OBJECTS, PLEASURES, AND ADVANTAGES OF SCIENCE. ix 



We see that a stone dropped from our hand falls to the ground ; this is a fact which we can only know 

 by experience ; before observing it, we could not have guessed it, and it is quite conceivable that it should 

 be otherwise : for instance, that when we remove our hand from the body it should stand still in the air ; 

 or fly upward, or go forward, or backward, or sideways ; there is nothing at all absurd, contradictory, or 

 inconceivable in any of these suppositions ; there is nothing impossible in any of them, as there would 

 be in supposing the stone equal to half of itself, or double of itself; or both falling down and rising 

 upwards at once; or going to the right and to the left at one and the same time. Our only reason for not 

 at once thinking it quite conceivable that the stone should stand still in the air, or fly upwards, is that we 

 have never seen it do BO, and have become accustomed to see it do otherwise. But for that, we should 

 at once think it aa natural that the stone should fly upwards or stand still, as that it should fall down. 

 But no degree of reflection for any length of time could accustom us to think 2 and 2 equal to anything but 

 4, or to believe the whole of any thing equal to a part of itself. 



After we have once, by observation or experiment, ascertained certain things to exist in fact, we may 

 then reason upon them by means of the mathematics ; that is, we may apply mathematics to our 

 experimental philosophy, and then such reasoning becomes absolutely certain, taking the fundamental facts 

 for granted. Thus, if we find that a stone falls in one direction when dropped, and we further observe the 

 peculiar war in which it falls, that is, quicker and quicker every instant till it reaches the ground, we learn 

 the rule or the proportion by which the quickness goes on increasing ; and we further find, that if the 

 same stone be pushed forward on a table, it moves in the direction of the push, till it is either stopped by 

 something, or comes to a pause by rubbing against the table and being hindered by the air. These 

 re facts which we learn by observing and trying, and they might all have been different if matter and 

 motion had been otherwise constituted ; but supposing them to be as they are, and as we find them, we 

 can, by reasoning mathematically from them, find out many most curious and important truths depending 

 upon those 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 be thrown forward : it 

 will go in the curve already mentioned, the parabola, somewhat altered by the resistance of the air, 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 dropped from the hand in a straight line 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 half way between 

 the level or horizorital,and the upright or perpendicular. These are mathematical truths, derived by mathe- 

 matical 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 BO by reasoning only, provided 

 we have once ascertained the facts ; but taken altogether, the result depends partly on the facts learned by 

 experiment or experience, partly on the reasoning from these facts. Thus it is found to be true by 

 reasoning, and necessarily true, that if the stone fall in a certain way when unsupported, it must, when 

 thrown forward, go in the curve called a parabola, provided there be no air to resist : 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 a 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 mathematical reasoning upon facts in nature, it is sometimes called a proposition 

 or truth in the Mixed Mathematict, so named in contradistinction to the Pure Mathematics, which are 

 employed in reasoning upon figures and numbers. The man in the dark room could never discover this 

 truth unless he bad been first informed, by those who had observed the fact, in what way the stone falls 

 when unsupported, and move* 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, lie, 

 could discover by reasoning merely, and with aa much certainty as if he lived iu daylight, and saw and 

 felt the moving body, that the motion is parabolic, and governed by certain rules. Aa experiment and 

 observation are the great source* 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 Experimental 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 OB EXPERIMISTAL SCIENCE. 



NATURAL PHILOSOPHY, in its most extensive sense, has for its province the investigation of the laws of 

 matter; that is, the properties and the motions of matter; and it may be divided into two great branches. 

 The first and most important (which ia sometimes, on that account, called Natural Philotophy by wuy 



