114 
is much worse than that. If we were not con- 
vinced that Professor Huntington is definitely 
mistaken in several important matters we 
would not, for a third time, take part in the 
discussion. 
1. Professor Huntington urges the use of 
the term standard weight, the weight of a body 
in London in “pounds,”! instead of mass. 
Now what we call the mass of a body is in- 
dependent of time and place, it is an invariant? 
relation between the given body and the stand- 
ard kilogram (a piece of metal), and extraneous 
and confusing ideas would be involved in the 
term standard weight, because this term im- 
plies location and a relationship between the 
given body and the earth. How awkward it 
would be, for example, to be obliged always 
to speak of the distance d between two points 
(a, y, z) and (2', y’, 2’) as [(a7—a’)?+- 
(y—y’')? + (2—2')?],. This function is an 
invariant, and the most useful name or symbol 
for it is a name or symbol which carries no 
redundant suggestions as to particular axes of 
reference, and this would be true even if we 
had always to make use of particular axes of 
reference in the measurement of d. The word 
mass is widely used by physicists and chemists 
for an idea which is independent of time and 
place and which does not involve any relation- 
ship with the earth (this is true even though 
mass be determined by weighing), and it is 
simply out of the question to use for this idea 
the term standard weight with its redundant 
and misleading suggestions. 
2. To be unfriendly to the term mass and to 
prefer the term standard weight is of course a 
small matter; but Professor Huntington seems 
to go much deeper than mere terminology. Ht 
insists, for example, on the equation #'/F’ = 
a/a' as THE fundamental equation of dynamics, 
although several correspondents in SCIENCE 
have called his attention to the fact that ac- 
celeration not only varies from force to force 
for a given body but also from body to body 
1 The ‘‘pound’’ here means the pull of the earth 
on a one-pound body in London. 
2 No consideration is here given to variations of 
mass as recognized in the recent developments of 
the principle of relativity. 
SCIENCE 
[N. S. Vou. XLVIII. No, 1231 
for a given force. Both of these fundamental 
modes of variation must be formulated as fun- 
damental equations of dynamics. Professor 
Huntington states? that the variation-from- 
body-to-body-for-a-given-force is logically de- 
rivable from the variation-from-force-to-force- 
for-a-given-body, and the object of the follow- 
ing discussion is to make it clearly evident 
that Professor Huntington’s statement is not 
true. 
Given three bodies A, B, and C, and three 
identifiable forces a,b and c. Let the accelera- 
tion of each body due to each force be observed, 
the results being shown in the accompanying 
table. Let us suppose that the table has been 
TABLE OF OBSERVED ACCELERATIONS 
Bodies 
extended so as to include a great many differ- 
ent forces and a great many different bodies, 
then a careful inspection of the table would 
lead to the following generalizations: 
(a) If one force produces twice as much 
acceleration as another force when acting on a 
given body, then the one force produces twice 
as much acceleration as the other force when 
acting on any body whatever. 
(b) If one body is accelerated twice as much 
as another body under the action of a given 
force, then the one body is accelerated twice as 
much as the other body under the action of 
any force whatever. 
The experimental fact (a) makes it conven- 
ient to define the ratio of two forces as the 
ratio of the accelerations they produce when 
acting on a given body, because this ratio is 
the same for all bodies. 
That is 
a. 
=4, (1) 
5 
8 ScIENCE, March 3, 1916, page 315. 
