January 25, 1906] 



NA TURE 



291 



of theory and demonstration. The student of physics 

 is somewhat differently circumstanced. From time 

 immemorial physical research and mathematical 

 methods have been more or less closely associated, 

 and every student of physics knew that a certain 

 knowledge of higher mathematics was demanded of 

 him. Yet complaints have been heard even from him 

 that the mathematical courses in our colleges lacked 

 a certain flavour of the real, and were not particu- 

 larly suited to his needs. It has often been said that 

 there is no royal road to mathematical knowledge. 

 To quote Dr. Mellor himself, a certain amount of 

 drudgery is necessary in some stages. But some 

 roads are easier than others; and in this book 

 chemical and physical problems are introduced, like 

 rest houses along a weary way, to cheer the flagging 

 traveller. Here he finds familiar food for his mind. 

 'Id change the metaphor, the student is given a new 

 weapon, and at the same time is taught how l<> iiv 

 it on material alreadv his. 



To what extent the reader, otherwise ignorant oi 

 th. principles of the differential calculus, will be able 

 to ippreciate the first chapter, experience alone can 

 tell. The introduction of sections on proportionality 

 and logarithms in the middle of the discussion of 

 differentiation does not strike one favourably. The 

 author's reference to this in the preface may, how- 

 ever, be accepted as sufficient excuse. 



The new edition is fundamentally the same work 

 as the old, but about a fifth more bulky. The increase 

 in size is due partly to a more sparing use of small 

 type, but chiefly to the introduction of new matter. 

 'I In re is also a good deal of re-arrangement of in- 

 dividual sections, such, for example, as the carrying 

 forward of the paragraphs on the Gamma and 

 elliptic functions from chapter iv. (the integral 

 calculus) to chapter vii. (how to solve differential 

 equations). From a physical point of view this is 

 undoubtedly the better arrangement; and there is 

 a further improvement which deserves notice, namely, 

 the leading up to each of these functions by the dis- 

 cussion of a comparatively simple dynamical problem. 

 The most obvious addition is the new chapter on the 

 calculus of variations, in which brachistochrones and 

 isoperimetrical problems are touched upon. Probably 

 the main service rendered by this chapter will be to 

 enlarge the outlook of the student. The class of 

 readers for whom the book is ostensibly written will 

 hardly ever be called upon to apply the calculus of 

 variations, and if they should be they would find the 

 discussion too meagre for them to make effectual use 

 of it; but it is a real service to open a man's mind 

 to the things which lie beyond the immediate purpose 

 of his life. The still too common utilitarian idea that 

 the practical man should be taught just as much 

 mathematics as we know to be necessary for his 

 immediate needs is an idea which cannot be too strenu- 

 ously contested. The truth is, we never know what 

 will be needed before the year is out. The chemist 

 of the last generation would as soon have thought 

 of studying the properties of Theta functions as of 

 familiarising himself with the modes of solution of 

 the simpler, differential equations, or even with the 

 NO 1891, VOL. 73] 



meaning of a differential coefficient ; but that attitude 

 of mind is impossible now. The theoretical chemist 

 of the rising generation must know his mathematics, 

 and we are convinced that many will bless Dr. Mellor 

 for providing them with an eminently readable and 

 thoroughly practical treatise. 



Throughout the book there are many historic notes 

 which are always interesting in their way. It will 

 not, then, be thought amiss to direct attention to the 

 section on pp. 59 and 60, and to ask why writers 

 are so slow to do Newton justice in regard to his 

 so-called law of cooling. It is now six years since 

 Prof. Crichton Mitchell, in a paper on the convection 

 of heat by air currents (Trans. R.S.E., vol. xl. 

 p. 39), pointed out, what seems to have escaped 

 the notice of every commentator except Fourier, 

 that Newton deliberately placed his cooling body 

 " non in aere tranquillo, sed in vento uniformiter 

 spirante." Dulong and Petit, therefore, and all their 

 copiers, including Dr. Mellor himself, are not giving 

 " a typical example of the way in which the logical 

 deductions of an hypothesis are tested " when they 

 try to apply Newton's law to a body cooling in 

 tranquil air. Crichton Mitchell showed that when 

 Newton's conditions wore realised Newton's law held 

 with wonderful accuracy over a considerable range 

 of temperature differences. C. G. K. 



PLANT DISE l.s/./v 



Minnesota Plant Diseases. By Dr. F. M. Freeman. 

 Pp. xiii + 432. (St. Paul, Minnesota: The Pioneer 

 Press.) 



THIS publication is issued for " the people of 

 Minnesota " by authority of the university of 

 that State. It may have special reference to a par-, 

 ticular State, bat it is quite evident, from a perusal 

 of its pages, that the book will be of service wherever 

 plants are cultivated. The author takes a broad view 

 of his subject, and rightly considers the prevention 

 ol disease as a more important matter, from the 

 point of view of the cultivator, than the application 

 of remedies. "Agriculture," says he, "really re- 

 solves itself into one great problem, the prevention 

 of plant-disease." Keep the "patient" in good 

 health by careful attention to his physiological re- 

 quirements, by cleanliness and by strict compliance 

 with the teachings of hygiene. Much more good, 

 will ensue from these measures than from the use 

 of insecticides or anti-fungus spravs. A knowledge 

 of the life-history of the plant, as well as a corre- 

 sponding familiarity with the mode of life of the 

 hostile insect or fungus, is, indeed, essential, but 

 unless combined with the faculty of turning that 

 knowledge to account, the information is, practically 

 speaking, of no value. 



The first question that is asked when a diseased 

 specimen is submitted is, " What is the matter with 

 this plant? " The next, and in the view of the 

 questioner the most important, is, " What am I to 

 do to get rid of the disease? " Not one in a hundred 

 cucumber-growers, cultivators of the vine or other 

 crops, asks a question as to the methods of preven- . 



