July 6, 1900.] 



SCIENCE. 



35 



been more or less familiar ever since its intro- 

 duction by Thomson and Tait, but to young 

 students it can scarcely fail to bring uncom- 

 pensated trouble. Among the problems on 

 this subject is the following : "What is the aim 

 of the clockmaker ; to produce an instrument 

 which will give constant angular speed or con- 

 stant angular velocity ?" It is perhaps safe to 

 say that few clockmakers would answer with 

 confidence ; and probably some teachers would 

 hesitate also, especially after trying to assure 

 themselves that ' ' an ordinary peg top may be 

 used to illustrate the case of a body having a 

 constant angular speed, but at the same instant 

 a variable angular velocity." For mental 

 gymnastics in following out the metaphysics of 

 a definition the distinction may have its value ; 

 but there are many whose maturity exceeds 

 that of high school pupils, and who find the 

 word velocity, with suitable adjuncts, quite 

 enough for all practical purposes. The facts 

 give little trouble, for velocity in any given di- 

 rection can always be specified, while wordg 

 may become tyrants. 



As an exact science physics is built up on dy- 

 namics as a foundation. The study of linear, 

 angular, and harmonic motion therefore consti- 

 tutes its most natural introduction, along with 

 the consideration of the general properties of 

 matter, of momentum, rotational inertia, and 

 universal gravitation. Each of these subjects 

 is treated with intelligence and skill, with 

 mathematics that is not abstruse for a college 

 student, but in a style that seems rather severe 

 for the preparatory schools. Indeed the first 

 hundred pages of the book, relating to subjects 

 that admit of but little experimental illustra- 

 tion, are certainly rather hard for students be- 

 low collegiate grade. Passing on then to wave 

 motion and acoustics, the rest of the volume is 

 non-mathematical and very attractive. 



In the discussion of sound the building of the 

 musical scale is brief, yet clear ; but it seems a 

 little unfortunate that the frequency of middle 

 C should be given as 264. This number was 

 adopted by the Stuttgart Congress in 1834, and 

 the scale built upon it was used in Helmholtz's 

 ' Sensations of Tone ' ; but it never won uni- 

 versal adoption. Within the last few years, 

 and largely through the activity of the late 



Governor L. K. Fuller, of Vermont, all the 

 civilized nations of the world have adopted A, 

 435, as standard pitch for the construction of 

 musical instruments, England being the last to 

 yield. As all keyed instruments are made with 

 the aim of producing the equally tempered 

 scale, rather than the diatonic scale, it is read- 

 ily found, by application of the proper factor, 

 (1.05946)-', that the frequency of the middle C, 

 for this international pitch, is 258.65. For the 

 purpose of the phj'sicist the diatonic scale will 

 probably continue in use, and Koenig's forks 

 are universally regarded as the best. These 

 are tuned, unless specially ordered otherwise, 

 to the so-called physical pitch, introduced a 

 century ago by Chladni, with 03 = 256. The 

 wild confusion of a generation ago has now been 

 reduced to order, with the survival of but two 

 definitely related systems. One of these is in- 

 ternational pitch, with ^3 = 435 as starting 

 point for the scale of equal temperament ; the 

 other is physical pitch, with Cj = 256 as start- 

 ing point for the diatonic scale. Each of these 

 is of course arbitrary, the result of agreement, 

 while the equally arbitrary Stuttgart pitch is 

 now of only historic interest. In a text-book 

 of physics it may be mentioned, but should no 

 longer be taught ; and 256 rather than 264 

 should be the basis for a diatonic table of fre- 

 quencies. 



The closing chapters on heat, magnetism, 

 electricity, and light are well arranged, clearly 

 expressed, and modern in style of treatment, 

 with judicious omission of much that the high 

 school pupil can well afford to disregard until 

 the subject is resumed in college. For example, 

 the polarization of light is not mentioned, while 

 diffraction comes in as an elementary illustra- 

 tion of the wave theory, a few simple experi- 

 ments being explained which are both interest- 

 ing and easily made. In the development of 

 the laws of geometrical optics, wave fronts are 

 freely indicated in the diagrams, but equally 

 free use is made of the convenient term 'ray.' 

 The fact that this means merely a direction is 

 no reason for abolishing it, as has been done in 

 a few recent text-books of physics. 



W. Le Conte Stevens. 

 Washington and Lee Univeesity. 



