Lowrie.J -^^^ [Sept, 17, 



given, becomes, as a cause, past and ended, and its assumed effect is 

 uniform velocity forever; but it does not assume to resist the retarding, 

 accelerating and other disturbances that assail the body, and it is impos- 

 sible that it can do so. Nor can it resist the attraction of its central 

 body, which is constant in its direction, and also in its degree so long as 

 the distance is unchanged. A force that interferes to deflect a moving 

 body must thereby decrease its velocity, and the more direct the inter- 

 ference the greater is this decrease, as a direct one may stop it altogether. 



In order to get a clear conception of some of these retardations and 

 accelerations, it is necessary to get beyond the motion of each body, in 

 so far as it is inerely relative to its primary, and consider it in a more ab- 

 solute way. Take the moon in its revolution round the earth, stai'ting 

 with it at its first quadrature. Then it is 240,000 miles in the rear of the 

 earth. It must of course overtake the earth, as it does at full moon, and 

 pass on to its second quadrature, where it will be 240, 000 miles in advance 

 of the earth; and then, in another half lunation, it must fall back, rela- 

 tively, twice 240,0(0 miles to the same relative position fi'om which we 

 started with it. 



And it is well to notice that this motion, apparently a circle round the 

 earth, is really, in relation to the sun and in a long period, a series of 

 alternate small undulations on each side of the earth's orbit, the longer 

 ones being on the outside and the shorter ones on the inside, and the dif- 

 ference between their chords being nearly a million of miles; and while 

 the moon is making this slow motion in relation to the earth, it advances 

 near fifty millions of miles with the earth along its orbit round the sun. 

 No other satellite moves so slowly, because no other is so little held by 

 the attraction of its primary compared with that of the sun, which is 

 2.2 of the earth's, while, in i-elation to most other satellites, it is meas- 

 ured by thousandths, and in relation to only the two outer satellites of 

 Saturn and Uranus does it rise above hundredths. 



Take also the earth in its revolution round the sun. Its apparently 

 circular orbit changes entirely when we take into account the sun's mo- 

 tion in its own orbit, said to be 150 millions of miles a year. If we start 

 with the earth at its vernal equinox, it is 95 millions of miles in the rear 

 of the sun, and in six months it moves forward to a position as far in 

 advance, with the chord of its curve elongated 75 millions of miles by its 

 motion with the sun. Passing its autumnal equinox to the inside of the 

 sun's orbit, it sweeps back in another six months to its original relative 

 position in the rear of the sun, and yet, having moved with the sun, 

 it is found 150 millions of miles in advance of the position whence we 

 started with it, and 115 millions in the rear of its position six months 

 before, and its real annual orbit turns out to be an immense scollop, the 

 loop of which on the sun's orbit is 115 millions of miles M'ide, the motion 

 being really retrogressive during the second half of each year, and the 

 length of its real journey in absolute space along its real orbit being 

 near twice as great in the first half of the year as in the second half. 



Thus all the planets and satellites have orbits consisting of very long 



