336 ON THE THEORY OF ENCKE'S COMET, 



It will not affect the question if we suppose the resistance 

 offered by this assumed setherial medium to act at any instant, 

 and at any place in the ellipse, as at C, when the direction of 

 the comet's motion is that of the tangent CT. The Comet is 

 under the influence of two forces, viz., the centrifugal force (as 

 it is commonly, though incorrectly, called), in direction CT, and 

 the sun's attraction in direction CS, towards the focus of the 

 ellipse. Consider any portion of time, however small, and let Cn 

 represent the space through which the comet would be pulled in 

 that time by the sun. Also let Cm represent the space through 

 which it would move in the same time in consequence of the 

 velocity it had at C. supposing it to have remained unchanged 

 in magnitude and direction. Then if we complete the parallelo- 

 gram Cm Pn, according to the Second Law of Motion, P will be 

 the place of the comet at the end of the supposed time. But 

 now suppose that a resistance is created by the setherial 

 medium in a direction contrary to that of the comet's motion 

 when at C, so that Co will represent the space described in the 

 same small time Cn as before, representing that due to the 

 sun's attraction then completing the parallelogram CoQn, as 

 before, Q will be the place of the comet a point evidently nearer 

 to the sun than P, and the ellipse will be deflected from CP to 

 CQ. Now this is true, however small the supposed interval of time 

 may be. Make it therefore infinitessim ally small, and suppose 

 the medium to be continually acting, then it is clear that the 

 boundary of the ellipse is being contracted continually, arid that 

 although -the orbit answers the elliptic condition at any parti- 

 cular time, yet the path of the Comet is, in reality, a spiral 

 terminating in the sun, into which body the comet must 

 eventually fall, unless some very uuforseen circumstances should 

 cause it to deviate from its present course. 



It must be remembered that Encke arrived at this theory 

 only after a most careful and elaborate calculation of the 

 planetary perturbations. These disturbances are duly allowed 

 for, so that any influence they might possess in changing the 

 comet's orbit, must be altogether excluded from the question. 



But before finally accepting Encke's solution, simple as it is, 

 we are bound to enquire whether there is any other that can be 

 offered, and if so, what are their respective merits. 



