Sir W. Herschel remarks, that ‘objects are viewed in their greatest perfection, when, in penetrating space, the magnifying power is so low as only to be sufficient to show the object well--and when, in magnifying objects, by way of examining them minutely, the space-penetrating power is no higher than what will suffice for the purpose; for in the use of either power, the injudicious overcharge of the other will prove hurtful to vision.’ When illuminating power is in too high a degree, the eye is offended by the extreme brightness of the object. When it is in too low a degree, the eye is distressed by its endeavours to see what is beyond its reach; and therefore it is desirable, when we wish to give the eye all the assistance possible, to have the illuminating and the magnifying powers in due proportion. What this proportion is, depends, in a certain degree, upon the brightness of the object. In proportion to its brightness or luminosity, the magnifying power may, to a certain extent, be increased. Sir W. Herschel remarks, in reference to α Lyræ, ‘This star, I surmise, has light enough to bear being magnified, at least a hundred thousand times, with no more than six inches of aperture.’ However beautifully perfect any telescopes may appear, and however sharp their _defining_ power, their performance is limited by their illuminating powers--which are as the squares of the diameters of the apertures of the respective instruments. Thus, a telescope whose object-glass is 4 inches diameter will have four times the quantity of light, or illuminating power, possessed by a telescope whose aperture is only 2 inches, or in the proportion of 16 to 4,--the square of 4 being 16, and the square of 2 being 4. The nature of the _space-penetrating power_, to which we are adverting, and the distinction between it, and magnifying power, may be illustrated from a few examples taken from Sir W. Herschel’s observations.