr prudiie 



medievalism as a whole. The lectures cover the de- 

 velopment of the idea of a national state out of the 

 theor}^ of an international organisation, spiritual or 

 temporal, and are therefore not without bearing upon 

 political theory of the present day. 



Hunters of the Great Xoih . \W Vilhjalmur Stefansson. 

 Pp. 288 + 16 plates + 2 maps. (London, Calcutta and 

 Sydney : G. G. Harrap and Co., Ltd., 1923.) "js. 6d. 

 net. 

 In this volume Mr. Stefansson recounts some of his 

 early experiences in the Arctic when he was a member 

 of the LtfTui-will expedition in igc^> - '" tells of 

 his ti,i\ek, \\u!i t!ie l-:.skimo, how tk = liim to 



hunt, to accept their diet and mode of hie, to build snow 

 houses and generally to live in comfort in a region 

 which people will persist in regarding as inhospitable 

 in the extreme. It is a volume of the lore el the Arctic 

 full of vivid des( riptions and personal ineicknts. The 

 chapters on hunting contain a great deal ol the natural 

 history of the caribou, polar bear and seal, and there is 

 of course much of interest regarding tlic Eskimo. 

 Mr. Stefansson has given us no book of polar travel of 

 greater interest than this vohmiC. It should help to 

 dispel some of the current i,ilk!eie> i.Larding the 

 Arctic climate and conditions of life in the tar north. 

 The call of the north is in its pages, which will awaken 

 memories among those who know the ice, and stir others 

 with a longing to go and see. R. N • K • B- 



Mirrors, Prisms, and Lenses: a Text-book of Geo- 

 iui/rird! Optics. By Prof. James P. C. Southall. 

 Ihtlarged and revised edition. Pp. xx-f-657. (New 

 York : The Macmillan Co. ; London : Macmillan 

 and Co., Ltd., 1923.) 



The revised edition of Prof. Southall's text-book of 

 geometrical o])tics. in addition to a number of new 

 problems scattered throughout the book, contains an 

 important new chapter at the end of the volume. The 

 historical notes dealing with the rectilinear propagation 

 of light, and optics in the seventeinth century are of 

 considerable interest. It is usuall\ statt <1 that Newton 

 was the first to distinguish s(\en (olours in the pris- 

 matic spectrum, but Maurolycus (1575) in the explana- 

 tion which he gave of the circular arc of the rainbow 

 directs attention to the four principal colours, together 

 with three other colours which he regarded as transi- 

 tion-.. i\efl( ction prisms are discus.sed at some length, 

 ind new and appio\ (d schemes of optical calculation, 

 |)artl\- (hie to Mi-. T. Sniitli, are described. A word of 

 piaise iiin-.t kr LM\en to the diagrams. 



u -0 o\ I lie 



•mi III rracticii! \!athi-ir.,;!:r<. I'\- \k Sr\ nionr 



editor. It uill he noted th- term " Mid.ll,' A-es " is, I I'.rvant l'|., w,^. (Oxi ! -uk-n : 



( )\lor(l 1 iu\ CI -ai \ I ' 



lologicalh 

 remaininL 



all\ ,lil)( rail\- interpreted. 



with joliii of Salisbnr\ ' Mi;. k.i'\ wi'-^ hi 



■ended to stip])lv the 

 M ^ -pr. i ' ih lor the entrance 



.iniin.itii'; ace in ruklic ."schools, 



upon .1 s\ llakus l^slled 1>\- the S. h in e 

 -itlion al the rciiuest o| ikr hunt 

 Head M;: ' leielK i , 



konk is ■> ^ i'lc and 



jiistitie-, till- ckiini lor the int<Test ol the -.ukject to the ■ inleristniu. and tiic expkinal ion- ottered shor.ld pio\e 

 modern readi'r who i-- not specially concerned with 1 ol value to the pupils. S. B. 



NO. 2819, VOL. 112] 



k ,d Mai.,: ,\ . .Mlco). klie 



I ' 'I Kind's ' 1 he introductoi'v 



111 I He. i!i will! h he diaw . .Ill illiiiiiinat iiiLT ili--tini tioii 

 between polil leal theor\ and pohiicij t hoii;jht , and hill\- i 



