792 THE POPULAR SCIENCE MONTHLY, 



Of the above, I indicates the position of the body in the orbit at 

 some definite time ; II gives the greatest semi-diameter of the ellipse ; 

 III gives the ratio of the distance of the focus from the center divided 

 by the semi-major axis ; lY, with YI, gives the position in space of 

 the greatest diameter of the ellipse ; Y gives the position of the line 

 of intersection between the plane of the unknown orbit and the plane 

 of the earth's orbit. 



From II may be determined immediately the period of revolution 

 by means of Kepler's law as follows : if a and a' are respectively the 

 semi-major axis of the unknown orbit and the earth's orbit, and ^ and 

 t' the respective periods of revolution, then we have from Kepler's law 



z= and t = 

 a' a" 



If the eccentricity of the orbit is very large, the portion of the ellipse 

 in the vicinity of the perihelion approximates to a parabola, which it 

 becomes when the eccentricity equals unity. 



As a matter of history, the great majority of comet orbits hitherto 

 studied are either parabolas or are portions of excessively elongated 

 ellipses, so as to be indistinguishable from parabolas, at least in the 

 part of the orbit traversed during visibility. This portion of the orbit 

 is always adjacent to the perihelion. 



From the foregoing fact, and moreover because the computation 

 of a parabolic orbit is much simpler, there being one less unknown 

 quantity, preliminary comet orbits are always parabolic. Subsequent 

 investigations show whether the comet deviates perceptibly from the 

 parabola computed. 



On October 10, 1880, Lewis Swift, of Rochester, New York, dis- 

 covered a comet which has proved to be of peculiar interest. From 

 its first discovery it has presented no brilliancy of appearance, for, 

 during its period of visibility, a telescope of considerable power was 

 necessary to observe it. Since this comet when in close proximity to 

 the earth was very faint indeed, its dimensions must be quite mod- 

 erate. 



As soon after its apparition as the necessary observations of posi- 

 tion were obtained, its parabolic elements were computed by several 

 astronomers. After carefully comparing these elements with those of 

 previous comets, Mr. S. C. Chandler, of Boston, remarked the striking 

 similarity between them and those of Comet III of 1869. He imme- 

 diately suspected them to be one and the same body, revolving in an 

 elongated ellipse, having a period of eleven years, or a sub-multiple of 

 eleven years. 



Mr. Chandler hereupon made some extended investigations, to de- 

 termine which period was the more probable. He showed that the 

 observed positions could be satisfied more closely with a period of five 

 and one half years. 



