Real dimensions of the nuclei and atmospheres of various comets–Uncertainty of these elements; variations of the nucleus of Lonali's comet–Observations of Hevelius upon the variations of the comet of 1652–Do cometary nebulosities diminish in size when their distance from the sun decreases?–Encke's comet considered in regard to this question at its apparitions in 1828 and 1838.

The observations that we have just recorded give an idea of the brightness of cometary light, and the intensity to which that brightness may attain ; but they afford no certain indication concerning the dimensions of cometary nuclei or atmospheres. Upon this point we are about to give the result of a few measurements ; but these measurements, it must be understood, are not so exact as those of the bodies of the solar system, the planets, the moon, and sun. The uncertainty we speak of does not arise from the difficulties experienced in the determination of the measures themselves, although they contribute to it, cometary nuclei being often as deficient in a clear and well-defined outline as the nebulosities; but what more especially prevents us from regarding the numbers we now give as constant, and therefore characteristic elements of the comets to which they belong, is the continual variation to which the different parts of the head are subject during the time of the comet's apparition.