Prof. Encke on the Calculation of the Orbits of 'DoubleStars.il '9 



which it extends being hardly fifty years, during which time 

 even the subject has neither been continually nor closely pur- 

 sued, as it is at most fifteen years during which the attention 

 of several astronomers has been simultaneously directed to it. 

 As there are, however, a few systems of stars the observations 

 of which embrace nearly a full revolution, and as in the case of 

 others considerable portions of the curve in which they move 

 may be determined, it cannot be deemed an idle speculation 

 to apply to those distant systems the laws by which our solar 

 system is governed, in order to perceive how far these laws 

 may then be confirmed. 



The only course we can adopt in this respect is to apply 

 the Newtonian law of gravity, whose truth, within the limits of 

 our solar system, may be considered as rigorously demon- 

 strated, and whose extension beyond those limits possesses 

 the highest degree of probability. Agreeably to that law the 

 relative orbits of two celestial bodies, subject only to their 

 present mutual action on one another, will be a conic section, 

 or, in the case here under consideration, an ellipse. 



The point in which most probably such systems of stars 

 will differ from our solar system, viz. that the difference be- 

 tween the two mutually attracting masses will not in them be 

 so considerable as in the case of the sun and planets, has no in- 

 fluence on the orbit; and instead of considering the motions of 

 both bodies around their common centre of gravity, we may 

 with perfect rigour suppose the one to be at rest, as it were, in 

 the seat of the central force. If we denote the mass, and the 

 three coordinates, referred to an arbitrarily assumed system of 

 three rectangular axes, of the one star by m, #, ?/, z 9 those of 

 the other by m 1 , d,y' 9 z 1 , their distance by , and the time by 

 t, the differential equations of the motion of the one star, as 

 far as it is only acted upon by the attractive forces of the 

 other, will be, agreeably to the Newtonian law of gravity, 



