352 THE POPULAR SCIENCE MONTHLY. 



which it would describe if the comet and sun were the only two 

 bodies in existence. The earth, Jupiter, all the planets are, in fact, 

 pulling and hauling at the unfortunate body : first one drags it a 

 little one way, then another pulls it in a different direction. The 

 real path of the comet about the sun is, then, a very complicated, 

 wavy sort of a curve, which, as a rule, does not depart very much 

 from the ellipse above figured. 



Now, while mathematicians have succeeded in completely solv- 

 ing the problem of two bodies, yet, up to the present day, that of 

 three or more bodies is still unsolved. If the sun and comet were 

 the only two bodies in the universe, then could a mathematician, 

 after a few moments' calculation, predict exactly where each 

 would be a thousand years hence ; could tell where they were ten 

 thousand years ago. But as soon as there is introduced into such 

 a simple system the earth, Jupiter, and the other planets, our 

 mathematics fails to give a complete solution. All that can be 

 done is to trace the course of the comet step by step, day by day, 

 almost. We know its position to-day, and we can accurately cal- 

 culate the direction and the amount of the pull of each planet ; 

 hence, we can find where it will be to-morrow, and, by repeating 

 the process, where it will be the next day, and the next. Of 

 course, this is a very laborious process ; the calculation of the 

 pull of a single planet requires the writing and the combination 

 of one hundred and fifty numbers of six figures each. But, 

 fortunately, the sun is over a thousand times as strong as the 

 great planet Jupiter, and over three hundred thousand times as 

 strong as the earth ; so that, unless the comet approach very near 

 to one of the larger planets, it will never deviate much from its 

 simple orbit around the sun. The steps in our computation may 

 be, therefore, lengthened. The ordinary length of step in such 

 work is forty days ; and, in a first computation, the pulls of the 

 smaller politicians — as the earth, Venus, and Mars — can be neg- 

 lected beside the very strong ones of Jupiter and Saturn. 



As we wished to trace the history of comet V, we started with 

 the earliest observed position, that of July 6, 1889, and we began 

 by taking steps of forty days each. Thus the path the comet had 

 traveled was slowly traced backward, and it was found to ap- 

 proach nearer and nearer to Jupiter. Proceeding backward thus 

 over a period of two years, we find that in March, 1887, the pull 

 of Jupiter was so strong that, in order to keep the work at all ac- 

 curate, we were obliged to shorten the steps to ten days. Con- 

 tinuing thus, the pull of Jupiter grew stronger and stronger, 

 until, in October, 1886, it was actually greater than that of the 

 sun, and a change of method had to be used in order to trace the 

 path beyond that point, and with this change in methods appears 

 the interesting mathematical part of the problem. 



