582 
NATURE 
| dpric 19, 1883 
elementary parts of kinematics, to include “the ideas and 
measures of velocity and acceleration, the parallelogram 
of velocities, and the parallelogram of accelerations, the 
motion of a point with a constant acceleration, and the 
acceleration of a point moving uniformly in a circle.” 
Then would come “ falling bodies and projectiles.” From 
these particular cases the student will get a general idea 
of the action of force, and so be prepared for a study of 
the laws of motion, and of the deductions from these laws. | 
“One of the first of these is the parallelogram of forces, 
and I am convinced by actual experiment of the ease with 
wh ch that mode of proof is appreciated by a beginner. 
The perception of the physical independence of forces, 
which is really the qualitative part of the second law of 
motion, is not a serious difficulty to the majority of 
beginners in mechanics, and from this principle, with the 
aid of the parallelogram of velocities, the parallelogram 
of forces is developed easily and naturally.” Next may 
be taken the mechanical powers and simple cases of 
equilibrium of bodies and systems of rods, a statement of 
the laws of friction, and the determination of the centres of | 
gravity of bodiesand systems. Mr. Besantalso laid great 
stress upon graphical modes of solution, referring to Mr. 
Minchin’s work on Statics for numerous examples in these | 
methods. ‘“ The discussion of the theory of moments of 
forces would naturally lead up to the idea of a couple 
and to the transformation and composition of couples.” 
The pupil might then proceed to the impact of balls on 
each other: ‘‘ The easiest method for every one... is to 
assume the invariability of momentum, and the constancy 
of the ratio of the relative velocities before and after im- 
pact. The consideration of the action of the forces of 
compression and of restitution is a more difficult idea, 
and should be deferred to a later stage of the student’s 
progress. In the discussion of these points the idea of 
work and of kinetic and potential energy may be intro- 
duced and illustrated, gradually leading up to the state- 
ment of the general principle of energy.” Dwelling 
upon the wonderful results that accompany the employ- 
ment of this general principle, ‘‘the very concentrated 
essence of science,” which in elementary mechanics 
“widens the path and shortens the road, and reduces to 
simple forms of thought many problems which used to 
be reckoned as belonging to advanced regions of the 
higher mechanics, and as depending for their solution on 
the complicated machinery of analytical process,” the 
paper alluded to the fact that it was only as recently as 
1877 that this principle of energy appeared in Part I. of 
the Tripos Examination—a result mainly to be attributed, 
we believe, to Prof. Clerk Maxwell’s advocacy of it. The 
principle is carefully laid down and discussed in ‘On 
Matter and Motion,” as well as elaborately discussed in 
Thomson and Tait’s ‘“ Natural Philosophy,’’ and in 
inany recent elementary treatises. With such views of 
its importance, we are not surprised to find Mr. Besant 
pleading for the introduction of the idea of energy as 
early as possible, and that every effort should be made to 
“illustrate the idea by means of simple cases and so to 
lead the student upwards, by gradual steps, to the con- 
ception of the most important principle which lies at the 
root of all modern science.’’ Another point on which 
the paper touches is that “ ill-chosen technical terms are 
likely to propagate erroneous ideas and confusion of 
thought,” and reference is made to recent remarks on the 
use of the word “force.” Then coming to the question of 
a syllabus of mechanics, Mr. Besant remarks that “ it will 
be a matter of supreme importance to discuss the defini- 
tions and axioms of the subject,” and instances a common 
definition of the word ‘‘ vertical’””—that it is the line in 
which a stone moves when let fall. 
with a few general remarks on the value of some branches 
of scientific study as an education, from which we select 
the two following extracts :—“ The safest and wisest plan 
The paper closes | 
| 
seems to be to let every man, who wishes to make research 
| be accompanied by acceleration 2?” 
in physics, find out for himself the kinds of tools which 
he wants, and then learn as much of the use of those tools 
as may be necessary.’’ ‘‘ The elementary subjects, such 
as mechanics and astronomy, are of more educational 
value to the majority of students than the higher regions 
of science, and only a select few should be encouraged to 
spend much of their time in such advanced forms of 
study.” 
(2) In this dynamics includes both statics and 
kinetics. The writer is in favour of continuing the old 
way of taking statics first, and of then proceeding to 
kinetics, and argues strongly against the taking the 
former as a particular case of the latter. Two important 
advantages, however, of the recent mode of treatment 
are not ignored, viz. that the student by concentrating his 
attention on force solely as change of motion, it at once 
proves for him the fundamental proposition of dynamics, 
viz. that of the “parallelogram of torces,” as an imme- 
diate result of the easily admitted parallelogram of velo- 
cities (‘‘if for the beginner the choice l:y between such 
proofs as Duchayla’s, and none, I should say, ‘Assume the 
proposition’”); ane next that ‘‘ the kinetical method has 
the very great practical advantage that it makes the 
student familiar at the outset with the idea of absolute 
measures Of force, momentum, energy, &c., such as are 
used in the C.G.S. system.’’ The notion of acceleration 
isan exceedingly difficult one for beginners, and sucha 
one, as a matter of fact, “is confined to the consideration 
of acceleration of constant magnitude, and, except in the 
case of uniform motion in a circle, to the case of acceler- 
ation in a constant direction. Thus he gets plenty of 
exercise in the motion of particles down inclined planes, 
. +... but what idea does our beginner obtain of the 
acceleration of the motion of a particle revolving uni- 
formly ina circle? Is there not something prima facie 
very difficult, if not absurd, to him in the statement that 
any motion which takes place with wmzform velocity can 
After a few more 
remarks to the same end, Prof. Minchin says, ‘‘ So far as 
my own work in teaching is concerned, I have not a 
moment’s hesitation in saying that the treatment first of 
kinetics and then of statics as a particular case is to be 
rejected. So difficult for the mere beginner are the con- 
ceptions involved in Newton’s second axiom, that three 
months’ work in combating difficulties and removing false 
impressions would, almost to a certainty, produce a merely 
negligible amount of positive knowledge.” Starting from 
| the kinetical definition of force, and thereby establishing 
the fundamental proposition (“this does not logically 
compel us to continue to treat of motion, deducing rest 
as a particular case’’), the writer, after protesting against 
the too great importance attached to the getting-up of 
“‘book-work,”! expresses the opinion that the student 
realises the subject only by incessant application of 
the principles to particular cases. For this purpose 
nothing, he believes, is so good as numerical examples: 
and this in contrast to examples dealing with magnitudes 
as algebraical symbols, and to geometrical examples. 
“So long as forces are XY, Y, Z, and moments are JZ, ./, 
ZV, and no particular consideration of the zséts of dif 
ferent quantities is required, they are comfortable enough, 
but when we have to deal with pounds and foot-pounds, 
dynes and ergs, the utter unavailability and inutility of 
their knowledge are made manifest.” Another point 
strongly insisted upon is Ze znvariable accompaniment of 
Jigures constructed accurately to scale with all the examples. 
| The result should be arrived at by calculations made by 
means of logarithmic and trigonometrical tables, and also 
by graphic construction by the aid of the instruments, 
and on all there should be, when possible, “the perpetual 
I have met students who could write out paragraph after paragraph of 
general propositions in statics, and who at the same time (although such 
might appear to a frterf reasoners impossible) could not make the faintest 
attempt to discuss any particular question involving the application of the 
principles of statics.” 
r& 
