;i6 



NA TURE 



[August 4, 1904 



in arts. 1-9 of chapter xiv., but more use might have 

 been made of the method. Applications may be found 

 in the theor)' of orthogonal substitutions (xiv., 19, 24) 

 and in " the equation of secular inequalities " (xi., 

 19). The expression given in xiv., 7, does not correctly 

 represent the square-root of a bilinear form ; in fact 

 [;^(.v)]- — .V is not divisible by \j/(.v), the last equation 

 on p. 185 being wrong. The right value will be found 

 in Muth's book (pp. 37, 38); see also froc. Camb. Phil. 

 Soc, vol. xi. p. 81. 



The reduction of a quadratic form to squares (xiv., 

 10) may prove misleading, for it is natural to sup- 

 pose that the reducing substitution belongs to the 

 same unitary type as those in the article quoted 

 (vii., 10). But this inference is not usually correct; 



thus 2x'- + 2xy + 2y'-, which has the matrix ("'')> 



cannot be reduced to the form ?^(ax + by)- + fi{cx + dvy-, 

 where x, fi, a, b, c, d are integers. It is remarkable 

 that a corresponding reduction is possible for an 

 alternate form ; this contrast might be mentioned. We 

 are surprised that Weierstrass's theorem on equi- 

 valence of bilinear forms is not stated, although 

 Kronecker's theorem (xiv., 8, 9) is proved; the latter 

 can hardly be appreciated without the former. 



Instead of the bibliographical list which closed the 

 first edition, Mr. Mathews has given a brief historical 

 note. It would have been better to add some refer- 

 ences in the course of the text, for, even with a biblio- 

 graphy at hand, it is often difficult to identify the 

 original sources from which extracts have been taken. 



T. J. I'A. B. 



-4 MANUAL OF MEDICINE. 

 A Manual of Medicine. Edited by W. H. .Allchin, 

 M.D., London, F.R.C.P. Vol. v. Pp. xii + 687.' 

 Plates ii. ; charts and diagrams. (London : Macmillan 

 and Co., Ltd., 1903.) Price los. net. 

 'T~"HE volume before us is the fifth of Dr. Allchin's 

 -»- manual of medicine, and is devoted to diseases 

 of the digestive system, the liver, the peritoneum, the 

 vessels of the abdomen, the kidneys, and the ductless 

 glands. 



The volume begins with two short articles by the 

 editor upon the normal anatomy of the alimentary 

 canal and the physiology of digestion. These articles 

 seem to be well up to date, and in the former due im- 

 portance is attached to the surface anatomv of the parts, 

 so important to the clinician. It is, however, rather to 

 be regretted that in the physiology of digestion no men- 

 tion is made of the recent work upon pancreatic 

 secretion. These articles are immediately followed by 

 one on food and diet by Dr. R. Hutchinson. In 

 twenty pages, only the merest outlines of this subject 

 could be discussed, and the value of articles so con- 

 densed is open to question ; the principles, however, of 

 dietetics and the chemical composition of the most im- 

 portant food-stuffs and food preparations are given. A 

 useful note upon the bacteria of the alimentary canal, 

 with some suggestions concerning the therapeutic use 

 and actions of so-called intestinal antiseptics, is written 

 by Dr. Lazarus Barlow. 



NO. 1 8 14, VOL. 70] 



The following eighty pages are devoted to diseases 

 of the mouth, tongue, pharynx and oesophagus, an 

 account of these being supplied by Dr. Bertram 

 .Abrahams. These diseases are treated in a comprehen- 

 sive and systematic manner. We would draw special 

 attention in this connection to the parts of the article 

 devoted to throat complications of acute infectious 

 diseases and the differential diagnosis of acute sore 

 throat. The practitioner will find these sections ex- 

 ceedingly useful. The next section of the work treats 

 of diseases of the stomach and intestines, this section 

 occupying practically 200 pages and being written by 

 the editor. Interpolated in the above is a short account 

 by Dr. Bertrand Dawson of the physical examination 

 of. the stomach and intestines. This includes the 

 ordinary clinical methods and the examination by the 

 Rontgen rays and by so-called gastro-diaphany, and also 

 directions for the chemical examination of the gastric 

 contents after the administration of test meals. The 

 reviewer cannot, however, find any directions for the 

 chemical or microscopic examination of the faeces, 

 which might well have been incorporated. In view of 

 recent work upon the subject, a short article by the 

 editor upon diseases of the pancreas will be of interest. 



-A hundred odd pages are devoted to diseases of the 

 liver, this subject being introduced by a general article 

 upon the morbid anatomy of the liver by Dr. Barlow. 

 Hepatic abscess and perihepatitis are dealt with by Dr. 

 Crombie ; degenerations, new growths and gall-stones 

 by Dr. Hebb. 



The next section of the book treats of diseases of the 

 peritoneum, and it is also introduced by a short note on 

 the general anatomy of the peritoneum. The consider- 

 ation of retro-peritoneal suppuration and tumours and 

 sub-phrenic abscess concludes this monograph, for 

 which Dr. Hale White is responsible. Dr. Bryant 

 writes a short account of the diseases of the abdominal 

 blood-vessels, and the volume concludes by an article 

 by Dr. Bradford upon diseases of the kidneys, and one 

 by Drs. Sydney Coupland and Bertram Abrahams upon 

 diseases of the ductless glands. 



It will be seen from the above remarks, which amount 

 to little more than an elaborated table of contents, that 

 the volume before us deals very fully with the diseases 

 of the abdominal organs. In conclusion, we may add 

 that this last addition to Dr. Allchin's manual of medi- 

 cine maintains the standard of its predecessors, and is 

 likely to be of much value to the professional reader. 

 Its usefulness is enhanced by a complete and accurate 

 index. F. W. T. 



OUR BOOK SHELF. 



The Racing World and its Inhabitants. Edited by 



.A. E. T. Watson. Pp. vii + 309; illustrated. 



(London: Macmillan and Co., Ltd., 1904.) Price 



12s. 6d. net. 



This volume, which consists of a reprint of a series 



of articles contributed by various writers to_ the 



Badminton Magazine, is essentially a work written 



by racing men for racing men, and as such seems 



admirably adapted for its purpose. An important 



feature is that each article is written by one who has 



