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from either." The discovery of the cause or causes 

 under such circumstances, cannot be effected by 

 the Experimental Methods. But this leads us to 

 the consideration of a method different from any 

 of these, which has a vast range of efficacy in 

 scientific research, and becomes more and more 

 powerful as the sciences advance, or as discovery 

 is extended. It is called 



The Deductive' Method. 



The Experimental Methods suppose that we 

 take up a subject that is as yet fresh and unex- 

 plored, or where no great general principles have 

 been attained. They are the methods adapted to 

 the commencement of inquiry. But when one or 

 two comprehensive laws have been arrived at, a 

 great deal is to be discovered by following out the 

 application of these laws wherever they are found 

 to operate. Thus, when the law of the persever- 

 ance of moving bodies was once discovered, it 

 was made use of to explain many motions that 

 would otherwise have remained inexplicable : 

 such as the rotation of the earth, and the tendency 

 of the planets to maintain their distance from the 

 sun. In like manner, the discovery of the general 

 law of reaction enabled Newton to determine the 

 cause, and even for the first time to ascertain the 

 existence, of the fluctuation of the sun in the 

 centre of the planetary system. By the Deductive 

 Method alone are we able to trace the operation 

 of that class of causes which, by intermixture, are 

 wholly neutralised, and produce no apparent con- 

 sequences whatever as in what are called the 

 laws of equilibrium or counterpoise. 



There are three different steps in the complete 

 working out of the Deductive Method. The first 

 is Induction, or the determination of the general 

 law by the Experimental Methods. The second 

 is the carrying out of the law to the explanation of 

 all cases where it seems to apply, and especially 

 the tracing out of the action that would result from 

 two or more principles acting in combination. 

 Thus, the Deductive Method applied to trace out 

 the cause of the curved motion of a projectile, 

 would consist in combining together the law of 

 perseverance with the law of accelerated motion 

 under a constantly acting force, and in determin- 

 ing what would be the path that a body would 

 describe under the two actions. The third step, 

 which is Verification, consists in comparing the 

 effect deduced with the effect witnessed, to see if 

 the two exactly agree : this agreement being the 

 proof that the laws supposed are the laws that 

 operate in the case. When Newton arrived, by 

 induction, at the law of universal gravitation, and 

 found that it decreased as the square of the dis- 

 tance increased, he applied this deductively to 

 explain the attachment, or perpetual fall, of the 

 moon to the earth. He calculated what would be 

 the amount of the moon's deflection, supposing 

 gravity were the cause of it ; and then compared 

 this calculated amount with the observed amount, 

 and found a perfect coincidence. The same 

 process he applied successively to the planets, and 

 proved that each of them was detained from 

 running off in a straight line through space by its 

 gravitation towards the central sun. 



Sometimes a law is assumed to exist for the 

 sake of trying how it would explain appearances, 

 although no such law has been discovered by 



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a regular inductive process. This is what is 

 called making a hypothesis or assumption. If, on 

 trial, the assumed law is completely verified by 

 agreeing with the facts, this of itself may be a 

 reason for believing it to be a true law of nature. 

 Thus, for example, Dalton's doctrines of atomic 

 affinity were at first mere suppositions, or hints 

 thrown out for trial and experiment ; but it turned 

 out that they had been so successfully conceived, 

 as to stand the test of verification. 



The laws thus employed deductively are the 

 most general or comprehensive laws of nature, 

 or the statements of what happens through the 

 entire range of appearances that nature has in- 

 cluded under a single cause. At all events, they 

 are the most general laws that man has been able 

 to discover ; they, moreover, refer to the smallest 

 and simplest trains or threads of causation, or to 

 the indivisible sequences of events. Thus, the law 

 of gravitation expresses the simplest train of causa- 

 tion that can be conceived ; there are the fewest 

 possible circumstances or conditions that can be 

 mixed up in the production of any effect. This 

 remark is necessary, in order to distinguish ulti- 

 mate laws from derivative laws, where additional 

 circumstances are introduced which make the 

 thread more complex, and the case more limited 

 in its application. Thus the law, that the planets 

 move in ellipses, is a derivative law, involving 

 the operation of two ultimate laws under certain 

 arrangements or collocations ; these arrangements 

 are, that the planet should have been projected 

 at a distance from the sun, in a certain direction, 

 and with a certain speed, bearing a proportion to 

 the above-mentioned distance. As only a very 

 few bodies comply with all these conditions and 

 arrangements, the law of elliptic motion is more 

 limited in its application than the more general 

 laws of perseverance and gravitation. When such 

 laws are got at deductively, they are called Deriv- 

 ative Laws ; when got at inductively, they are 

 called Empirical Laws. The law of elliptic motion 

 was first proved inductively by Kepler, and after- 

 wards proved deductively by Newton. As given 

 by Kepler, it was therefore only empirical. All 

 inductions of complicated sequences, or trains of 

 causation, are of the empirical kind, and have 

 the peculiarity of being of very limited application ; 

 they must be confined to the cases where all the 

 conditions and arrangements are strictly contained. 

 If we observe that a draught of cold air is the 

 cause of catching cold, the sequence is only an 

 empirical one, and is confined to cases where 

 certain conditions are present ; and until the con- 

 ditions are strictly defined, the observation cannot 

 be stated as a general fact even of the empirical 

 kind. Many of the assertions made in everyday 

 life are of this undefined description. An effect 

 is assigned to a cause, without stating the exact 

 conditions and circumstances necessary to insure 

 the sequence. 



When we turn from the Inductive Problem of 

 Causation to the other kinds of propositions 

 namely, Co-existence, Order in place, and Similar- 

 ity we find a somewhat different process of in- 

 vention and proof requisite. The most important 

 class of propositions of co-existence are such as 

 assert the properties of kinds, or the attributes 

 that always accompany one another in the objects 

 presented to us in nature. Thus, when we affirm 

 all the properties of gold, iron, oxygen, oak, horse, 





