I70 



NATURE 



[June 23, 1898 



tueight, and shall be called the imperial standard pound, 

 and shall be the only unit or standard of lueight from 

 which all other 7veights and all measures having reference 

 to weight shall be ascertained." 



How does Mr. Love propose to edit this clause ? The 

 word xveight makes its appearance seven times where Mr. 

 Love says the right word to employ is mass; he cuts the 

 Act of Parliament to pieces on p. 98 ; and we have mass 

 occur in almost every line. And if the word weight is 

 to go, what is to be done with pouttd, poids (de kilo- 

 gramme), and avoirdupois, all derived from the Latin 

 pondus? According to § gi,pondus is given in dynes, 

 and the word pondus above must be replaced by massa. 



If this process of Restoration (to use the banal 

 architectural word — 



" to erect 

 New buildings of correctest conformation 

 And throw down old, which he called restoration." 



Don Juan.) 



is to be carried out systematically, what is to be done 

 with the words " in ponderibus movendis" of Newton's 

 preface ? and how are Ovid's lines to be restored describing 

 the statue of Ladas, the work of the sculptor Myro ? — 



" Qure nunc nomen habent operosi signa Myronis 

 . Pondus iners quondam duraque massa fuit." 



Or again the lines — 



" . . . at gravitate carentem .^ithera. . . . 



Cum quae pressa diu massa latuere sub ilia ..." 



Love's Dynamics versus Ovid's Ars ainatoria ! not to 

 mention the ecclesiastical usage of Christmas, Childer- 

 mass, Candlemass, Ladymass, Lammas, Loafmass, Mar- 

 tinmass, Soulmass, Michaelmass, . . . now exciting con- 

 troversy in another place. 



" The common use of the word " weight " covers two 

 notions which are essentially distinct, the notion of 

 pressure which a heavy body e.xerts on a support, and 

 the notion of quantity of matter. In scientific writing 

 and speaking, different words must be used to express 

 distinct notions " (p. 99). 



A very useful aphorism, worth adding to Newton's 

 " Regulae Philosophandi " ; and so scientific wi'iters must 

 invent' two new words to express these two distinct 

 notions, and not attempt to force a word of common 

 currency out of its most extended meaning. 



At the same time another rule might have been made 

 — '■ The names of a thing must not be multiplied more 

 than is necessary." 



" Since the centre of inertia of body small enough to 

 be handled coincides with its centre of gravity as defined 

 in Statics, we shall denote it by the letter G " (p. 102). 



And now we have three names, centre of mass (d'Alem- 

 bert), ccntroid (Clifford), and centre of inertia, where the 

 single name centre of gravity is sufficient for ordinary 

 purposes. It is a pity to waste the expression "centre 

 of inertia " in this way, as it may prove useful for desig- 

 nating a point distinct from the centre of gravity, in the 

 case of non-rigid systems, such as a carriage on wheels, 

 or a fish, bird, or projectile moving in its medium. 



This brings us to the " Conception of a Rigid System " 

 in § 114— 



" If the particles of a rigid system continuously fill a 

 surface, the system is a rigid body, and the surface is 

 the surface of the body." 



At this rate the ball-bearings of a bicycle constitute 



NO. 1495, VOL. 58] 



a rigid system, contrary to the function for which they 

 are designed. 



The bicycle has done wonders in familiarising our 

 youth with dynamical sensations ; and the machine it- 

 self can be used in a variety of ways to illustrate the 

 theory of the pendulum and the gyroscope. When test- 

 ing the wheels for friction and balance, the elliptic 

 functions, defined in rather a condensed way in § 191, can 

 easily be watched in their fluctuations ; while the new 

 drawing-room game of trying to walk round holding a 

 revolving wheel serves to emphasise gyroscopic domin- 

 ation. With this stimulus the languishing study of 

 elliptic functions may again become popular, and lead 

 on to the dynamical applications of the hyper-elliptic 

 functions, sketched out by Prof Klein in his Princeton 

 lectures, as required for the complete solution of the 

 bicycle problem, especially as the Prize offered by the 

 French Academy for this subject is still open. 



The influence of wind will excite an interest in § 212,. 

 on the motion in a resisting medium. In this article the 

 author could have simplified the treatment, by introducing 

 the notion of " terminal velocity," as in ex. 155, p. 227. 



The statement on p. 195, that the resistance of the 

 air is better represented by the cubic law, is not valid, 

 except for a very limited region in the neighbourhood 

 of the velocity of sound ; but, considering that th^ re- 

 tardation 



can be replaced by 



— v^, 



Mr. Bashforth found it convenient, in the reduction of 

 his screen records, to take out the factor v^, and to 



d-^t 



measure carefully the other factor, 



ds' 



The Science of Dynamics does not consist in labelling 

 certain physical quantities with letters, such as ;«, W^ 

 f g, . . . ; these letters really mean numbers, expressed 

 each in its own unit. Mathematical Tripos questions un- 

 fortunately pay scant attention to the units involved, and 

 our mathematical students learn to loathe all numerical 

 applications, and so lose sight of the true meaning of 

 these algebraical symbols for numbers. One reason for 

 this dislike of numerical computation is the absurd 

 system of using 7 figure logarithms, where, as in the 

 case of the gravitation constant y, upon which all Celestial 

 Dynamics depend, the numbers do not warrant such 

 refinement. A gigantic cheese-auger cannot be driven 

 into the earth, to determine the density of the strata up 

 to the centre, so we have to be content with the indi- 

 cation of the Cavendish experiment, which, even in the 

 experienced hands of Mr. Boys, do not warrant the use 

 of logarithms of more than 4 places. 



The two papers on the theory of the oscillations of a 

 ship, and of the stresses produced thereby, read recently 

 before the Institution of Naval Architects by Captaiii 

 Kriloff, Professor at the Naval Academy of St. Petersburg, 

 are worth the attention of theoretical students in showing 

 the numerical computations, given to 3 significant figures 

 only, required in a complicated problem of Rigid Dy- 

 namics, and showing also the system of gravitation units 

 invariably employed in such calculations. 



