166 On the Meteors of 13th November, 1833. 



plane of the ecliptic, and having its aphelion near to the orbit of the 

 earth. 



Let us inquire, next, what is the periodical time? Since the same 

 phenomenon was exhibited at Mocha, on the morning of the 13th 

 November, 1832, and on a much larger scale than that, in various 

 parts of the world, on the morning of the 12th November, 1799, we 

 cannot suppose such a coincidence in the time of the year to have 

 been purely accidental, but must conclude that the periodical time of 

 the comet, and that of the earth, bear to each other a ratio which can 

 be expressed in whole numbers ; so that after a certain number of 

 revolutions of the two bodies, corresponding to the terms that ex- 

 press their ratio, they will come together again. They could not 

 come together, as they did, on two successive years, unless the peri- 

 odical time of the comet was nearly an aliquot part of that of the 

 earth, such as one half, one third, &c. Now, if the time be any ali- 

 quot part of a year, it must be one half, so that the comet would per- 

 form two revolutions, while the earth performs one ; for, were its pe- 

 riod only one third of a year, the line of the apsides would not be long 

 enough to reach the earth. This will be obvious from the following 

 estimate. Let D represent the axis major of the earth, and d that of 

 the comet's orbit, their times being as 3 to 1. Then, by Kepler's 



Law, 3 2 : i 2 ::D 3 : d\ 



Taking D=190,000,000 miles, ^=91,343,000 for the whole ma- 

 jor axis, which is not equal to the distance from the sun to the earth. 

 But, supposing the times as 2 to 1, we have 



2 3 : 1 2 ::D 3 ; d 3 , whence ^=119,692,000 miles; giving for the 

 perihelion distance 24,692,000, and for the aphelion 95,000,000 

 miles. Hence we conclude, (3.) that the body has a period of near- 

 ly six months, and its perihelion a little below the orbit of Mercury. 



The transverse axis and the foci being determined, the ellipse 

 may be described. Therefore, join CS, and produce the line CS 

 to D, making SD equal to the perihelion distance, and upon CD de- 

 scribe the ellipse CFD, and it will represent the orbit of the comet. 



This is to be regarded only as a first approximation to the true 

 periodic time. The distance from the sun, instead of being taken, as 

 here, at the extremity of the body, ought to be reckoned from the 

 center of gravity, if we knew where to fix that. Nor can we sup- 

 pose that the periodical time is very uniform, since a light nebulous 

 body like the one in question, crossing as it does the orbits of Venus 



and Mercury, and having its perihelion near the orbit of the latter, 



