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 attracting bodies, the mass being measured by, or proportional to inertia. Similarly, in all cases of “direct unimpeded action,” as Herschel has remarked,20 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 chemical power of the current of electricity is in direct proportion 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 complexity; 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. We should be on our guard against a tendency to assume that the connection of cause and effect is one of direct proportion. Bacon reminds us of the woman in Æsop’s fable, who expected that her hen, with a double measure of barley, would lay two eggs a day instead of one, whereas it grew fat, and ceased to lay any eggs at all. It is a wise maxim that the half is often better than the whole.