336 



INDUCTION. 



mathematical questions, and to be 

 treated, therefore, deductively. If, 

 as we have seen, cases of the Com- 

 position of Causes are seldom adapted 

 for any other than deductive investi- 

 gation, this is especially true in the 

 case now examined, the continual 

 composition of a cause with its own 

 previous effects ; since such a case is 

 peculiarly amenable to the deductive 

 method, while the undistinguishable 

 manner in which the effects are blended 

 with one another and with the causes 

 must make the treatment of such an 

 instance experimentally still more chi- 

 merical than in any other case. 



§ 2. We shall next advert to a 

 rather more intricate operation of the 

 same principle, namely, when the 

 cause does not merely continue in 

 action, but undergoes, during the 

 same time, a progressive change in 

 those of its circumstances which con- 

 tribute to determine the effect. In 

 this case, as in the former, the total 

 effect goes on accumulating by the 

 continual addition of a fresh effect to 

 that already produced, but it is no 

 longer by the addition of equal quan- 

 tities in equal times ; the quantities 

 added are unequal, and even the 

 quality may now be different. If the 

 change in the state of the permanent 

 cause be progressive, the effect will 

 go through a double series of changes, 

 arising partly from the accumulated 

 action of the cause, and partly from 

 the changes in its action. The effect 

 is still a progressive effect, produced, 

 however, not by the mere continuance 

 of a cause, but by its continuance and 

 its progressiveness combined. 



A familiar example is afforded by 

 the increase of the temperature as 

 summer advances, that is, as the sun 

 draws nearer to a vertical position, 

 and remains a greater number of 

 hours above the horizon. This in- 

 stance exemplifies in a very interest- 

 ing manner the twofold operation on 

 the effect, arising from the continu- 

 ance of the cause, and from its pro- 

 ^rressive change. When once the sun 



has come near enough to the zenith, 

 and remains above the horizon long 

 enough to give more warmth during 

 one diurnal rotation than the counter- 

 acting cause, the earth's radiation, 

 can carry off, the mere continuance 

 of the cause would progressively in- 

 crease the effect, even if the sun 

 came no nearer and the days grew 

 no longer ; but in addition to this, 

 a change takes place in the accidents 

 of the cause (its series of diurnal 

 positions) tending to increase the 

 quantity of the effect. When the 

 summer solstice has passed, the pro- 

 gressive change in the cause begins 

 to take place the reverse way ; but, 

 for some time, the accumulating effect 

 of the mere continuance of the cause 

 exceeds the effect of the changes in 

 it, and the temperature continues to 

 increase. 



Again, the motion of a planet is a 

 progressive effect, prodiiced by causes 

 at once permanent and progressive. 

 The orbit of a planet is determined 

 ( omitting perturbations ) by two causes : 

 first, the action of the central body, 

 a permanent cause, which alternately 

 increases and diminishes as the planet 

 draws nearer to or goes farther from 

 its perihelion, and which acts at every 

 point in a different direction ; and, 

 secondly, the tendency of the planet 

 to continue moving in the direction 

 and with the velocity which it has 

 already acquired. This force also 

 grows greater as the planet draws 

 nearer to its perihelion, because as it 

 does so its velocity increases ; and 

 less, as it recedes from its perihelion : 

 and this force as well as the other 

 acts at each point in a different direc- 

 tion, because at every point the action 

 of the central force, by deflecting the 

 planet from its previous direction, 

 alters the line in which it tends to 

 continue moving. The motion at 

 each instant is determined by the 

 amount and direction of the motion, 

 and the amount and direction of the 

 sun's action, at the previous instant : 

 and if we speak of the entire revolu- 

 tion of the planet as one phenomenon, 



