On the Use of DeJinitio7is. 265 be complete we need no other materials of knowledge. The example of geometry, therefore, gives us no encouragement to endeavour to make other sciences equally complete and logical, by selecting such definitions as will but lend them- selves to our syllogistic process ; except we can find other sciences which, like geometry, are independent of the ex- ternal world, and require no verification of their principles by experience. Mechanics is the most perfect of the branches of mixed mathematics. It has also been the most happy in its defi- nitions. But its happiness consisted in this ; that mechanical philosophers resolved beforehand to employ words in such a manner, that those laws of nature which experience proved to be true^ should be expressed in the simplest terms. Galileo and his opponents agreed in asserting that bodies, falling by the action of gravity, were uniformly accelerated : but there was a real question between them, whether the velocity increased proportionally to the space, or to the time. When the latter appeared to be the fact, it was no longer €ontested that the expression should be appropriated to this Saw, and disjoined from the other. The definition followed the settlement of the dispute. In Optics such terms as ' the angle of incidence"* ' of re- fraction," &c. were introduced after it had been found that the appearances of objects were governed by the course of the rays of light passing from them to the eye, and that the course of these rays, when they fell on transparent bodies, was regulated by the angle they made with the surface. A lady who was describing an optical experiment which had been shewn her by a great philosopher, said, " He talked about increasing and diminishing the angle of incidence; and at last I found he only meant moving my head up and down.'" The philosopher's phraseology would have been far less commendable than the lady's, if he had not known that his terms referred to an essential, and her's to an accidental, condition of the experiment. If he had defined the angle of incidence to be that which is increased by moving the head up and diminished by moving it down, he might have deduced geometrical inferences from his definition, but he would not have been able to see the image by the help of them.
