108 A Calculation of the Orbit of the Comet. 



is only as .0004, and a centripetal force commensurate 

 with this, would change such an orbit from finite to in- 

 finite. Hence it is evident, that the periods of those 

 comets, which run into very eccentric orbits, cannot be 

 calculated, a priori^ from any observations of their mo- 

 tions made from the earth. Those mathematicians, who 

 have attempted to derive the elliptical orbits of comets 

 in this way, have foiled to produce results, in any degree 

 corresponding with phenomena. The periodical times 

 of the comets must, therefore, remain unknown, till a 

 sufficient time has elapsed for finding them by observa- 

 tions of their returns. It will readily be conceived, that 

 many ages must pass away, before such observations on 

 all the comets can be obtained. But supposing this to 

 have been accomplished, there would still remain an un- 

 certainty in respect to their future periods. One, or 

 more revolutions being completed in a certain time, will 

 by no means justify the inference, that this will be the 

 tase in other revolutions ; on the contrary, it would be 

 consistent with physical principles, if the period of the 

 same comet be at one time, t^vice or thrice, more or less, 

 than at another, and even that it be infinitely greater, or 

 never return. Modern astronomers have found, that 

 agreeably to the principles of gravity, the planets, by 

 their actions one on another, are considerably disturbed 

 in their motions about the sun, and that the form and 

 position of the orbits in which they move, are thereby 

 not a little affected. The same causes operating to the 

 increase or diminution of centripetal force, or of the ve- 

 locity of bodies moving in very eccentric orbits, will, as 

 it respects the figure and dimensions of their orbits, pro- 

 duce effects vastly great, compared with those of the 

 planets on one another ; and the periodical times will be 

 in proportion to those effects. If for example, the ratio 

 of the axes of an ellipsis he as 10 to 1, which by no 

 means is equal in eccentricity to the orbits of some 

 comets, and the velocity of the body moving in its cir- 

 cuiTiference, be increased by one five hundredth part of 

 that with which it moves, the body v/ould no longer 

 move in the ellipsis, but in a parabola, in which it could 

 ynake no return; and if the ratio of the axes of the ellip- 



