of Edinburgh, Session 1882-83. 11 
second law of motion, we see that (as above stated) in Newton’s 
view — 
Force is whatever causes (but not, or tends to cause) a change in 
a body's state of rest or motion. 
Newton gives no sanction to the so-called statical ideas of force. 
Every force, in his view, produces its effect. The effects may be 
such as to balance or compensate one another ; but there is no 
balancing of forces. 
(Next comes a discussion as to the objectivity or subjectivity of 
force. . An abstract of this is given in §§ 288-296 of the article 
above referred to, and therefore need not be reproduced here.) 
But, just as there can be no doubt that force has no objective 
existence, so there can be no doubt that the introduction of this 
conception enabled Newton to put his Axiomata in their exceed- 
ingly simple form. And there would be, even now, no really valid 
objection to Newton’s system (with all its exquisite simplicity and 
convenience) could we only substitute for the words “ force ” and 
“ action,” &c., in the statement of his laws, words which (like rate or 
gradient, &c.) do not imply objectivity or causation in the idea 
expressed. It is not easy to see how such words could be intro- 
duced ; but assuredly they will be required if Newton’s system is 
to be maintained. The word stress might, even yet, be introduced 
for this purpose ; though, like force, it has come to be regarded as 
something objective. Were this possible, we might avoid the 
necessity for any very serious change in the form of Newton’s 
system. I intend, on another occasion, to consider this question. 
How complete Newton’s statement is, is most easily seen by con- 
sidering the so-called “ additions ” which have been made to it. 
The second and third laws, together with the scholium to the 
latter, expressly include the whole system of “ effective forces,” &c. 
for which D’Alembert even now receives in many quarters' such 
extraordinarily exaggerated credit. The “ reversed effective force ” 
on a particle revolving uniformly in a circle is nothing but an old 
friend — “ centrifugal force.” And even this phantom is still of use, 
in skilled hands, in forming the equations for certain cases of motion. 
The chief arguments for and against a modern modification of the 
laws of motion are therefore as follows — where we must remember 
that they refer exclusively to the elementary teaching of the subject, 
