
—< 
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FEBRUARY 17, 1923] 
NATURE 
225 

Thus, in “Matter and Motion,’ Maxwell reduces 
the uniplanar motion of any rigid body to an equivalent 
particle pair, rigidly connected, having the same total 
weight, the same centre of gravity, and the same 
moment of inertia about the centre of gravity. 
The compound clock pendulum of Huygens is 
replaced in this way by its equivalent pair of particles, 
one being placed at O in the axle of suspension, and 
the other will be at P the centre of oscillation ; and 
then OP is the length of the simple equivalent pendulum, 
a plumb bob P at the end of a thread OP. 
Provided with these additional ideas in dynamics, 
the young engineer will be able to investigate the 
motion of the revolving parts of his machinery, such, 
as a flywheel, a revolving shaft, a screw propeller, 
and the influence of the rotation of the wheels of a 
carriage. 
Whatever the system of units employed, it is essential 
in the dynamical interpretation for g to be assigned 
its proper place, here under v. It must not be allowed 
to straggle and take cover under W, as in the old- 
fashioned treatise, where the author, to save trouble 
in writing and printing, adopted the mischievous 
delusive plan of replacing his W/g by the single letter 
label M, and then calling it the mass, a quantity 
Sui generis, not its Corpus. He then wrote, with v/t=f, 
the acceleration, time rate of growth of velocity, 
(4) F=Mf, with W=Mg. 
These relations are not seen in the “ Principia- 
Elements,” where g does not occur explicitly but is 
concealed in the length L of the seconds-pendulum, 
g=7*L. The “Principia” is chiefly kinematics ; 
very little of kinetics until the second book, and 
then of experiments on fluid resistance, aways expressed 
in gravitation units. 
Lex III. Actioni contrariam semper et aequalem 
esse reactionem: sive corporum duorum actiones in 
se mutuo semper esse aequales et in partes contrarias 
dirigi. 
According to Maxwell, this Law—Action and 
Reaction are equal and opposite—amounts to no more 
than the definition of a stress, a pull or thrust, tension 
or pressure. 
The sequel of Corollaries of Law III is important 
in introducing the ideas of vector composition, the 
conservation of momentum, and immunity of the 
centre of gravity to the internal actions and stress. 
The Law was put forth probably as a contradiction 
to some accepted law in vogue before Newton, now 
forgotten. In some recent figurative language of 
the Press, we read ‘‘ The pendulum is always swing- 
ing. Action, especially if violent, is apt to entail 
reaction.” The former Law can still be traced in 
the popular idea current that the horse advances by 
pulling the cart harder than the cart pulls back. 
I remember a similar question about a double-headed 
express train; I was asked to explain what would 
happen if the second engine was going faster than 
the first : pulling harder I presume was meant. 
The definitions come first in the “ Principia,” but 
we prefer to discuss them after the Laws, when the 
ideas they imply have been employed already in some 
tangible application, and so are capable of a better 
appreciation, and we can refer to them. Abstract 
NO. 2781, VOL. 111] 

definition requires to settle on some hard base of fact 
and comes after action in order of thought. 
Definitio I. Quantitas Materiae est mensura 
ejusdem orta ex illius Densitate et Magnitudine 
conjunctim. 
According to Mach, this is really no more than a 
definition of density, and quaniitas is used as a synonym 
for Corpus, Moles, Massa, Pondus, five names to one 
entity. Nomina-Entia non sunt multiplicanda praeter 
quam necesse est. 
Here Corpus would connote a body, Moles or Mola 
the bulk, Massa the aggregation of its stuff, and 
Pondus the quantity of its stuff measured out in a 
balance against standard lumps of metal called weights ; 
revealed also roughly in the heft required to lift the 
body off the earth’s surface. 
The Greek equivalent for Massa would be pdypa, 
paga, something kneaded and fashioned into shape ; 
and the distinction in Latin between the words is 
brought out clearly in Ovid’s lines (A. A. iii. 219): 
‘‘Quae nunc nomen habent operosi signa Myronis, 
Pondus iners quondam duraque massa fuit’’ ; 
assigning the quality of Inertia to Pondus. 
But because Newton in this definition goes on to 
say—Innotescit ea (Quantitas) per corporis cujusque 
Pondus. Nam Ponderi proportionalem esse reperi per 
experimenta Pendulorum accuratissime instituta, uti 
posthac docebitur (meaning experiments to prove that 
the quality of the Matter does not matter)—1t is rigidly 
insisted to-day in elementary instruction that Pondus 
should never be used except in this subsidiary sense 
of the accident of the gravitation of it, due to its 
situation on the surface of the earth. Moreover, we 
find Newton using Pondus elsewhere in both of the 
meanings of ordinary language; as, for example, in 
his preface—Unde solvitur in omni aptorum instru- 
mentorum genere Problemata. Datum pondus data 
vi movendi. Sic pondera aequipollent ad movenda 
brachia Librae, quae oscillante Libra sunt reciproce 
ut eorum velocitates sursum et deorsum: hoc est, 
pondera, si recta ascendunt et descendunt, aequipollent, 
etc. 
Definitio II. Quantitas Motus est mensura ejusdem 
orta ex Velocitate et Quantitate Materiae conjunctim. 
This is the quantity called momentum to-day, our 
Wz, lb.-ft. per sec. And—Motus totius est summa 
motuum in partibus _Singulis — requires amplification 
to-day of ‘‘ sum ” to “ vector sum. 
Definitio III. Materiae Vis Insita . . . etc., is 
qualified as undistinguishable from Inertia massae, the 
pondus iners of Ovid, so here the two names are 
convertible, and one of them would serve. 
The Vis Impressa, Vis Centripeta, Vis centripetae 
Quantitas Absoluta, Acceleratrix, Motrix (felt forcibly 
on the top of a motibus), and so on of the subsequent 
Definitions display a curious profusion of the word 
Vis, as much as in Hooke’s vaunted Law: Ut Tensio 
sic Vis. 
Vis, like moment, momentum,moment of momentum, 
moment of inertia, is a word too hackneyed in dynamics. 
A. N. Whitehead, in the “ Concepts of Nature,” uses 
the word moment to mean “ all Nature at any instant.” 
“Two moments of the same family are parallel.” 
“4 point flash of Nature is an event particle.” 
