earliest times till 1760 which deserve mention here. His object was to arrange in order of magnitude those comets whose orbits have been computed, in much the same way that stars are classified in orders of brightness. In addition, he has attempted to derive the true length of the tail from the records of apparent length, and to examine to what extent the developement of tails depends upon the magnitude of comets and their perihelion distances. Holetschek endeavoured, and with some success, to apply mathematical formulæ to the question of the comparative brilliancy of different comets. His chief conclusions are that some 70 comets lend themselves to a fairly satisfactory determination of magnitude when reduced to the common standard of the Earth's distance from the Sun taken as Unity; and that to about 50 a numerical value can be assigned to the length of their tails. The magnitudes (taken in star magnitudes) range from −1 (the great Comet of 1744) to 912[1]; but the greater number fall between the magnitudes 4 and 6. So far as regards the tails it would not be safe to draw any more precise conclusion than, that the tail is greater the greater the magnitude, and the closer the approach to the Sun. When the magnitude of a comet (reckoned in star magnitudes) is about the 6th or less, then, as a rule, no tail is developed that can be seen with the naked eye; except under specially advantageous circumstances, as when the comet comes near the Earth. When the magnitude is as great as the 4th, almost all comets when near perihelion have tails visible without optical aid. But when the perihelion distance is large the tail developement is very slight.[2]
Plate II represents the comparative diameters of the heads of the well-known comets which are named, as they were measured on particular occasions, compared with the size of the Moon's orbit round the Earth. The woodcut is drawn to scale, but it must not be inferred that the dimensions indicated are in any sense permanent, or very trustworthy.
