Avaust 2, 1918] 
where a is the acceleration of a given body 
produced by force F, and a’ is the acceleration 
produced by force F’. 
The experimental fact (b) makes it conven- 
ient to define the ratio of the masses of two 
bodies as the inverse ratio of the accelerations 
produced by a given force, because this ratio 
is the same for all forces. 
That is 
, (2) 
where a is the acceleration of body No. 1 and 
a’ is the acceleration of body No. 2, both pro- 
duced by a given force, and m and m’ are the 
masses of the respective bodies. 
We prefer to define mass quantitatively in 
terms of the operation of weighing by a bal- 
ance scale and to look upon equation (2) as an 
experimental discovery; but in any case equa- 
tions (1) and (2) are independent and they 
are the fundamental equations of dynamics. 
Equation (1) applies to a given body, and 
pure logic would not even know of the ex- 
istence of another body, so that equation (2), 
inasmuch as it refers to at least two bodies, 
can not be a logical consequence of equation 
(1). It is surprising to us to have Professor 
Huntington refer* to the above table of ob- 
served accelerations in support of his state- 
ment that equation (2) is a logical or mathe- 
matical consequence of equation (1). Of 
course we have not observed these accelera- 
tions, but in the last analysis they are depend- 
ent on observation and upon nothing else. 
3. Professor Huntington’s statements as to 
systematic units are very much like most cur- 
rent text-book statements touching this matter. 
“Fundamental units may be chosen at pleas- 
ure ”—so all of our talking physicists say, men- 
tioning only the evident condition that mate- 
tial standards thereof must be carefully pre- 
served. Working physicists, however, know 
that the fundamental quantities must be sus- 
ceptible of very accurate measurement under 
all sorts of conditions and in all kinds of re- 
lations because the definition of a derived unit 
can not be realized with greater accuracy than 
the fundamental quantities can be measured. 
4 Science, March 3, 1916, page 315. 
SCIENCE 
115 
Think of the years of confusion in electrical 
measurements when the theoretical ohm could 
not be produced with greater accuracy than, 
Say, one per cent., but when almost anybody 
could make resistance measurements to, say, a 
hundredth of one per cent! When we recall 
that old nightmare we are inclined to smile 
at the childish pleasure with which many 
teachers talk about choosing fundamental 
units. Indeed, one fundamental unit would 
be enough if certain measurements, which 
would then be fundamental, could be made 
with sufficient accuracy. This important con- 
dition of accurate realization of derived units 
makes it undesirable to use the pull of the 
earth on a one-pound body in London (or on a 
one-gram body) as a fundamental unit in any 
universally practicable system. As a matter 
of widest practise the use of the unit of force 
as a fundamental unit is out of the question. 
We admit, however, and here we differ from 
some of our colleagues in physics, that the 
C.G.S. system (or the F.P.S. system) is less 
convenient than the foot-slug-second system 
in some fields of engineering.® 
4, It is extremely amusing to read Professor 
Huntington’s naive suggestion that a unit of 
force might be preserved in the form of a 
standard spring. This is laughable for two 
reasons, namely, (a) because the pull of the 
earth on a one-pound body in London is per- 
haps as invariable as its mass so that no stand- 
ard spring is needed to preserve a unit of 
force, and (b) because, as every working phys- 
icist knows, the most carefully “aged” springs 
grow very perceptibly softer in time. Tem- 
pered steel and phosphor bronze and fused 
quartz are unstable substances. 
5. We are at a loss to understand the signifi- 
eance of Professor Huntington’s efforts to es- 
tablish order in: the fundamental view points 
of mechanics except on the assumption that he 
has felt, somewhat vaguely, the central fallacy, 
5 We publish in a current number of the Bulletin 
of the Society for the Promotion of Engineering 
Edueation a brief and simple discussion of this 
subject, a discussion which we think may show the 
way to a general agreement among writers on me- 
chanics, 
