On the Formation of the Tails of Comets. 121 



positions, the law of variation of the whole attraction considered, 

 will not sensibly differ from that of the accelerating force of the 

 comet in its orbitual motion. The arm of lever will also remain 

 very nearly the same. Thus, proceeding as on page 117, we 

 shall have an approximate value of the velocity sought, viz. 

 9,153 miles. Multiplying by \/2, we find for the velocity in 

 the interval of three hours 12,943 miles (nearly). The average 

 intensity of the accelerating force of the comet in this interval 

 (=0.0S614 miles per second) is very nearly the same as that of 

 the force producing the rotation. In three hours this latter force, 

 acting in the varying direction of the radius-vector, will then 

 generate a velocity of 584 miles per second. Whence it appears 

 that it is twenty two times smaller than the force requisite to 

 produce the rotation. But it is to be observed that it would be 

 more correct in the present case to take the true interval answer- 

 ing to the anomaly 90°, as calculated on page 116 ; which is one 

 hour, instead of one hour and a half. If this be done, the sun's 

 force will be found to be fifty times too small. This result, it 

 will be recollected, answers to the supposition that the tail had a 

 length of 50,000,000 miles at the perihelion. If we suppose its 

 length to have been only 10,000,000 miles, the force of the sun 

 will then be only ten times too small ; and a length of 5,000,000 

 miles will make it six times too small. This deficiency may be 

 made to disappear by supposing the quantity of matter in the 

 head to be about six times greater, or six thousand times more 

 than in the tail. I conclude, therefore, that if the head and tail 

 of a comet revolve and rotate as one connected mass, the force 

 which generates the rotation is the attractive instead of the re- 

 pulsive power of the sun ; for any supposition that will reconcile 

 the observations upon the comet of 1843 with the action of a 

 repulsion, will more than suffice to make the attraction great 

 enough to produce the rotation. But it will be observed that a 

 discussion of the observations upon this comet, in connection 

 with the history of comets in general, has led to the adoption of 

 elements quite different from those which the sun's attraction, 

 considered as the cause of the rotation, requires. 



3. Whichever of the two forces that have now been under 

 consideration be conceived to be in action, there would seem to 

 be certain almost inevitable results flowing from their action 

 which are opposed to observation. The first that I would notice 



Vol. xlvi, No. 1.— Oct.-Dec. 1843. 16 



