RECORDS 23 



Whenever a quantitative relation between the factors of phe- 

 nomena is observed, then measurements may be made in re- 

 sponse to the question, What is the magnitude of the relation, 

 if constant, or what are the extent and law of variation of the 

 relation if it is not constant ? When the law of relation is known, 

 related quantities are subject to calculation, the measured values 

 of some of them sufficing, through computation, to give the 

 values of the others. All calculations, therefore, presuppose a 

 knowledge of the laws of connection of related quantities or 

 quantitative theories of the phenomena considered. 



Measurements and calculations are of all grades of definite- 

 ness, ranging from the smallest probabilities of the doctrine of 

 chances up to the rigorous certainties of mathematical deduc- 

 tion. Thus the degree of precision attainable in the measured 

 and computed quantities of a science is commonly taken as a 

 gauge of its perfection. But it would be a mistake to infer 

 complete perfection from the precision attainable in one or 

 more branches of science. Astronomy, for example, is a mar- 

 velously perfect science in certain of its branches, but never- 

 theless some of its fundamental constants, notably the gravita- 

 tion constant and the aberration constant, are known with only 

 a low degree of precision.^ Whether any quantity may be 



1 The gravitation constant is the factor by which the product of two masses 

 divided by the square of their distance asunder must be multiplied in order to ex- 

 press the force exerted by those masses on one another. Thus, if Wj and Wj 

 denote two masses, s their distance asunder, /^the force of attraction between them, 

 and ^ the gravitation constant, then 



It should be remarked that ^ is not a mere numeral, as many eminent writers on 

 the law of gravitation would seem to imply, but that it is the cube of a distance 

 divided by the product of a mass and the square of a time ; or that its dimensions 

 are shown by the exponents in (Z+^J/— ' 7"— 2) if z, Af, T denote the units of 

 length, mass and time respectively. 



It should be remarked also that the above expression of Newton's law of gravi- 

 tation lacks the precision essential for mathematical calculations. To make the 

 statement definite and general, w, and in^ must be regarded as infinitesimals, so 

 that the resultant attraction between two finite bodies requires, in general, a sum- 

 mation, or integration, for its exact expression. A widespread error exists in the 

 notion that the above equation is exact if the distance j is the distance between the 



