September io, 1903] 



NATURE 



435 



which is so frequently exhibited by draughtsmen and 

 .students of engineering-. 



Again, the definition of an angle — " an angle is the 

 difference in direction of two lines drawn from a 

 point " — has nothing really quantitative about it, and 

 should be used rather as a familiar description than 

 as a quantitative definition. 



After the definition of parallel lines — *' parallel lines 

 are such as are the same distance apart throughout 

 their whole length " — we have the warning " be 

 careful to distinguish between parallel and horizontal," 

 which unintelligibility is, doubtless, in some way con- 

 nected with the strange conception of horizontal above 

 noticed. 



We are now done with the blemishes; for the rest 

 we have nothing but commendation. The book is 

 divided into a series of lessons, each of which is 

 followed by several exercises in the copying of various 

 figures and patterns on squared paper, accompanied 

 by arithmetical calculation. The little pupil is led 

 easily into the subject, and he meets with nothing like 

 severe reasoning until lesson vii. is reached. The 

 grouping of propositions and constructions is through- 

 out very good, and the chapters on areas particularly 

 excellent. The most useful propositions of Euclid's 

 books ii. and iii. are included, and the concluding 

 lessons deal with loci, ratio and proportion, similar 

 figures, &c., and include a large number of important 

 problems, theorems, and constructions. This portion 

 of the book (the most important) can scarcely be im- 

 proved upon, and, indeed, for this part of the subject, 

 we do not know of any work for beginners which 

 deserves higher commendation. 



The book by Mr. Millis can be very strongly re- 

 commended as one the study of which should go hand 

 in hand with that of books on purely deductive geo- 

 metry. It begins with the definitions and figures of 

 geometry, and the use of instruments for the solutions 

 of the problems which are usually treated of in geo- 

 metrical drawing. Then follows the treatment of 

 fractions, vulgar and decimal, their nature being ex- 

 plained and illustrated by geometrical construction. 

 Contracted methods of multiplication and division are 

 explained. The nature of ratio and proportion follows, 

 and then the enlargement and reduction of figures, 

 square root, propositions relating to areas— in the 

 whole of which work arithmetic goes hand in hand 

 with geometry. After the usual figures of elementary 

 plane geometry are dealt with, conic .sections and 

 irregular curvilinear figures are taken, and their 

 properties illustrated by arithmetical examples, with 

 the use of squared paper. Simpson's rule and 

 Henrici's method are explained. The last third of the 

 book deals very fully with the mensuration of solids. 



The pupil who uses this work will receive a thorough 

 drilling in neat and accurate drawing — a thing which 

 was very much needed when Euclid held sole sway in 

 the schools. 



Mr. Murray's book is a sequel to the work which 

 we noticed some months ago. It is meant for teachers, 

 inasmuch as no answers are given to the various ques- 

 tions. Comparing the work with either of the two 

 books on arithmetic now noticed, it would appear that 

 NO. 1767, VOL. 68] 



in the American schools the subject is taught in a very 

 leisurely manner, since there is nothing of a very 

 advanced nature in this work, and a great deal of the 

 mere elements is included. This, of course, may in 

 the end make for thoroughness. It seems somewhat 

 strange that addition and subtraction of decimals are 

 employed in the beginning (p. 31, &c.), while the 

 subject of decimals is subsequently taken (p. 127, 

 &'C.) and treated ab initio. 



.Arithmetic and a certain amount of elementary 

 algebra go hand in hand in the book — an arrangement 

 which makes things simple for the beginner; but the 

 purpose of several pages on very elementary algebra 

 at the end of the chapter on percentage is not clear. 



The metric system is, of course, explained and illus- 

 trated, but the large amount of space devoted to 

 English weights and measures, with their antediluvian 

 lawlessness and complexity, induces sad reflections on 

 the utter waste of time which we impose upon our 

 youth. 



The chapter on " Computations and Approxim- 

 ations " contains a useful exposition of the use of 

 squared paper for the plotting of curves and the deter- 

 mination of missing values by graphic interpolation. 

 As compared with our English works, the most 

 striking characteristic of this book is, perhaps, the 

 absence of complexity and useless difficulty in the 

 various examples. It is a merit of the author that 

 he is very particular about the accurate use of 

 language— a great desideratum in these davs of slip- 

 shod writing, when English grammar and a logical 

 arrangement of thought are steadily vanishing from 

 our scientific treatises. 



Teachers everywhere will find the work very helpful 

 and suggestive for a natural and logical way of teach- 

 ing the subject to young pupils, inasmuch as the 

 methods employed are the result of many years' prac- 

 tical experience in the work of instruction. 



Mr. Chope has prepared a treatise of the usual kind 

 on arithmetic. It contains a very large collection of 

 examples illustrating the various rules, and is just as 

 good a handbook of the subject as the student can 

 desire. 



THE NEURONE THEORY. 

 Die Neuronenlehre und ihre Anhanger. By Dr 

 Franz Nissl. Pp. vi + 478. (Jena : Gustav Fischer.) 

 Price 12 marks. 



/^NE approaches this work with rather mixed feel- 

 V-y ings. While there is no doubt that an ex- 

 haustive survey of our present knowledge in any 

 branch of science is certain to well repay the investi- 

 gator, yet a book of the magnitude of \he one now 

 under consideration, which contains only a contro- 

 versial view of already known facts, wi'thout intro- 

 ducing anything beyond what is familiar to us, leaves 

 on the mind of the reader something of a feeling of 

 weariness, and a suspicion that the same amount of 

 labour would have been better expended in quarrying 

 fresh knowledge rather than reshaping the blocks that 

 have been already brought out. The author himself 

 has realised this, and in the preface gives the reasons 

 which induced him to give the present form to the 



