FEpruary 23, 1912] 
mass. Since we can only define density in 
terms of the concept of mass, it is surely 
uncritical to define mass in terms of 
density. In fact Newton on a later page 
uses the true definition when he says that 
bodies are of the same density if their 
vires inertie (that is, their masses) are 
proportional to their volumes. 
The same sort of uncritical treatment 
appears in his presentation of the various 
types of force. He mentions first the vis 
insita, which he defines as the power of 
resisting, by which a body persists in its 
state of rest or of uniform motion. He 
says it differs in no respect, except in the 
way of conceiving of it, from the inertia of 
a mass. 
Then comes vis impressa, the action 
(actio) exerted on a body to change its 
state of rest or of uniform motion. This is 
force in our ordinary sense. Newton says 
that it arises from a blow, from pressures 
or from centripetal force. 
Vis centripeta is the force by which 
bodies are drawn or impelled from all 
directions toward any point as a center, or 
tend toward it in any way whatever. The 
force of gravitation and magnetic force are 
examples of this centripetal force. So also 
is the force by which a sling draws a stone 
in it toward the hand, which force Newton 
explains as arising from the stretching of 
the cord of the sling. 
Newton then goes on to define the vari- 
ous measures or modes of giving quantita- 
tive expressions for centripetal forces. He 
first describes the vis centripete quantitas 
absoluta as the measure of it as greater or 
less by comparison with the efficiency of 
the cause which transmits it from the cen- 
ter through the surrounding region. Thus 
the magnetic force is greater in one magnet 
than in another, either because of the 
greater mass of the one or of the intensity 
of its power. 
SCIENCE 
283 
The vis centripete quantitas acceleratrix 
is the measure of it as proportional to the 
velocity which it generates in a given time. 
Thus the power (virtus) of a magnet is 
greater at lesser distances, and less at 
ereater distances; gravitating force is 
ereater in valleys, less on mountain peaks, 
and less still at greater distances from the 
earth. At equal distances, he says, this 
gravitating vis acceleratrix is the same 
everywhere, because all falling bodies are 
equally accelerated. 
The vis centripete quantitas motria is 
the measure of it as proportional to the 
momentum which it generates in a given 
time. This quantity is the center-seeking 
or tendency to the center of the whole 
body, and (as Newton says, with an evi- 
dent appreciation that he is lmiting the 
generality of his conception) is the weight 
of the body. It is always known by the 
force opposite to it, and equal to it, by 
which the fall of the body can be pre- 
vented. 
Newton calls these quantities of force of 
the various sorts described by the shorter 
terms motive, accelerative and absolute 
forces, that is, he substitutes the general 
terms for the measured quantities of the 
forces which can be conceived only in those 
general terms. With this understanding 
he states that the vis acceleratrixz is to the 
vis motri# as velocity is to momentum; for 
the quantity of motion (momentum) arises 
from the velocity and quantity of matter, 
and the vis motrix arises from the vis ac- 
celeratriz and the quantity of matter. For 
the sum of the actions of the vis accelera- 
tric upon the several particles of a body is 
the vis motria of the whole body. Newton 
relates the vis motriz to a body as a stri- 
ving of the whole body towards the center, 
made up of the striving of all its parts; 
the vis acceleratrix to the position of the 
body, as a certain efficiency, diffused from 
