On the Formation of the Tails of Comets. 115 



rial difference between the brilliancy of the nucleus and that of 

 the nebulosity and of the parts of the tail nearest the head. Ac- 

 cording to the determinations of Mr. Caldecott, as Prof. Peirce 

 informs us, the diameter of the nucleus several days after the pe- 

 rihelion passage was 5,000 miles. (At this time the nucleus 

 shone with a stronger lustre than the tail, and generally, indeed, 

 after the 28th of February.) Judging, then, from the appearance 

 of the comet on Feb. 28th, and the relative size of the head and 

 tail, we should infer that there was less matter in the former 

 than in the latter. Mr. Walker also quotes the great astronomer, 

 Bessel, as saying " this comet seems to have expended the greater 

 part of its nucleus in building up its splendid tail." This state- 

 ment was made on the 28th of March. Whatever may have 

 been the actual length of the tail at the time of the perihelion 

 passage, it cannot be doubted that it received considerable acces- 

 sions of matter afterwards. It is to be observed, however, that 

 the increase in the length of tail seen, is in fact attributable to 

 the increased obliquity under which it was viewed in receding 

 from the earth. Taking all that has now been stated into ac- 

 count, it would seem to be a large allowance to regard the nu- 

 cleus and nebulosity as containing a thousand times more matter 

 than the tail. 



Now let w= the angular velocity of rotation, that is, the space 

 passed over in the unit of time (one second) by a point at the 

 unit of distance (one mile) ; v=velocity of translation of centre 

 of gravity; p— arm of lever of the resultant of all the forces of 

 rotation acting upon the various parts of the comet; and k 2 = 

 moment of inertia with respect to the centre of gravity of the 

 whole mass of the comet, divided by the mass ; then we have, 



k 2 w 

 from mechanics, v— , (1). We will first find the value of 



k 2 . Whatever may be the breadth of the tail, and whatever 

 its precise form, its moment of inertia will be diminished by sup- 

 posing all the particles to approach its axis. (I conceive, for 

 reasons already given, each section of the tail to contain the same 

 quantity of matter.) It is therefore allowable to imagine the 

 whole mass of the tail to be condensed upon the axis, so as to 

 form one heavy line of uniform density. The middle of this line 

 will be the centre of gravity of the tail. Let x— distance of any 

 point of this line from the centre of gravity ; I— half the length 



