It is therefore necessary, as we shall see presently, to take particular precautions in working with a reflecting telescope, which is, so to speak, materially more tender as regards external conditions than the refractor. As regards light-grasp, the power of rendering faint objects visible, there is more room for honest variety of opinion. It was often assumed in earlier days that a reflector was not much brighter than a refractor of half the aperture, _i.e._, of one quarter the working area. This might have been true in the case of an old speculum metal reflector in bad condition, but is certainly a libel on the silver-on-glass instrument, which Foucault on the other hand claimed to be, aperture for aperture, brighter than the refractor. Such a relation might in fact temporarily exist, but it is far from typical. The real relation depends merely on the light losses demonstrably occurring in the two types of telescopes. These are now quite well known. The losses in a refractor are those due to absorption of light in the two lenses, plus those due to the four free surfaces of these lenses. The former item in objectives of moderate size aggregates hardly more than 2 to 3 per cent. The latter, assuming the polish to be quite perfect, amount to 18 to 20 per cent of the incident light, for the glasses commonly used. The total light transmitted is therefore not over 80 per cent of the whole, more often somewhat under this figure. For example, a test by Steinheil of one of Fraunhofer’s refractors gave a transmission of 78 per cent, and other tests show similar results. The relation between the light transmitted by glass of various thickness is very simple. If unit thickness transmits m per cent of the incident light then n units in thickness will pass m^n per cent. Thus if one half inch passes .98, two inches will transmit .98^4, or .922. Evidently the bigger the objective the greater the absorptive loss. If the loss by reflection at a single surface leaves m per cent to be transmitted then n surfaces will transmit m^n. And m being usually about .95, the four surfaces of an objective let pass nearly .815, and the thicker objective as a whole transmits approximately 75 per cent. As to the reflector the whole relation hinges on the coefficient of reflection from a silvered surface, under the circumstances of the comparison. In the case of a reflecting telescope as a whole, there are commonly two reflections from silver and if the coefficient of reflection is m then the total light reflected is m². Now the reflectivity of a silver-on-glass film has been repeatedly measured. (Chant Ap. J. 21, 211) found values slightly in excess of 95 per cent, Rayleigh (Sci. Papers 2, 4) got 93.9, Zeiss (Landolt u. Bornstein, Tabellen) about 93.0 for light of average wave length.