Junk 23, 1899.] 



SCIENCE. 



873 



course of preparation by the authors, the others 

 relating to 'Properties of Matter,' 'Heat,' 

 'Magnetism and Electricity,' and 'Light,' re- 

 spectively. 



These test-books are intended " chiefly for 

 the use of students who lay most stress on the 

 study of the experimental part of physics, and 

 who have not yet reached the stage at which 

 the reading of advanced treatises on special 

 subjects is desirable." The nature of sound 

 and its chief characteristics are first considered 

 in a chapter that is wholly free of mathematics. 

 The velocity of sound in air aud other media is 

 then discussed, the reflection and refraction of 

 sound, frequency and pitch of notes, resonance 

 and forced oscillations, the analysis of vibra- 

 tions by Fourier's theorem, the transverse 

 vibrations of stretched cords, longitudinal vi- 

 brations in pipes and other air cavities, vibra- 

 tion of rods, plates and membranes, the 

 Trevelyan rocker, sensitive flames and musical 

 sand. The last chapter is on the superposition 

 of waves, with application to the physical basis 

 of concord and discord, and on combination 

 tones. 



The distinguished authors are so well known 

 for their original and accurate work as investi- 

 gators that the critic who is in search of mis- 

 takes will find little to note, beyond a very 

 small number of obvious typographical errors. 

 In the descriptive parts the style is clear and 

 the paragraphing is good. A majority of the 

 illustrations are in the form of diagrams. In 

 the mathematical parts the use of calculus is 

 wholly avoided. 



In judging the practical value of a text-book 

 it is necessary to take into view a number of 

 considerations which have no place in connec- 

 tion with what is intended for the advanced 

 reader. Regard must be had also for diflTerences 

 of educational method in different countries. 

 If instruction is given by lectures entirely the 

 text-book is merely an accompaniment for pri- 

 vate reading. But if the text book is to be a 

 drill book, as is, perhaps, most frequently the 

 case in America, and especially if much of its 

 contents be mathematical, it will almost surely 

 be unsatisfactory unless prepared by one who 

 has had much experience, not merely in the 

 art of presentation, but especially in that of 



testing the student's success in acquisition. At 

 the outset there must be a clear understanding 

 as to the amount of preliminary knowledge 

 that can be reasonably assumed on the part of 

 the student. It is a matter of common obser- 

 vation that a mathematical genius is rarely 

 ever a good mathematical teacher, because he 

 usually fails to appreciate the difficulties ex- 

 perienced by those who are less gifted than 

 himself. Even when the teaching is to be not 

 oral, but by use of the printed page, it is 

 wonderfully easy to express mathematical truths 

 in such form as to put them quite beyond the 

 grasp of a fairly intelligent student. 



It is not in the domain of acoustic science, 

 but in the art of text-book adaptation that the 

 present volume is found somewhat wanting. 

 If the reader can be assumed to possess already 

 a good knowledge of general physics he will 

 find much to interest him. But if he is to obtain 

 his introduction to acoustics through the me- 

 dium of this text-book he will not proceed 

 very far without becoming discouraged. Unde- 

 rived formulas are employed so frequently that 

 the reader who does not recognize them is jus- 

 tified in being impatient. He takes little satis- 

 faction in reading that an unfamiliar mathe- 

 matical statement ' can be proved ; ' or that it 

 'can be shown from the equation, etc.,' which 

 in turn ' can be reduced to ' another unrecog- 

 nized form. Such statements are, of course, 

 occasionally necessary, but in a text-book their 

 use should be reduced to a minimum. In the 

 great majority of cases such demonstrations 

 amount to no demonstration at all. It is readily 

 perceived that the author has gone through the 

 requisite mathematical work, but does not wish 

 to cumber his page with the details that are 

 indispensable to a clear understanding of the 

 subject by the student. 



In a mathematical text-book, whether this 

 term be applied to pure mathematics or to a 

 book involving the applications of mathematics, 

 it is of the utmost importance that all para- 

 graphs shall be numbered, that equations shall 

 also be numbered, and that the relation between 

 new and old topics shall be indicated by fre- 

 quent cross references. Attention to such 

 details increases the labor of composition for 

 the author, while the neglect of them greatly 



