On the Formation of the Tails of Comets. 117 



gives 0.00066 of a mile for the angular velocity at the perihelion, 

 little more than twice the average velocity. But as the tail prob- 

 ably fell back somewhat while the comet was passing around the 

 sun, we will take the angular velocity of rotation at the perihe- 

 lion no greater than 0.000291 of a mile, the average velocity 

 above given. It cannot have been much less than this, for if we 

 suppose it to have been one half less, then, while the motion of 

 revolution in the" interval 2t was 180°, that of rotation would 

 have been only 45°, and thus the tail would have been nearly 

 perpendicular to the radius vector when the comet was at its peri- 

 helion, and have fallen far within the orbit an hour and a half 

 afterwards, which is opposed to all analogies. The velocity re- 

 ally taken makes the deviation at the latter date as much as 90°. 

 Now, substituting the values of w and k 2 in equa. (1), we get 



242,076,201 

 v— , (5). It still remains to find the value of p. 



Supposing that the sun's repulsive force takes effect only upon 

 the tail, and is the same in the same angular space, which is the 

 case with all central emanations, so far as known \ also that the 

 deviation of the tail from the position of opposition to the sun is 

 45°, the resultant of the sun's actions will bisect the angle sub- 

 tended by the tail, and will act with an arm of lever equal to 

 188,110 miles. For a deviation of 90° the leverage will be 

 nearly twice as great. It will be seen farther on, that the sup- 

 position that the repulsive force keeps the tail continually oppo- 

 site to the sun, requires that this force should vary more rapidly 

 than central forces in general, which would make the arm of 

 lever still less. The value of p, just found, being substituted in 

 equation (5), we obtain, finally, v — 1287 miles. This is the ve- 

 locity of translation due to an instantaneous force of impulsion 

 acting with the above arm of lever, and of such intensity as to 

 give a velocity of rotation equal to the average velocity of revo- 

 lution during the period of three hours employed by the comet 

 in passing immediately around the sun. It would also be the 

 velocity due to the supposed repulsion of the sun acting up to 

 the time of the perihelion passage, if this had always retained 

 the same direction.* But as it did not, we have now to seek 



* The arm of lever would be very nearly the same in the different positions of 

 the comet, for the same length of tail and the same deviation. The change of 

 length of the tail may be neglected. 



