436 



NA TURE 



[March 13, 1902 



the practical methods and terminology used in navigation 

 receive some notice. 



In the department of spherical geometry more exten- 

 sive additions have been made. New chapters have 

 been added on Properties of the Spherical Trian^jle, 

 I'roperties of Circles on the Sphere, The Principle of 

 Duality, Hart's Theorem, The Generalised Triangle, The 

 Application of Determinants to Spherical Geometry, 

 while some additions and modifications have been intro- 

 duced elsewhere. The chapter on the principle of duality 

 gives an excellent resume of the subject, illustrated by the 

 exhibition in parallel columns of corresponding properties 

 of a co-axal system of circles on the sphere and its dual 

 a co-lunar system. The principle is also utilised in what 

 the reviser styles, in the preface, a new treatment of Sir 

 Andrew Hart's very striking and fertile theorem that the 

 inscribed and escribed circles of a spherical triangle 

 touch a fourth circle besides the three sides of the triangle. 

 The bearings of the principle of duality on Hart's 

 theorem have, however, been already discussed, and Dr. 

 Leathem's treatment does not seem to add much that is 

 essentially novel. The proof of the theorem, as here 

 presented, appears, indeed, to be open to objection ; the 

 proof in § 178 of the condition for the contact of a given 

 circle with the circumcircle of a given triangle assumes 

 that the circles have a real limiting point L, while in 

 §§ 203 and 204 all that has been proved is that the cone 

 joining the circle H to the centre of the sphere touches, 

 internally or externally, the inscribed and escribed circles 

 of the triangle — an appeal to the particular case of the 

 equilateral triangle, without further discussion, in order 

 to determine the nature of the contacts hardly carries 

 conviction. The plane analogue of this mode of treatment 

 of Hart's theorem may be found in Lachlan's "Modern 

 Pure Geometry," pp. 206 and 25*, where also an adapta- 

 tion to plane geometry of the theory of duality on the 

 sphere is given at p. 257. Needless to say, the subject 

 admits of wide development. 



Among the chapters devoted to spherical geometry, 

 one dealing with inversion, stereographic projection, &c., 

 would have been welcome, but it was possibly excluded 

 by want of space. 



In the new chapters admirable judgment is displayed 

 in the selection and arrangement of materials from a wide 

 range of original sources, numerous historical and biblio- 

 graphical references forming an excellent feature of the 

 work. The style throughout is clear and attractive, and 

 most of the examples which have been added possess the 

 merit of elegance and real scientific interest. A. L. 



A CONSUL IN CHINA. 

 John Chinaman and a Few Others. By E. H. Parker. 

 Pp. xx-f38o. (London: John Murray, 1901.) Price 

 8j. net. 



THIS is an interesting book of personal reminiscences 

 during a long official residence in China. Mr. 

 Parker served in the consular service for many years at a 

 time when our relations with the Flowery Land were even 

 more precarious and uncertain than they are to-day, and 

 it is interesting to observe how under these conditions, 

 and with Sir Harry Parkes as our Minister at Peking, a 

 NO. 1689, VOL. 65] 



spirit of self-reliance was engendered among all holding 

 authority at the outlying ports. The riots directed 

 against foreigners which are now occasional were chronic 

 in the 'eighties, and Mr. Parker came into a fair share of 

 them. Being ever ready to accept responsibility, he in 

 most cases undertook the defence of his countrymen 

 during the acute stages of the crises, and when the hurly- 

 burly was over arranged with the local authorities for 

 the necessary punishment of offenders and compensa- 

 tion for the destruction of property. As he remarks, after 

 describing a serious outbreak at Wenchou, 



"The moral of this story is that Chinese nerves are so 

 constructed that every Mandarin seems to have in him 

 the makings of a murderer or a saviour, accordingly as 

 the tide in the affairs of men is taken at the flood or on 

 the ebb ; that rows are seldom so dangerous or so serious 

 as their noise and appearance is(j-/V) appalling ; and that 

 a readiness to make allowances for foolish human nature 

 is commonly appreciated at its full value on the Chinese 

 side. The same missionaries had to take refuge on the 

 island once more dur ng the Boxer riots of 1900, but I 

 see that my sensible and accomplished successor has 

 been able to abstract ample compensation in the same 

 friendly spirit as that evinced sixteen years ago. I see 

 no reason why the whole Chinese question should not be 

 treated on analogous lines." 



To the principle here involved we entirely agree, but, 

 unfortunately, the whole Chinese question has to be 

 settled, not by one plain-dealing man, but by a dozen 

 plenipotentiaries whose interests are conflicting, and 

 some of whom find in a disturbed China a prospect of 

 the realisation of their best hopes. 



.Another source of diplomatic difficulty at the present 

 time is the absence of sound statesmanship at Peking. In 

 the 'sixties, as Mr. Parker points out, there were men 

 like Prince Kung, Wen-Hsiang and Kui-Hsiang, who 

 were giants in comparison with the Prince Chings of the 

 present day. Sir Thomas Wade used to call Wen- 

 Hsiang "the last of the Manchus," and it is difficult to 

 point to another of the race who has risen to anything 

 like the same level of wisdom and knowledge. 



But Mr. Parker has much to say of the Chinese and 

 their affairs outside the political arena. He mixed more 

 with the natives and gained a better insight into their 

 characteristics and peculiarities than most Chinese-speak- 

 ing foreigners, with the result that he has much to say in 

 their favour and many strange peculiarities to note. 

 Among the latter he mentions the curious tendency there 

 is among the people to commit suicide. 



"Women are the chief delinquents, or heroines, as 

 they often imagine ; it only needs a harsh word or a fit 

 of passion, when down goes an ounce of opium — a most 

 comfortable death. It will be noticed that the recent 

 Boxer troubles are responsible for the suicide gf at least 

 a score of prominent statesmen. In some cases whole 

 families have dived head foremost into wells in order to 

 share the master's disgrace or self-sacrifice. In others 

 the Emperor has ' bestowed the cord ' ; which means 

 that a man sits with his back to a panel and his friends 

 strangle him through two holes. So far from being con- 

 sidered a crime, suicide is under many circumstances re- 

 garded as a noble act ; rarely as a despicable one, unless 

 done in pure spite, or out of revenge." 



The position of women in China is well illustrated by the 

 many stories the author has to tell of native life, and the 

 conclusion at which he arrives is that on which all close 



