1^6 



NA TURE 



[August 5, 1909 



material bearing on the physics and biology of the 

 waters has still to be published. 



The bathymetry of the lake-basins was determined 

 by series of close soundings in lines transverse to the 

 long axis, and the scale of the maps is sufficiently large 

 (3 inches to i mile) to allow of all the soundings 

 being represented in figures as well as by contour 

 lines. We think that a longitudinal line of soundings 

 along the axis of maximum depth would have been 

 a useful addition in all cases, and a valuable check on 

 the transverse series. Supplementary soundings 

 would also have been useful in many places where 

 the exceptional run of the contours suggests some 

 unusual configuration. Such additional lines have 

 been run on some of the lochs, and the maps of these 

 inspire a more complete confidence as to detail than 

 do the others. We should have liked to see some 

 larger-scale surveys of such individual features as the 

 sub-lacustrine slopes of delta fans, screes, steep rockv 

 shores, and the transition belt between the steep sides 

 and flat floors of many of the basins. 



The sounding of the large area of fresh water which 

 fell between the two stools of the Admiralty and the 

 Ordnance surveys is a splendid example of public- 

 spirited private enterprise undertaking and carrving 

 through work which should have been included in 

 the routine of a Government department. It is, hap- 

 pily, not the only case in wliich the collective short- 

 comings of the nation in matters affecting the ad- 

 vancement of scientific knowledge have been made 

 good by individual effort and at private expense. 

 When the right men are at the head of such an in- 

 vestigation, and their labours are not trammelled by 

 the want of means, we are of opinion that better work 

 can be done at a smaller outlay than if the operations 

 were conducted by an official department or under the 

 auspices of a committee of many specialists on dif- 

 ferent subjects; but when the right men are not to 

 be found the lack of Government interest in the com- 

 pletion of our knowledge of our own land' and its 

 resources may lead to unhappy consequences. It is 

 fortunate, indeed, that Sir John Murray and Mr. 

 Pullar have had both the will and the power to carry 

 out the work, which, when completed by the publica- 

 tion of the additional material already collected, will 

 form a noble monument to the memorv of the laic 

 Mr. Fred Pullar, to whose energetic assistance the 

 early stages of the research were so much indebted. 



H. R. M. 



THE OLD AND THE NEW MECHANICS. 

 (i) A First Dynamics. By C. S. Jackson and W. U. 

 Roberts. Edited by W. J. Greenstreet. Pp. viii + 

 412. (London : J. M. Dent and Co., 1909.) Price 



(2) Elementary Mechanics. By Prof. C. M. Jessop 



and Dr. T. H. Havelock. Pp. viii + 277. (London : 



George Bell and Sons, :909.) Price 4s. 6d. 



(') CO many new series of mathematical school- 



'^ books have appeared during the last few years 



that the present series has remained almost unnoticed. 



This is the more remarkable in view of the wide 



reputation of the editor, Mr. Greenstreet, and also of 



NO. 2075, VOL. 81] 



the fact that the contributors are also mostly well- 

 known authorities in the mathematical teaching 

 world. Messrs. Jackson and Roberts have fully justi- 

 fied the e.xistence of their book by the amount of 

 freshness and originality they have put into it, and 

 particularly by the extent they have treated the subject 

 from a common-sense, practical point of view. As 

 the authors point out in the preface, there have been 

 in the past two classes of book in which the rela- 

 tions between force, matter, and motion are dealt with. 

 There has been, first, the book on apnlied mechanics, 

 in which the principal object has perhaps been to 

 describe machines, and there has next been the 

 " academic " book, in which dynamics might perhaps 

 better be described as "dogmatics," the most pro- 

 minent feature of which has been a collection of 

 exercises in algebra. 



It has been the object of the present authors to j 

 make the principles of dynamics the prominent feature 

 of their book, and to illustrate them by applications 

 to phenomena of everyday life rather than by algebraic 

 drill. In this they have been very successful, so far 

 as can be judged without an extended trial of the 

 book in the class-room. 



The main crux in writing a book on dynamics is 

 the question of units. Shall the author use poundals 

 and please one class of teachers, or shall he use 

 slugs and be commended by another section ? It 

 seems to have been generally forgotten that there 

 is a third alternative which still allows those who 

 wish to do so to replace Newton's " proportional " 

 by " equal " in the laws of motion. That alternative 

 is to take the gee (g) as unit of acceleration, and 

 write force in lbs. wt. = mass in pounds and accelera- 

 tion in gees ; and if any writer chose to champion 

 the claims of the gee, he could point to the fact that 

 the foot, if defined by the length of the seconds pen- 

 dulum, is really a gravitation unit of length. 



Messrs. Jackson and Roberts, while discussing the 

 two generally recognised systems, adopt the more 

 rational plan of basing their treatment on the pro- 

 portion : — 



force _ acceleration 

 Weight ff 



It has been popularly supposed that this plan is 

 theoretically good, but how would the equations of 

 motion of complicated systems be written ? Now in 

 Mr. Jackson's hands the equations all look delight- 

 fully simple; not only is there no more difficulty than 

 occurs somewhere in every system, but it is very easy 

 to see if the results written down are correct in 

 their dimensions. The suppression of constant multi- 

 pliers in physical equations does not always conduce 

 to simplicity; it more often causes confusion, espe- 

 cially in connection with electrostatic and electro- 

 magnetic units, and also in hydrodynamics, where 

 problems of discontinuous motion are solved for jets 

 of one particular breadth (generally t) with one par- 

 ticular velocity, and the solution appears inapplicable 

 to other jets differing in size and velocity. A little 

 doubt may occur as to whether momentum should 

 be defined as \\'v/g, as Mr. Jackson does, or simply 

 as Wv ; but this is a matter in which experience will 

 indicate the wisest choice. 



