962 



SCIENCE. 



[N. S. Vol. XV. No. 390. 



tween the factors of phenomena is ob- 

 served, then measurements may be made 

 in response 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 quan- 

 tities are subject to calculation, the meas- 

 ured values of some of them sufficing, 

 through computation, to give the values of 

 the others. All calculations, therefore, pre- 

 suppose a knowledge of the laws of con- 

 nection of related quantities, or quantita- 

 tive theories of the phenomena considered. 



Measurements and calculations are of all 

 grades of ■ definiteness, ranging from the 

 smallest probabilities of the doctrine of 

 ■chances up to the rigorous certainties of 

 mathematical deduction. Thus the degree 

 of precision attainable in the measured and 

 ■computed quantities of a science is com- 

 monly taken as a gauge of its perfection. 

 But it would be a mistake to infer com- 

 plete perfection from the precision attain- 

 able in one or more branches of science. 

 Astronomy, for example, is a marvelouslj^ 

 perfect science in certain of its branches, 

 but nevertheless some of its fundamental 

 ■constants, notably the gravitation con- 

 stant and the aberration constant, are 

 known with only a low degree of preci- 

 sion.* Whether any quantity may be meas- 



* The gravitation constant is the factor by 

 . which the product of two masses divided by the 

 square of their distance asunder must be multi- 

 plied in order to express the force exerted by those 

 masses on one another. Tlius, .if m^ and 7ji, de- 

 note two masses, s their distance asunder, F the 

 ■force of attraction between them, and k the gravi- 

 tation constant, then 



It should be remarked that k 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 squares of a time; or that its 

 ■ dimensions are sho-svn by the exponents in 



ured or calculated with precision depends, 

 in general, on the degree of complication 

 of its connections with other quantities, 

 and on the applicability of methods 

 already applied in the detei-mination of 

 other quantities. Frequently, a quantity 

 may be measured directly; but it oftener 

 happens, either by reason of the inappli- 

 cability 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 appar- 

 ent diversity of nature, that all of the 

 numerous quantities with which physical 

 science has to deal may be expressed in 

 terms of a certain very limited number of 

 arbitrarily chosen quantities, or units. 

 The units most conmionly used, and those 

 which seem best suited to the present re- 

 quirements of science, are the units of 

 length, mass and time. All other quanti- 

 ties, however complex, may be expressed 

 readily in terms of these arbitrarily as- 



{ L-i-^M-^T-^ ) if L, M, T denote the units of 

 length, mass and time respectively. 



It should be remarked also that the above 

 expression of Newton's law of gravitation lacks 

 the precision essential for mathematical calcula- 

 tions. To make the statement definite and gen- 

 eral 5»i and in^ must be regarded as infinitesi- 

 mals, so that the resultant attraction between 

 two finite bodies requires, in. general, a summa- 

 tion, or integration, for its exact expression. A 

 widespread error exists in the notion that the 

 above equation is exact if the distance s is the 

 distance between the 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 centro- 

 baric. 



The gravitation constant is, in C. G. S. units, 

 about 667 X 10-'^, with some uncertainty in the 

 last significant figure. 



The aberration constant, which 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 20.5" with some 

 uncertainty in the next significant figure. 



