In order to convey an idea of the _numbers_ by which the degree of space-penetrating power is expressed, and the general grounds on which they rest, the following statements may be made. The depth to which the naked eye can penetrate into the spaces of the heavens, is considered as extending to the twelfth order of distances--in other words, it can perceive a star at a distance 12 times farther than those luminaries, such as Sirius, Arcturus or Capella, which, from their vivid light, we presume to be nearest to us. It has been stated above, that Herschel calculated his 10 feet telescope to have a space-penetrating power of 28.67, that is, it could enable us to descry a star 28 times farther distant than the naked eye can reach. His 20 feet Newtonian was considered as having a similar power of 61; his 25 feet, nearly 96, and his 40 feet instrument, a power of 191.69. If each of these numbers be multiplied by 12, the product will indicate how much farther these telescopes will penetrate into space than the nearest range of the fixed stars, such as those of the first magnitude. For instance, the penetrating power of the 40 feet reflector being 191.69, this number multiplied by 12, gives a product of 2,300, which shows, that were there a series of two thousand three hundred stars extended in a line beyond Sirius, Capella and similar stars--each star separated from the one beyond it, by a space equal to the distance of Sirius from the earth--they might be all seen through the 40 feet telescope. In short, the penetrating power of telescopes is a circumstance which requires to be particularly attended to in our observations of celestial phenomena, and in many cases, is of more importance than _magnifying_ power. It is the effect produced by illuminating power that renders telescopes, furnished with comparatively small magnifying powers, much more efficient in observing comets and certain nebulæ and clusters of stars, than when high powers are attempted. Every telescope may be so adjusted, as to produce different space-penetrating powers. If we wish to diminish such a power, we have only to contract the object-glass or speculum, by placing circular rims, or apertures of different degrees of breadth, across the mouth of the great tube of the instrument. But we cannot increase this illuminating power beyond a certain extent, which is limited by the diameter of the object-glass. When we wish illuminating power beyond this limit, we must be furnished with an object-glass or speculum of a larger size; and hence, the rapid advance in price of instruments which have large apertures, and consequently high illuminating powers. Mr. Tulley’s 3-1/2 feet achromatics of 2-3/4 inches aperture, sell at £26 5s. When the aperture is 3-1/4 inches, the price is £42. When 3-3/4 inches, £68 5s. The following table contains a statement of the ‘comparative lengths, apertures, illuminating powers, and prices, of Achromatic Refractors, and Gregorian Reflectors,’