328 THE PRINCIPLES OF SCIENCE. [CHAP. 



must be altered in like manner. Changing the unit from 

 the foot to the inch, numerical expressions of volume must 

 be multiplied by 12 x 12 x 12. When a dimension enters 

 negatively the opposite rule will hold. If for the minute 

 we substitute the second as unit of time, then we must 

 divide all numbers expressing angular velocities by 60, 

 and numbers expressing angular acceleration by 60 x 60. 

 The rule is that a numerical expression varies inversely as 

 the magnitude of the unit as regards each whole dimension 

 entering positively, and it varies directly as the magnitude 

 of the unit for each whole dimension entering negatively. 

 In the case of fractional exponents, the proper root of the 

 ratio of change has to be taken. 



The study of this subject may be continued in Professor 

 J. D. Everett's " Illustrations of the Centimetre-gramme- 

 second System of Units," published by Taylor and Francis, 

 1875 ; in Professor Maxwell's " Theory of Heat ; " or Pro- 

 fessor Fleeming Jenkin's " Text Book of Electricity." 



Natural Constants. 



Having acquired accurate measuring instruments, and 

 decided upon the units in which the results shall be ex- 

 pressed, there remains the question, What use shall be 

 made of our powers of measurement ? Our principal 

 object must be to discover general quantitative laws of 

 nature ; but a very large amount of preliminary labour is 

 employed in the accurate determination of the dimensions 

 of existing objects, and the numerical relations between 

 diverse forces and phenomena. Step by step every part 

 of the material universe is surveyed and brought into 

 known relations with other parts. Each manifestation of 

 energy is correlated with each other kind of manifestation. 

 Professor Tyndall has described the care with which such 

 operations are conducted. 1 



"Those who are unacquainted with the details of 

 scientific investigation, have no idea of the amount of 

 labour expended on the determination of those numbers 

 on which important calculations or inferences depend. 

 They have no idea of the patience shown by a Berzelius 

 in determining atomic weights ; by a Kegnault in deter- 

 1 Tyndall's Sound, ist ed. p. 26. 



