Variations of length in the tail of Halley's comet at its different apparitions– Similar phenomena exhibited by Donati's comet in 1858–Does the maximum development of the tail always coincide with the perihelion passage of the comet?

It is now desirable to consider a phenomenon of high importance as regards the physical constitution of comets, viz., the development and variation of their tails according to the position which the comet occupies in its orbit; that is to say, according to its greater or less distance from the sun.

It has been already seen that the tails of comets frequently are formed and developed during the period of the comet's visibility, and generally before the perihelion passage. ‘ It has been constantly observed, ’ says Pingré, ‘ that a comet advancing to its perihelion begins to assume a tail only on its near approach to the sun. The fine comet of 1680 had no tail on the 14th of November, thirty-four days before its perihelion passage. The real length of the tail increases day by day, and the head, or rather the coma surrounding the head, seems, on the contrary, to diminish. The tail attains its greatest length shortly after the comet has passed its perihelion; it then diminishes by degrees, but in such wise that at equal distances from the perihelion the tail is longer after the perihelion passage than before. It has been, moreover, observed that comets whose perihelion distance has much exceeded the mean distance of the sun from the earth have not developed tails, and that the tails of others, all else being the same, have been more magnificent in proportion as the perihelion distances have been less.’