SECT, in.] INEQUALITY OF JUPITER AND SATURN. 29 



other methods. Jupiter and Saturn, however, exhibit in- 

 equalities which for a long time seemed discordant with that 

 law. All observations, from those of the Chinese and Arabs 

 down to the present 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 observation 

 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 con- 

 junction (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 re- 

 volution 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 con- 

 junction always happened in the same point of the orbit, this 

 uncompensated inequality in the mean motion would go on 

 increasing till the periodic times and forms of the orbits were 

 completely and permanently changed : a case that would 

 actually take place if Jupiter accomplished exactly five revo- 

 lutions in the time Saturn performed two. These revolutions 

 are, however, not exactly commensurable; the points in 

 which the conjunctions take place are in advance each time as 



