For if their quantities of matter be equal, and times of burning the same, they will give equal quantities of light, by the experiments.
And if the times of burning be equal, the quantities of light will be directly as their weights of matter expended.
Therefore the light is universally in the compound ratio of the time of burning and weight of matter consumed.
If the law which Mr. Walker has endeavoured to prove, both by reason and experiment, be admitted, we have a standard with which we may compare the strength of any other light.
Let a small mould candle, when lighted, be so placed as neither to produce smoke nor require snuffing, and it will lose an ounce of its weight in three hours. Let this quantity of light produced under these circumstances, be represented by 1.00.
Then should this candle at any other time, lose more or less of its weight in three hours than an ounce, the quantity of light will be still known, because the quantity of light in a given time is directly as the weight of the candle consumed.[6]
[6] To investigate rules for this purpose, 1. Let M represent the mould candle, a its distance from the wall, on which the shadows were compared, x its quantity of matter consumed in a given time, (t) and Q the quantity of light emitted by M in the same time: 2. Let m represent any other candle, b its distance from the same wall, and y its quantity of matter consumed, in the time t.
Then as the intensities of light are directly as the squares of the distances of the two candles from the wall, we have as a2 : Q ∷:: b2 : b2 + Qa2 = the quantity of light, emitted by m in the time.
Then let us suppose that the quantities of light are directly as the quantities of matter consumed in the time t, and we have, As x : Q ∷:: y : y + Qx = the quantity of light emitted by m in that time, by hypothesis.
Now, when b2 + Qa2 (Theo. 1.) is = Y + QX (Theo. 2.) the quantities of light of M and m are directly as their quantities of matter consumed in any given time.