It has long been observed that the power of distinguishing objects at great distances depends not only on the magnifying power applied to the telescope through which they are viewed, but also on the quantity of light emitted by the object, and collected and conveyed to the eye by means of the instrument. The superiority of telescopes with large apertures must hence appear obvious; and We have long witnessed the essential improvements made in this respect by Dr. Herschel, which have enabled him to extend his view into the firmament to distances, the bare mention of which is sufficient to astonish a mind unaccustomed to investigations of this nature. That it is principally the increased quantity of light that enables us to view luminous objects at great distances will appear manifest if we reflect that, since the density of light decreases in the ratio of the squares of the distances of the objects emitting the light, it follows that an object may be removed to distances at which its light will be so rarefied as to produce no longer any sensation upon the optic nerve: that if an optical instrument be used with an object-glass of a larger diameter than the pupil of the eye, the quantity of light collected by this means in the eye will be greater in proportion to the greater extent of the object-glass compared with that of the pupil: and that hence the most distant star that can be seen with the naked eye, if it be viewed through a tube with an object-glass of twice the diameter of the pupil, it will without any magnifying power be visible at a distance four times greater than that at which the naked eye ceased to perceive it. Dr. Herschel many years ago adverted to this circumstance, when in his paper on the Construction of the Heavens, he introduced what he then figuratively called his sounding line, to which he now substitutes the appellation of the power of penetrating into space. And in the present paper he fully investigates a comparative determination of the extent of that power in natural vision, and in telescopes of various sizes and constructions; all which he illustrates by a number of select and curious observations.
In the first part of the paper he establishes the difference between magnifying and penetrating powers; he rejects some vague terms in common acceptation, to which he substitutes algebraic symbols and such accurate definitions as enable him to proceed upon solid ground. And after distinguishing between self-luminous objects and those which shine by a reflected light, and likewise noticing those whose
