DISCOVERIES RESULTING FROM MEASUREMENTS. 391 



in chemistry. The laws of action of the forces of heat, 

 electricity, magnetism, have all been ascertained by the 

 combined application of qualitative and quantitative 

 methods ; and the whole of the sciences are penetrated in 

 all directions by laws requiring for their discovery both 

 arithmetical as well as logical processes. 



Quantitative measurements also greatly aid us in 

 discovering residues of substances, forces, or effects. It 

 is clear that as neither matter nor force can be destroyed 

 by human agency, from one hundred parts of a mixture 

 of substances taken for analysis we ought to be able to 

 obtain neither more nor less than one hundred ; and, 

 similarly, if we expend one hundred parts of a given 

 force, we ought to be able to obtain as a result, in the 

 form of other forces, a total which is equivalent to neither 

 more nor less than the whole amount of power ex- 

 pended. 



Some phenomena (such as those of small periodic 

 changes of terrestrial magnetism) are so hidden by larger 

 phenomena of a similar kind, that they could hardly be 

 discovered at all except by the aid of long-continued 

 series of systematic measurements, and taking the average 

 of numerous results. The average strength and direc- 

 tion of the wind, the mean pressure of the air, the true 

 sea-level, and many other facts, are arrived at in this 

 way. 



Some quantitative processes and contrivances save 

 much labour in research. It has been said that the inven- 

 tion of logarithms doubled the life of astronomers, and 

 that that of the differential calculus was as great an aid to 

 scientific discovery as that of the steam-engine was to the 

 mechanical arts. 



In consequence of the great flood of light which is 

 thrown upon every scientific truth, by a knowledge of its 



