364 INDUCTION. 



summer advances, that is, as the sun draws nearer to a vertical position, and 

 remains a greater number of hours above the horizon. This instance ex- 

 emplifies in a very interesting manner the twofold operation on the effect, 

 arising from the continuance of the cause, and from its progressive 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 counteracting cause, the earth's radiation, can carry off, the mere 

 continuance of the cause would progressively increase 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 po- 

 sitions), tending to increase the quantity of the effect. When the suminer 

 solstice has passed, the progressive 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, produced 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 direction, 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 rev- 

 olution of the planet as one phenomenon (which, as it is periodical and 

 similar to itself, we often find it convenient to do), that phenomenon is the 

 progressive effect of two permanent and progressive causes, the central 

 force and the acquired motion. Those causes happening to be progressive 

 in the particular way which is called periodical, the effect necessarily is so 

 too; because the quantities to be added together returning in a regular 

 order, the same sums must also regularly return. 



This example is worthy of consideration also in another respect. Though 

 the causes themselves ai-e permanent, and independent of all conditions 

 known to us, the changes which take place in the quantities and relations 

 of the causes are actually caused by the periodical changes in the effects. 

 The causes, as they exist at any moment, having produced a certain motion, 

 that motion, becoming itself a cause, reacts upon the causes, and produces 

 a change in them. By altering the distance and direction of the central 

 body relatively to the planet, and the direction and quantity of the force in 

 the direction of the tangent, it alters the elements which determine the mo- 

 tion at the next succeeding instant. This change renders the next motion 

 somewhat different ; and this difference, by a fresh reaction upon the causes, 

 renders the next motion again different, and so on. The original state of 

 the causes might have been such that this series of actions modified by- 

 reactions would not have been periodical. The sun's action, and the origi- 

 nal impelling force, might have been in such a ratio to one another, that the 

 reaction of the effect would have been such as to alter the causes more and 



