502 THE PRINCIPLES OF SCIENCE. [CHAP. 



manner. Until reason to the contrary is shown, we should 

 do well to look upon every law of simple proportion as 

 only provisionally true. 



Nevertheless many important laws of nature are in the 

 form of simple proportions. Wherever a cause acts in 

 independence of its previous effects, we may expect this 

 relation. An accelerating force acts equally upon a 

 moving and a motionless body. Hence the velocity 

 produced is in simple proportion to the force, and to the 

 duration of its uniform action. As gravitating bodies 

 never interfere with each other's gravity, this force is in 

 direct simple proportion to the mass of each of the at- 

 tracting bodies, the mass being measured by, or proportional 

 to inertia. Similarly, in all cases of " direct unimpeded 

 action," as Herschel has remarked, 1 we may expect simple 

 proportion to manifest itself. In such cases the equation 

 expressing the relation may have the simple form y = mx. 



A similar relation holds true when there is conversion 

 of one substance or form of energy into another. The 

 quantity of a compound is equal to the quantity of the 

 elements which combine. The heat produced in friction 

 is exactly proportional to the mechanical energy absorbed. 

 It was experimentally proved by Faraday that " the chemi- 

 cal power of the current of electricity is in direct pro- 

 portion to the quantity of electricity which passes." "When 

 an electric current is produced, the quantity of electric 

 energy is simply proportional to the weight of metal 

 dissolved. If electricity is turned into heat, there is 

 again simple proportion. Wherever, in fact, one thing 

 is but another thing with a new aspect, we may expect 

 to find the law of simple proportion. But it is only in 

 the most elementary cases that this simple relation will 

 hold true. Simple conditions do not, generally speaking, 

 produce simple results. The planets move in approximate 

 circles round the sun, but the apparent motions, as seen 

 from the earth, are very various. All those motions, again, 

 are summed up in the law of gravity, of no great com- 

 plexity ; yet men never have been, and never will be, able 

 to exhaust the complications of action and reaction arising 

 from that law, even among a small number of planets. 



4 Prdimiwnt Discourse, &c., p. 1 52. 



