where A represents the surface illuminated by one of the lights only; B, the surface illuminated by the other light; C, the perfect shadow from which both lights are excluded. It will easily be understood that the lights about D and E, near the angle F, will fall with equal incidences when the double shadow is made to occupy the middle of the paper; and consequently, if one or both of the lights be removed directly towards or from the paper, as the appearances may require, until the two shadows at E and D have the same intensity, the quantities of light emitted by each will be as the squares of the distances from the paper. By some experiments made in this way, the degree of illumination of different lights may readily be ascertained to the tenth part of the whole. And, by experiments of this kind, many useful particulars may be shewn. For, since the cost and duration of candles, and the consumption of oil in lamps, are easily ascertainable, it may be shewn whether more or less light is obtained at the same expence during a given time, by burning a number of small candles instead of one or more of greater thickness. It will therefore be easy to compare the power of different kinds of lamps or candles, or gas lights, so as to determine the relative cost of each particular kind of the combustible substance employed for furnishing light:--for example, if a candle and a gas-burner supplying coal-gas, adjusted by a stop-cock, produce the same darkness of shadow, at the same distance from the wall, the strength or intensity of light is the same. An uniform degree of intensity of the gas-light may readily be produced, by opening or shutting the stop-cock, if more or less be required, and the candle is carefully snuffed to produce the most regular and greatest quantity of light. The size of the flame in experiments of this kind of course becomes unnecessary, and will vary very much with the quality of the coal gas. The bulk of the gas consumed, and the quantity of tallow used, by weighing the candle before and after the experiment, furnish the data for ascertaining the relative costs of tallow and gas-light, when compared with each other. From experiments made by Count RUMFORD, concerning the quantity of materials requisite for producing a light of a certain intensity for a given time: it was found that we must burn of wax 100, of tallow 101, of oil, in an Argand’s lamp, 129, of an ill-snuffed tallow candle 229 parts, by weight. And with regard to the quantity of carburetted hydrogen, or coal-gas, I have found that from 18 to 20 cubic feet (according to the purity of the gas) are required to give a light equal in duration and in illuminating powers to 1lb. of tallow candles, six to the pound, provided they were set up and burnt out one after another.[4] [4] 112lbs. of Newcastle coal, called Tanfield Moor, produce, upon an average, from 250 to 300 cubic feet of gas, fit for illumination.