24 RECORDS 



measured or calculated with precision depends, in general, on 

 the degree of complication of its connections with other quan- 

 tities, and on the applicability of methods already applied in 

 the determination of other quantities. Frequently, a quantity 

 may be measured directly ; but it oftener happens, either by 

 reason of the inapplicability or of the disadvantage of a direct 

 method, that resort is had to an indirect method. 



It is a remarkable fact, illustrating the essential unity which 

 pervades the apparent diversity of nature, that all of the numer- 

 ous quantities with which physical science has to deal may be 

 expressed in terms of a certain very limited number of arbi- 

 trarily chosen quantities, or units. The units most commonly 

 used, and those which seem best suited to the present require- 

 ments of science, are the units of length, mass and time. All 

 other quantities, however complex, may be expressed readily in 

 terms of these arbitrarily assumed fundamental quantities. It 

 is by no means certain, however, that these units will best 

 satisfy the requirements of science in the future. On the con- 

 trary, it seems rather probable that advancing knowledge will 

 find some other system of units preferable, if it does not find 

 several different though interconvertible systems essential. We 

 have, in fact, already attained two such diverse systems in the 

 units of electromagnetic science. 



The study of such systems by the aid of the theory of dimen- 

 sions, which shows algebraically how the assumed units enter 

 into more complex quantities, is very instructive, not only to 

 the mathematical physicist, but to the general student of physical 

 science.^ To illustrate this idea by some simple examples, it is 



centers of gravity of the masses. This is true, indeed, for the class of bodies called 

 centrobaric, like homogeneous spheres ; but masses in general are not centrobaric. 



The gravitation constant is in C.G.S. units, about 667 X lO— 12, with some un- 

 certainty in the last significant figure. 



The aberration constant, vi^hich is (if it is nothing more than a kinematical 

 quantity) the ratio of the velocity of the earth in its orbit to the velocity of light 

 multiplied by the number of seconds in a radian, is about 10.^" with some uncer- 

 tainty in the next significant figure. 



1 Designating the units of energy, length, mass and time by E, L, M, T re- 

 spectively, the dimensions of some of the most frequently used quantities in me- 

 chanics are shown in the following tables. In the first of these length, mass and 



