NA TURE 



60 1 



THURSDAY, OCTOBER 19, 1905. 



.UECH.4.V/CS FOR STUDENTS. 

 Mechanics, a School Course. By W. D. Eggar, 



Pp. viii + 2SS. (London : Edward Arnold, 1905.) 



Price 3s. 6d. 

 Elements of Mechanics. By Prof. Mansfield Merri- 



man. Pp. 172. (New York : John Wiley and Sons; 



London: Chapman and Hall, Ltd., 1905.) Price 



I dollar net. 

 All Intermediate Course of Mechanics. By A. W. 



Porter. Pp. viii + 422. (London : John Murray.) 



Price 5x. 



MR. EGGAR is doing good work in tlie move- 

 :Tient which aims at the extension of quanti- 

 tative measurements in the courses of mathematical 

 studies for youths, and a school book of mechanics 

 from the author of the well known experimental 

 introduction to geometry is sure to be received with 

 favour and interest by teacher and pupil alike. \A'e 

 ■may say at once that readers are not likely to be 

 ■disappointed, for the experimental work on which 

 the fundamental principles are based is simple, 

 suggestive, and thorough, and the essence of the 

 subject is not obscured by an undue amount of mathe- 

 matical dressing. 



The first five chapters are concerned with the verifi- 

 cation and elucidation of Newton's laws of motion, 

 and some ver\- efficient apparatus is introduced and 

 described in this admittedly difficult portion of the 

 subject; we agree with the author that "velocities, 

 accelerations, moments, work, and momentum can 

 be made clear to a student if he has to measure 

 them." Experiments of Galileo by means of whicli 

 the laws of falling bodies were discovered are intro- 

 duced with suitable modifications ; a clever method 

 •of measuring time by the use of a vibrating spring 

 carrying a paint brush (due to Mr. Fletcher) is 

 ■employed, and altogether this section, treating kinetics 

 ■experimentally, is most interesting and very satis- 

 factory. The next five chapters relate to statics and 

 the equilibrium of forces, and the remaining portion 

 of the book deals with work, friction, simple 

 machines, projectiles, circular and simple harmonic 

 motions, stress and strain, and fluids. 



There is little in the book to which exception can 

 be taken. When the author seems to imply that the 

 unit of force in the " engineer's " system is a variable 

 quantity, he appears to misapprehend the system. 

 The experiments on change of motion are confined to 

 straight-line motion. The student would liave been 

 led to a more comprehensive view of the subject if 

 there could have been introduced an experiment illus- 

 trating vector change in plane motion, accompanied 

 by the plotting of a hodograph. Then, instead of 

 resorting to an antiquated and non-instructive proof 

 for the acceleration in uniform circular motion, the 

 hodograph could have been used to illuminate the 

 principle that force is the time rate of change of 

 momentum. 



The tiest is arranged so that statics can be taken 

 NO. 1S77, VOL. 72] 



before kinetics if this procedure is thought desirable, 

 but the sequence adopted by Mr. Eggar seems to us 

 the right one. In addition to the experimental work, 

 numbers of good and suggestive exercises are pro- 

 vided at appropriate intervals. The author has 

 succeeded in producing a most admirable text-book, 

 and one which we should like to see largely used 

 throughout the schools of the country. 



The aim of Prof. Merriman in his volume is to 

 introduce mechanics to young engineering students 

 in a manner whereby the principles are established 

 by constant appeals to experience, and are not lost 

 sight of by the introduction of a mass of algebraical 

 matter. The intention is good, but the experience 

 sliould be that g-ained first-hand by the student him- 

 self from experimental work in a laboratory. The 

 method employed by the author is to base the science 

 on axioms which the reader has to take largely on 

 trust, .\fter the first four pages, si.x of these are 

 suddenly introduced. Thus : — " Axiom i. Where only 

 one force acts on a body, it moves in a straight line 

 in the direction of that force." 



As a professor of civil engineering, the author 

 naturally gives more attention to statics than to 

 d\namics. In fact, the latter branch is very feebly 

 presented, and the subject does not gain by the sub- 

 stitution of the axioms for Newton's laws. For 

 example, the fundamental principle that impulse is 

 equal to change of momentum is nowhere found. 

 For the acquirement of a knowledge of the subject 

 reliance is largely placed on the working of the four 

 hundred problems, moslly niunerical, which are spread 

 over the book. 



In Prof. Porter's elementary text-book of theoretical 

 mechanics the subject is presented so as to appeal 

 to physicists rather than to engineers. Students read- 

 ing for the intermediate pass examination of London 

 L'niversity will find the book very helpful. A few- 

 experiments in verification of the laws of mechanics 

 are described, but the treatment is almost wholly 

 deductive. The author begins by discussing the 

 kinematics and kinetics of the rectilinear motion of 

 a rigid body, and is very happy in his explanations 

 of the fundamental conceptions of space, time, mass, 

 momentum, &c., particular attention being paid to 

 the units of measurement and to the change -from one 

 set of units to another. In defining the several 

 systems, however, the author seems to be mistaken 

 in his view that the unit of force adopted by engineers 

 is a variable one depending upon latitude. 



The consideration of the mechanics of a particle 

 is preceded by a chapter on the addition of vectors, 

 in which some elementary trigonometry is intro- 

 duced. The author might here have improved 

 his definitions of the trigonometrical ratios for 

 angles of any magnitude bv making' use of 

 the projections of a rotation vector. The action of 

 couples and the dynamics of rigid bodies having 

 plane motion are next (considered, and very logically, 

 but here a few additional experiments personallv 

 carried out would have materially added to tlie 

 student's grip of this somewhat difficult part of the 

 subject. There is a chapter dealing mathematicallv 



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