When a comet is first discovered with the telescope at a great distance from the Sun, it is difficult to predict whether it will become visible to the naked eye, or will remain a telescopic object, as it is only in approaching the Sun that these singular bodies acquire their full development. Thus, Donati's comet, whose tail became so conspicuous an object at its full appearance in 1858, remained two months after its discovery by the telescope without any indication of a tail. The comet of Halley, which before and after its return in 1759, remained five years inside of the orbit of Saturn, showed not the least trace of its presence during the greater part of this time. Nothing but calculation could then indicate the position in the sky of this invisible object, which was so prominent when it approached the Sun. Another curious phenomenon exhibited by comets, and first noticed by Valz, is that in approaching the Sun the nebulosity composing these bodies contracts, instead of dilating, as would be naturally supposed from the greater amount of solar heat which they must then receive. In receding from the Sun, on the contrary, they expand gradually. As comets approach the Sun, the tail and nucleus are developed, while the nebulosity originally constituting these comets contracts, as if its material had been partly consumed in this development. In a certain sense it may be said that the comets are partly created by the Sun; in more exact terms, the changes of form which they undergo are induced by the Sun's action upon them at different distances and under varying conditions. Moreover, they are rendered visible by its influence, without which they would pass unperceived in our sky. When a comet disappears from view, it is not because its apparent diameter is so much reduced by the distance that it vanishes, but rather on account of the diminution of its light, both that which it receives from the Sun, and its own light; these bodies being in some degree self-luminous, as will be shown below.