558 



NA TURE 



[April 12, 1906 



The Integration oj Functions oj a Single Variable. 

 Cambridge Tracts in Mathematics and Mathe- 

 matical Physics, No. 2. By G. H. Hardy, M.A. 

 Pp. viii + 53. (Cambridge: University Press, 1905.) 

 Price Ji. i>d. net. 

 Now that function-theory i- fairly well developed, it 

 is much easier than it used to be to discuss in an 

 orderly way the elementary problems of explicit in- 

 tegration. By showing how this can be dune, Mr. 

 Hardy has produced a very instructive and pleasant 

 supplement to the ordinary text-books. Moreover, he 

 has done a useful service i>\ emphasising the work of 

 Liouville, whose theorem (quoted on p. 49) is of great 

 generality, and occurs with others in memoirs which 

 have net, perhaps, received all the attention they 

 deserve. To these memoirs, as well as those of Abel, 

 Tchebichef, &c, reference is made in the notes ami 

 appendix; this, of course, adds greatly to the value 

 of the pamphlet. 



It must be remembered that the " Cambridge 

 Tracts," of which this is No. 2, are not intended to 

 he exhaustive, hut rather suggestive and helpful to 

 those who are really interested in the progress of 

 mathematical theory, and prepared to study it at first 

 hand. Mr. Hardy stems to have carried out this idea 

 as well as his opportunity admitted ; and his reader 

 ought to feel that he gets his half-crown's worth of 

 entertainment. For example, on pp. 13-16 we have 

 Hermite's beautiful way of finding, by elementary 

 rational operations, the rational part of the integral 

 of a rational function, and in connection with this 

 an example involving, in an unexpected fashion, the 

 theory of invariants. To the remark on p. 38 it may 

 be added that the problem of deciding whether a 

 given integral is pseudo-elliptic or not is likely to be 

 of a nature quite similar to that of deciding" whether 

 two given conies can be associated with poristic 

 circum-inscribed polygons. No finite number of 

 rational operations can give an answer ; but we can 

 decide whether poristic polygons of any assigned 

 number of sides exist or not. To the references on 

 this subject the names of Halphen and Kowalevsky 

 might have been added. 



The Laboratory Book of Dairy Analysis. By H. 

 Droop Richmond, F.I.C. Pp. viii + 90. (London: 

 C. Griffin and Co., Ltd., 1905.) Price 2s. 6d. net. 

 With the progress of technical instruction in dairy- 

 ing a need has arisen for a little handbook on milk 

 •composition and simple methods of milk analysis for 

 dairy managers. There is also a need for a short 

 handbook of dairy analysis for the trained chemists 

 who find themselves called upon to undertake analyses 

 ■of milk, cream, butter, and cheese in the laboratories 

 of agricultural colleges and institutions. Mr. Rich- 

 mond has attempted to serve both purposes in one 

 little volume, and, as might be expected, the result 

 "is not entirely successful. For the chemist the illus- 

 trations of laboratory assistants performing simple 

 laboratory operations, such as using a wash-bottle, 

 ttre, to say the least, unnecessary, while to the dairy 

 manager who is not a chemist the directions for the 

 more difficult analyses would be quite unintelligible. 



However, for the chemist the book provides a mass 

 of useful details in a concise form. The analytical 

 methods are well chosen, though it is curious to find 

 no mention of the Westphal balance for the determin- 

 ation of the specific gravity of milk; and we can 

 ■detect no errors or inaccuracies, though there is 

 occasional need for greater clearness, for example, in 

 the meaning of " the Reichert-Wollny figure." These 

 •defects are unimportant, and the book will find a 

 useful place in many an agricultural laboratory. 



T. S. I). 



NO I O02. VOI . 73] 



LETTERS TO THE EDITOR. 



[Tlie Editor does not hold himself responsible for opinions 

 expressed by his correspondents. Neither can he undertake 

 to return, or to correspond with the writers of, rejected 

 manuscripts intended for this or any other part of Nature. 

 No notice is taken of anonymous communications.] 



Chemistry in Rural Schools. 



It lias no doubt caused as much surprise to others as it 

 has to myself to read, on the authority of the principal of 

 the South-Eastern Agricultural College, that " chemistry is 

 one of the least suitable of the natural sciences to teach 

 children whose lives will be, or ought to be, spent in the 

 country" (M. J. R. Dunstan, Nature, March 29, p. 511). 

 I have no doubt that Mr. Dunstan has good reasons to 

 assign for this expression of opinion, but those who are 

 interested in the subject of education in rural schools will 

 probably want some more explicit statement before re- 

 considering their curricula. For my own part I had come 

 to an opposite conclusion. It has been my privilege during 

 ill- last Few years to have been associated with the founders 

 of two rural schools, one in Essex and the other in Suther- 

 land. The curricula of these schools were very carefully 

 considered by my colleagues and myself, and the question 

 of the suitability of chemistry was never raised ; on the 

 contrary, we considered that from the disciplinary as well 

 as from the utilitarian point of view it had everything in 

 its favour. Nor have we had any reason during the exist- 

 ence of these schools to doubt the wisdom of including 

 cheajistry in the curricula. As a means of training in ex- 

 perimental method and of inculcating habits of careful 

 observation and accurate reasoning, this science (with 

 physics) has been taught with the greatest success. It is 

 popular with the pupils and of distinct value to them in 

 .ill -1 lit'', even when that lit'' is " spent in the country." 



Perhaps the best justification 1 can offer for the con- 

 clusion to which my own experience has led me is furnished 

 l'\ the Sutherland Technical School, founded three years 

 ago at Golspie by the Duchess of Sutherland. The pupils 

 in this school are as " rural " a set of lads as could be 

 gathered from any part of the Highlands, being for the 

 most part of the crofter and fishing class. Their age varies 

 from twelve and a half years upwards, and the course of 

 instruction extends over a period of three years. During 

 the fust year four hours a week are given to elementary 

 practical physics, and the same amount of time to prac- 

 ] tical chemistry during the second year. Both physics and 

 chemistry will be continued in the third year. The head- 

 master, Sir. E. \V. Read, writes to me as follows : — " The 

 boys like the work, and find no particular difficulty with it : 

 besides, I find their knowledge a great help in the natural 

 historj lessons and in the gardening. Further, I feel 

 strongly that the mental discipline of chemistry properly 

 taught U very great, and is likely to put a boy's mind in 

 the attitude of desiring to keep pace with the progress of 

 the times. Most of our boys will have to go straight to 

 work, and 1 should be very sorry if a single one left with- 

 out some knowledge of elementary chemistry." 



We have had a similar experience in Essex, and it 

 would be of interest to learn from others who have 

 first-hand knowledge of the teaching of science in rural 

 schools of a similar type to those founded by the Countess 

 of Warwick and the Duchess of Sutherland how far chem- 

 istry has been successful as a recognised part of the curri- 

 culum, ft would appear from Mr. Dunstan's letter that 

 he considers this science to have been inserted in the 

 curricula at the expense of the biological sciences. This 

 is not the case in the two schools with which I am con- 

 cerned. Natural history subjects (in the broad sense) are 

 also taught, and one of the reasons which weighed with 

 us in including chemistry was that an elementary training 

 in this subject was considered essential as a preliminary 

 foundation for the biological subjects. With respect to the 

 education of young men who are actually " on the land " 

 or who are preparing for rural occupations, the teaching of 

 chemistry at the Central School of the Essex County 

 Council at Chelmsford has always been most successful, 

 lie, 1I1 in popularity and in subsequent results. The former 

 stall instructor, Mr. T. S. Dymond, now of the Board of 

 Education, to whose zeal and ability the successful intro- 



