ESSAY-REVIEWS 691 



other than rational integral ones of low degree. This, of course, can easily be 

 done without impairing the proof of the really useful propositions. 



Nevertheless, Prof. Dickson's book is more practical than some on the same 

 subject. It is pleasant to see that he recognises the advantage of Newton's 

 method over Horner's for the solution of numerical equations, in that the former 

 applies as well to non-algebraic as to algebraic equations— in spite of De Morgan's 

 advocacy of the latter method. But neither this book nor the recent one of 

 Burnside and Panton make any mention of Michael Dary's beautiful method 

 (further studied by Heymann and others). The development of roots in conver- 

 gent infinite series is left altogether untouched, possibly because Newton said that 

 such series were not useful in the solution of equations. There is also no 

 reference to the analysis of equations by considering them as the intersections of 

 two independent curves, and we are still supposed to use Sturm's theorem where 

 an equation can be analysed in two minutes in this way. 



The whole subject of mathematical textbooks needs revision in the interests 

 of men of science who are frequently required to make calculations for the study 

 of their own subject, even in biology, but who have no time to make themselves 

 expert mathematicians in general. After all, what we want is a working know- 

 ledge of the Calculus, of the management of series, and of the solution of equations, 

 and as regards all of these the existing academical textbooks give us little help, 

 unless we are prepared to spend months of study over them. Each book seems 

 to be copied from the previous one, and to be meant merely for schoolboys 

 and undergraduates, and not for men who have their work in the world to do. 



PACT AND FANCY IN HEMATOLOGY, by H. C. Ross : on The 

 Biology of the Blood-Cells, by O. C. Gruner, M.D., Lond. [Pp. xii + 

 392 and 83 Illustrations, 7 in colour.] (John Wright & Sons, Ltd., Bristol, 

 price 21s. net.) 



One of the first instruments bought by the medical student is a microscope, and 

 the first operation he does is usually to prick his own finger, or preferably that of 

 his laboratory neighbour, and examine the blood. Thus from the outset he becomes 

 an authority on the blood-cells and their biology. The examination of the blood is 

 so easy and the cells look so pretty, that the subject is one of great interest to the 

 medical man throughout his career. Should he, by chance, drift to become a 

 professor of pathology, it will be expected of him to write a treatise on the blood at 

 least once in his life-time. On an average these textbooks appear about once a 

 quarter, and have done so for nearly half a century ; moreover, nearly every one 

 of them bears a dedication or acknowledgment to Pappenheim. 



The book under review is one of these textbooks, although it is modestly styled 

 a companion to other textbooks ; but it does contain some novel points which 

 make it differ from most of them. It is clearly and pleasantly written ; the author 

 has a charming style in those few paragraphs where he can depart from Pappenheim 

 and embark on description. There are no chapters on or paintings of malaria 

 parasites or trypanosomes ; there is no description of how to make a blood-count 

 or stain a film ; and from this work it is impossible to make a lightning diagnosis 

 of osteoarthropathy or mental aberration. But there is an excellent glossary of 

 hematological terms which must have involved immense work ; and the biblio- 

 graphy is complete. 



The subject-matter of the book itself is occupied in describing how certain cells 

 of the body go to form other cells, and the other cells to form other cells, and at 



