56 RELATIONS PERTAINING SIMPLY [BOOK I. 



III. The semi-axis major, which indeed might be omitted when the mass of 

 the body is known or can be neglected, since it is already given by the mean 

 motion, (article 7) ; both, nevertheless, are usually given for the sake of con 

 venience. 



IV. Eccentricity. V. Longitude of the perihelion. VI. Longitude of the 

 ascending node. VII. Inclination of the orbit. 



These seven things are called the elements of the motion of the body. 



In the parabola and hyperbola, the time of passage through the perihelion 

 serves in place of the first element ; instead of II, are given what in these 

 species of conic sections are analogous to the mean daily motion, (see article 

 19 ; in the hyperbolic motion the quantity X kl~*, article 23). In the hyperbola, 

 the remaining elements may be retained the same, but in the parabola, where 

 the major axis is infinite and the eccentricity = 1, the perihelion distance alone 

 will be given in place of the elements III. and IV. 



49. 



According to the common mode of speaking, the inclination of the orbit, 

 which we count from to 180, is only extended to 90, and if the angle made 

 by the orbit with the arc Q, B exceeds a right angle, the angle of the orbit with 

 the arc & A, which is its complement to 180, is regarded as the inclination of 

 the orbit ; in this case then it will be necessary to add that the motion is retrograde 

 (as if, in our fiigure, E Q, F should represent a part of the orbit), in order that it 

 may be distinguished from the other case where the motion is called direct. The 

 longitude in orbit is then usually so reckoned that in Q it may agree with the 

 longitude of this point in the ecliptic, but decrease in the direction & F; the initial 

 point, therefore, from which longitudes are counted contrary to the order of 

 motion in the direction Q, F, is just so far distant from 8, as the vernal equinox 

 from the same Q in the direction Q A. Wherefore, in this case the longitude of 

 the perihelion will be the longitude of the node diminished by the distance of 

 the perihelion from the node. In this way either form of expression is easily con 

 verted into the other, but we have preferred our own, for the reason that we 

 might do away with the distinction between the direct and retrograde motion, 



