24 INEQUALITY OF JUPITER AND SATURN. SECT. III. 



All the periodic and secular inequalities deduced from 

 the law of gravitation are so perfectly confirmed by 

 observation, that analysis has become one of the most 

 certain means of discovering the planetary irregularities, 

 either when they are too small, or too long in their 

 periods, to be detected by other methods. Jupiter and 

 Saturn, however, exhibit inequalities which for a long 

 time seemed discordant with that law. All observations, 

 from those of the Chinese and Arabs down to the pres- 

 ent day, prove that for ages the mean motions of Jupiter 

 and Saturn have been affected by a great inequality of 

 a very long period, forming an apparent anomaly in the 

 theory of the planets. It was long known by observa- 

 tion that five times the mean motion of Saturn is nearly 

 equal to twice that of Jupiter : a relation which the 

 sagacity of La Place perceived to be the cause of a 

 periodic irregularity in the mean motion of each of these 

 planets, which completes its period in nearly 918 years, 

 the one being retarded while the other is accelerated ; 

 but both the magnitude and period of these quantities 

 vary in consequence of the secular variations in the 

 elements of the orbits. Suppose the two planets to be 

 on the same side of the sun, and all three in the same 

 straight line, they are then said to be in conjunction 

 (N. 83). Now, if they begin to move at the same time, 

 one making exactly five revolutions in its orbit, while the 

 other only accomplishes two, it is clear that Saturn, the 

 slow-moving body, will only have got through a part of 

 its orbit during the time that Jupiter has made one 

 whole revolution and part of another, before they be 

 again in conjunction. It is found that during this time 

 their mutual action is such as to produce a great many 

 perturbations which compensate each other, but that 

 there still remains a portion outstanding, owing to the 

 length of time during which the forces act in the same 

 manner ; and if the conjunction always happened in the 

 same point of the orbit, this uncompensated inequality 

 in the mean motion would go on increasing till the peri- 

 odic times and forms of the orbits were completely and 

 permanently changed : a case that would actually take 

 place if Jupiter accomplished exactly five revolutions in 

 the time Saturn performed two. These revolutions 



