170 



NATURE 



[December 7, 191 



a man as Wiseman, the really distinguished, saga- 

 cious, and learned sorj^eant surgeon to Charles the 

 Second, who said of his master's potency, with prob- 

 ably more than a courtier's sincerity, that " he cureth 

 more in any one year than all the Chirurgions of 

 London have done in an age." This testimony is the 

 more remarkable as Wiseman was not himself officially 

 concerned with the ceremony. In one passage, in- 

 deed, Wiseman attributes a relapse to the loss of the 

 angel from the neck of the patient. Like .Alexander of 

 Tralles, good doctor as for his time he was, he still 

 clung to amulets and such magic. We read 

 then with no surprise the devout appreciations of such 

 men as Fuller and Collier. Shortly before Wise- 

 man, we have the curious story, one better known to 

 medical men, of the arraignment of one Lcverett, at 

 the instance of William Clowes the Younger, surgeon 

 to Charles the First, before the College of Physicians 

 for his imposture, which this august body had no 

 difficulty in proving by convincing evidence of facts, in 

 pretending to vie with the king in the power of curing 

 the evil, even by methods still more magical. 

 We do not find, however, that the College did the 

 fairest thing in its power; it might have put the King 

 and Leverett severally to trial on the same patient 

 or patients. But, as Clowes aptly remarked, Leverett 

 was not even a seventh son of a seventh son ; he 

 proved to be only the fourth. He was a hollow rogue. 



Still, the sceptic had crept near the ears of his world, 

 even at an early date ; not always knowing himself to 

 be a sceptic. John of Gaddesden (under Edward the 

 First) assigned to the royal touch a place midway 

 between the polypharmacy of the physician and the 

 craft of the surgeon — "a delicate provision," says Dr. 

 Crawfurd, " for the contingency of the king's thera- 

 peutical impotence." .As this passage is almost the 

 only original suggestion in his " Rosa Anglica," we 

 may guess that John, like the many persons who do not 

 know that they are humorists, was naively unaware 

 of his own scepticism. It is a happy biographical 

 trait of Henry of Navarre that, at Ivry, on cutting 

 down a man with his sabre, he exclaimed, "Je te 

 touche, que Dieu te gudrisse." But perhaps this says 

 less for Henry's scepticism than Dr. Crawfurd thinks, 

 characteristic of him as the story is. Even in the 

 sixteenth century the stronger the creed the safer to 

 jest with it; the Church has always tolerated the 

 jester, while handing over the wrangler to the secular 

 arm. 



The first great sceptic, to whose robust disdain of 

 this item of his divinity the discredit of the touch is 

 due, was William the Third. His sturdiness did him 

 the more honour as such a proof of his dynastic 

 authenticity would have been convenient. This testi- 

 mony had more weight with Anne; though it would 

 have gone hard with her heirship had it depended on 

 her cure of Samuel Johnson. The gold touch-piece 

 she bestowed upon her eminent patient is, we are 

 told, in the British Museum. It is hard to believe 

 that such great modern surgeons as Alibert and 

 Dupuytren presented sufferers from the evil to Charles 

 the Tenth ; perhaps they were the last medical authori- 

 ties to be so complaisant; though the later Stuarts 

 NO. 2197, VOL. 88] 



amused themselveg, and others, by clinging to this last 

 rag of their divinity until their dissolution. 



I hope my readers will agree with me that I hav* 

 taken no improper liberty with them in dwelling at 

 »his length upon so able and entertaining a volume. 



Clifford Allbltt 



GROUP'TIIEORY. 

 Theory of Groups of Finite Order. By Prof. W. 

 Burnside, F.R.S. Second edition. Pp. xxiv + 512. 

 (Cambridge: University Press, 191 1.) Price 15s. net. 



IN the new edition of Prof. Burnside's standard 

 work important changes have been made by re- 

 arrangement of old material, and by addition of new. 

 The main feature, for which many English readers 

 will be very grateful, is the addition of several 

 chapters on groups of linear substitutions. .Among 

 the most important of all contributions to group- 

 theory must be reckoned the memoirs of Frobeniu* 

 in the Berlin Sitzutigsberichte ; unfortunately they are 

 not very accessible to English students, and are by no 

 means easy to read; hence, Prof. Burnside's connected, 

 and in many ways independent, discussion of this 

 part of the theory is very welcome. In particular, there 

 is a chapter on characteristics, and another on various 

 special applications ; it may be noticed, as showing 

 the power and value of the characteristic-theory, that 

 the theorem "every group whose order contains only 

 two distinct primes is soluble," appears as a corollary. 



At present, the theory of groups is in a very interest- 

 ing state for various independent reasons. Several 

 great mathematical theories are intimately associated 

 with group-theory, or at least with some aspect of it; 

 thus, there is the theory of algebraic equations, the 

 division of period and argument in elliptic functions, 

 and the immense field of elliptic modular functions — 

 to mention these alone. But, besides this, the theory 

 of groups, which so long seemed a rather arid apf>en- 

 dix to the theory of permutations and combinations, 

 has changed its aspect into a definite, independent, 

 and fascinating branch of analysis, as peculiar and 

 baffling as the theory of numbers, if not more so. It 

 has now been approached and studied under four, at 

 least, of its Protean aspects; as defined, in the 

 abstract, by a multiplication-table, or, equivalently, by 

 a set of foimal equations like a' = &* = (a&)*= i ; as a 

 set of permutations; as a set of linear substitutions; 

 and as a set of geometrical operations. Each of thes 

 methods has suggested intrinsic properties of groups 

 and we have now a considerable set of distinctii 

 epithets, such as "self-conjugate," "Abelian," " meta 

 belian," "soluble," and so on, each of which marks 

 definite advance in classification. But some of tl 

 most obvious problems seem as far from solution 

 ever; for instance, it seems probable that no group 

 odd order, except a cyclical one, can be simple, but tl 

 proof has still to be found. 



There is, therefore, abundant field for research, an^ 

 the more varied the interests and attainments of thos 

 who undertake it the better, because some new syi 

 holism, or some new association with geometry, 

 the like, may lead to the discovery of new propertie 



