15 OBJECTS, ADVANTAGES, AND 



reasoning mathematically from them, find out many most curious and 

 important truths depending upon these facts, and depending upon them 

 not accidentally, but of necessity. For example, we can find, in what 

 course the stone will move, if, instead of being dropped to the ground, 

 it is thrown forward : it will go in the curve already mentioned, the 

 parabola, and it will run through that curve in a peculiar way, so that 

 there will always be a certain proportion between the time it takes and 

 the space it moves through, and the time it would have taken, and the 

 space it would have moved through had it fallen from the hand to the 

 ground. So we can prove, in like manner, what we before stated of 

 the relation between the distance at which it will come to the ground, 

 and the direction it is thrown in ; the distance being greatest of all 

 when the direction is nearly half way between the level or horizontal 

 and the upright or perpendicular. These are mathematical truths, 

 derived by mathematical reasoning upon physical grounds ; that is, 

 upon matter of fact found to exist by actual observation and experiment. 

 The result, therefore, is necessarily true, and proved to be so by reasoning 

 only, provided we have once ascertained the facts ; but taken altogether, 

 the result depends partly on the facts learned by experiment or expe- 

 rience, partly on the reasoning from these facts. Thus it is found to be 

 true by reasoning, and necessarily true, that if the stone falls in a cer- 

 tain way when unsupported, it must when thrown forward go in the 

 curve called a parabola : this is a necessary or mathematical truth, and 

 it cannot possibly be otherwise. But when we state the matter without 

 any supposition, without any " if" and say, a stone thrown forward 

 goes in the curve called a parabola, we state a truth, partly fact, and 

 partly drawn from reasoning on the fact ; and it might be otherwise if 

 the nature of things were different. It is called a proposition or truth 

 in Natural Philosophy ; and as it is discovered and proved by mathe- 

 matical reasoning, it is sometimes called a proposition or truth in the 

 Mixed Mathematics. The man in the dark room could never discover 

 this truth unless he had been first informed, by those who had observed 

 the fact, in what way the stone falls when unsupported, and moves 

 along the table when pushed. These things he never could have found 

 out by reasoning : they are facts, and he could only reason from them 

 after learning them, by his own experience, or taking them on the 

 credit of other people's experience. But having once so learnt them, 

 he could discover by reasoning merely, and with as much certainty as 

 if he lived in daylight, and saw and felt the moving body, that the 

 motion is in a parabola, and governed by certain rules. As experi- 

 ment and observation are the great sources of our knowledge of 

 Nature, and as the judicious and careful making of experiments is the 

 only way by which her secrets can be known, Natural and Experi- 

 mental Philosophy mean one and the same thing; mathematical 

 reasoning being applied to certain branches of it, particularly those, 

 which relate to motion and pressure. 



III. Natural Philosophy, in its most extensive sense, has for its pro- 

 vince the investigation of the laws of matter ; that is, the properties and 

 the motions of matter ; and may be divided into two great branches. The 

 first and most important (which is sometimes on that account called 



