438 



NA TURE 



[April 8, 1922 



of statement is overwhelming. We recognise that it 

 would be unreasonable to ask Prof. Carslaw for an 

 account of the modern theories of integration. We 

 hope, however, that, when next he has an opportunity 

 of preparing a new edition, he will remedy the omission 

 ■which we have emphasised. He should also certainly 

 include the fundamental theorem that the Fourier 

 •constants of any integrable function tend to zero (a 

 rather startling omission), and some account of 

 Parseval's theorem. He would thus add greatly to 

 the value of an already valuable book. 



(3) Prof. Hobson gives us the mathematics of 1921, 

 and Prof. Carslaw is not far behind him. Mr. Edwards's 

 book may serve to remind us that the early nineteenth 

 century is not yet dead. He directs our attention to 

 " the admirable and exhaustive works of Legendre, 

 Laplace, Lacroix, Jacobi, Serret, Bertrand, Todhunter, 

 etc." ; from which he has learnt, for example, that 

 " a limit may be of finite, infinite, or indeterminate 

 value," that " the processes of integration are neces- 

 sarily of a tentative nature," and that any convergent 

 series may be integrated term by term. Two proofs 

 are offered of the last proposition. In the first it is 

 stated to be valid " provided the series V itself, and 

 the series V formed by the integrations of the separate 

 terms, are both absolutely convergent.^'' Mr. Edwards 

 italicises the last condition, but we have no idea why 

 it is inserted, for there is no pretence of making any 

 use of it, nor is its meaning explained. 



It is difficult for a reviewer to know what to say 

 about such a book, except that it cannot be treated 

 as a serious contribution to analysis. Twenty years 

 ago it might have been necessary to establish the point 

 in detail ; it would be waste of time now, when the 

 battle for accuracy has been won. There is always 

 the danger, however, that a student who reads a text- 

 book may suppose that the statements which it con- 

 tains are true. We should therefore state explicitly 

 that the " general theorems " asserted in this book are 

 often false, and that, even when they are true, the 

 arguments by which they are supported are generally 

 invalid. 



One ought, of course, to judge the book by a different 

 standard, as a storehouse of formulae useful for in- 

 structional purposes. Of such there is an abundance, 

 including a good many which are seldom found in other 

 books, and often entertaining or even important. We 

 may mention Catalan's formula for the surface of an 

 eUipsoid, results concerning roulettes and glissettes, 

 the theorems of Fagnano, Burstall, Graves, MacCuUagh, 

 Schulz, and others. The book, in short, maj be useful 

 to a sufficiently sophisticated teacher, provided he is 

 careful not to allow it to pass into his pupil's hands. 



G. H. Hardy. 



NO. 2736, VOL. 109] 



Greek and Arab in Medicine, 



(i) Greeli Medicine in Rome : The FitzPatrick Lectures 

 on the History of Medicine delivered at the Royal 

 College of Physicians of London in 1909-10, with 

 other Historical Essays. By Rt. Hon. Sir T. Clifford 

 Allbutt. Pp. xiv + 633. (London: Macmillan and 

 Co., Ltd., 1921.) 305. net. 



(2) Arabian Medicine : Being the FitzPatrick Lectures 

 delivered at the College of Physicians in November 

 1919 and November 1920. By Prof. Edward G. 

 Browne. Pp. viii+138. (Cambridge: At the 

 University Press, 1921.) 12s. net. 



SINCE the great revival of historic interest in 

 the eighteenth century the labour of historians 

 has been directed mainly towards political institu- 

 tions. Sociological and cultural history have been of 

 much slower growth, and we are only now beginning 

 to be able to treat the history of European life as a 

 whole, to look upon it as one majestic panorama 

 developing from the early Mediterranean culture in 

 which first Egypt, then Crete, then Greece was leader, 

 to the time when Rome herself, in receipt of tributaiy 

 streams from^ Syria, Persia, Mesopotamia, and India, 

 acted as the cultural intermediary to the European 

 peoples, and, finally, to the diffusion by those peoples 

 of the infectious elements of the ancient tradition 

 throughout the world. It will thus one day become 

 possible to present this panorama with its various 

 aspects in adequate relation to each other. Mr. 

 Marvin, in his " Living Past," and Mr. Wells, in his 

 " Outline of History," have produced tentative 

 sketches in that direction. Such works point to a 

 time when the history of civilisation, the most absorb- 

 ing of all topics, will form the humane basis of educa- 

 tion. There are, however, large departments in which 

 the material is not yet to hand for this consummation. 

 Especially defective is our record of certain aspects 

 of the development of thought. Formal thought, 

 philosophy, has, it is true, found fairly adequate treat- 

 ment. A real history of religion is, however, still 

 strangely absent, despite the vast literature which 

 professes to deal with that topic, and the history of 

 psychology is very backward. The history of science, 

 too, presents vast gaps which are sometimes vainly 

 treated as though they represented breaches in con- 

 tinuity of the phenomena rather than breaches in our 

 knowledge, and the two works before us represent the 

 efforts of two eminent scholars in two separate depart- 

 ments to establish continuity across these gaps. 



(i) Sir CUfford Allbutt has been distinguished for 

 two full generations and more as an exponent alike 

 of modern scientific medicine and of the scientific 



