PROCEEDINGS. 
587 
Since are the direction cosines of the tangent at the point 
d 2 § 
xyz, we see that is the 'accelerating force along the tangent to the 
curve. The other component of R acts at a right angle to the tangent 
and contributes nothing to the velocity of the particle, hut changes the 
direction of its motion. This component is called the “ centrifugal force.” 
Since it does not change the velocity of the particle, and would not even 
if its connection with the center of motion were severed, it is common to 
speak of it as a fiction; but it is a component of R that must be consid¬ 
ered in many questions, and the old nomenclature of Huygens is con¬ 
venient. At the equator of the earth centrifugal force diminishes gravity 
by ^jgth part of its value. The effect varies as the square of the cosine 
of the latitude, the general expression being 
G is the value of gravity if the earth had no rotation, and <p is the lati¬ 
tude. 
Another expression which is disputed, and which indeed seems to be 
unfortunate, is the “ force of inertia.” Correctly speaking, there does not 
appear to be a force of this kind, and we mean by this phrase the reac¬ 
tion we experience when we attempt to put a body in motion or to resist 
a moving body. If a mass be placed on a smooth surface where there is 
no friction, and if it be acted on by a force however small, it will begin 
to move with a certain velocity. If the mass be increased, the force must 
also be increased in order to obtain the same velocity ; and if we could 
accurately compare the forces we could in this way determine the masses 
of bodies. But it does not follow that matter opposes a resistance to the 
action of force. 
» 
Still another expression which seems to me incorrect is that of “ specific 
gravity.” Gravity is a general force and does not depend on the nature 
of bodies; but so delightfully inconsistent are we that writers who strain 
at the term “ centrifugal force ” have no trouble with “ specific gravity.” 
The preceding examples are sufficient to convince me that the only 
safe way in such matters is first to obtain the general equations of mo¬ 
tions (a), and then to deduce results by the proper analytical transforma¬ 
tions. This method has the great advantage of starting from grounds 
that are fundamentally correct; so that a slip in the use of a word or 
phrase need not make our result wrong. 
After the reading of Mr. Hall’s paper Mr. H. H. Bates said: 
In the paper to which we have just had the pleasure of listening 
Professor Hall states some well-known mathematical truths with his 
accustomed accuracy and ability. His presentation has no flaw as a 
