Prof. Tait on the Laivs of Motion. 441 
phrases of the kind must be taken as wholes ; and, in them, 
vis does not mean force. 
The absurdity of translating the word vis by force comes out 
still more clearly when we think of the term vis viva, or living 
force as it is sometimes called ; a name for kinetic energy, 
which depends on the unit of length in a different way from 
force. It must be looked upon as one of the most extraordi- 
nary instances of Newton's clearness of insight that, at a time 
when the very terminology of science was only as it were 
shaping itself, he laid down with such wonderful precision a 
system absolutely self-consistent. 
From the passages just quoted, taken in conjunction with 
the 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 Mechanics in the new edition of the Encyc. Brit., and 
need not be reproduced here.) 
But, just as there can be no doubt that force has no objec-,^ 
tive existence, so there can be no doubt that the introduction 
of this conception enabled Newton to put his Axiomata in 
their exceedingly 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 introduced ; 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 i 
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 " re- 
