48 



SCIENCE. 



[YOL. VI., No. 128. 



For the ellipse the eccentricity is always greater 

 than 0, and less than 1 ; and, the nearer it is to 

 1, the more elongated is the ellipse. 



■LINEOFNDDES 



Fig. 3. — Orbit of Barnard's comet. 



Instead of e, the ' eccentric angle 



or 



CBF in the figure, is sometimes given ; but 

 from it we can obtain e 

 by means of the relation 



I might say that the 

 linear distances a and e 

 are usually expressed as 

 decimal parts of the 

 earth's mean distance 

 from the sun. If a = 

 2.98 (as in the case of 

 Barnard's comet), it 

 means that the mean dis- 

 tance of the comet, or 

 the semi-major axis of 

 the orbit, is 2.98 times 

 that of the earth, or 

 about two hundred and 

 seventy-six million miles. 

 So, generally, measure- 

 ments expressed in this 

 way are reduced to miles 

 by multiplying by nine- 

 ty-two and a half mil- 

 lion. 



Having settled the 

 shape of the orbit, we 

 must determine its posi- 

 tion in space. For this 

 purpose three more ele- 

 ments are required : — 



3. The longitude of 

 the ascending node, the 

 angular distance from the first point of Aries 

 (T, fig. 2) to the point in which the comet 



pierces the plane of the ecliptic in passing 

 from the southern to the northern side. It is 

 usually denoted by the symbol Q,. The op- 

 posite or descending node is denoted by the 

 symbol ^. 



4. The inclination, ^, of the plane of the 

 comet's orbit to that of the ecliptic. 



5. The longitude of perihelion, n^ which in 

 fig. 2 is the arc T $^ + ^P, or 



6. Finally, we must state where the comet is 

 in its orbit at some specified time. For comets 

 we generally give the date of perihelion pas- 

 sage, T, 



To these six elements there might be added 

 the mean daily motion, ^, expressed in seconds 

 of arc ; and the period of revolution, some- 

 times called U, in days or years. 



With the semi-axes a and h given (& is 

 obtained from a and <^ by means of the 

 formula, b = a cos (/>) , the curve is constructed 

 to any scale we please. I have found it con- 



SEPT.17,1884. 



Fig. 4. — Orbits of comets 1884 ii and hi. 



venient to use a scale of two inches. The 

 earth's orbit is then represented with suflScient 



