XLII PHILOSOPHICAL SOCIETY OF WASHINGTON. 
4, The fundamental units should be such as to admit of easy defi- 
nitions and simple dimensions for the various derived units. 
Scientific men have long agreed that these requirements are best 
fulfilled by adopting as the fundamental units, a definite length, a 
definite mass, and a definite interval of time. Length is an element 
which can be very accurately measured and copied, but it must be 
defined by reference to some concrete material standard, as for 
example, a bar of metal, and as all substances expand and contract 
with changes of temperature, it is necessary to state the temperature 
at which the standard is correct. A standard of mass, consisting 
of a piece of platinum, quartz, or other material not easily affected 
by atmospheric influences, probably fulfills the conditions set forth 
above better than any other kind of magnitude. Its comparison 
with other bodies of approximately equal mass is effected by weigh- 
ing, and as that is among the most exact of all laboratory operations, 
very accurate copies of the standard can be made, and they can be 
carried from place to place with little risk of injury. Time is also 
an element which can be measured with extreme precision. The 
immediate instruments of measurement are clocks and chronometers, 
‘but their running is checked by astronomical observations and the 
ultimate standard is the rotation of the earth itself. 
It is important to note that the use of three fundamental units is 
simply a matter of convenience and not a theoretical necessity, for 
the unit of mass might be defined as that which at unit distance 
would generate in a material point unit velocity in unit time; and 
thus we should have a perfectly general system of measurement 
based upon only two fundamental units—namely, those of space and 
time. Such a system is quite practicable in astronomy, but cannot 
yet be applied with accuracy to ordinary terrestrial purposes. Ac- 
cording to the law of gravitation 
Mass = Acceleration X (Distance)? 
and as in the case of the earth we can measure the quantities on 
the right-hand side of that equation with considerable accuracy, we 
can satisfactorily determine the earth’s mass in terms of the supposed 
unit. That suffices for the needs of astronomy, but for other scien- 
tific and commercial purposes a standard of mass having a magni- 
tude of about a pound is necessary, and as two such,masses can be 
compared with each other from five to ten thousand times more 
