Page:Philosophical Transactions of the Royal Society A - Volume 184.djvu/8

In order to obtain from these measures a scale of the darkening obtained by arithmetical progression in the intensity of light, we have only to recollect that each hole admits ${\sqrt[{3}]{2}}$ times the light that the next smaller admits. By easy calculation this scale can be obtained, and is shown in the diagram.

Fig. 3.

I have shown elsewhere that the curves of blackness on platinum paper can be represented by the formula, $\mathrm {A} ^{\prime }=\mathrm {A} \epsilon ^{-\mu x^{2}}$ where $\mathrm {A} ^{\prime }$ is the amount of reflected white light, and $\mathrm {A}$ the amount reflected from the white paper, $\mu$ being a coefficient, and $x$ any power of 2. In this case, for curve $\mathrm {I} .$, $\mu =.00302$, and for curve $\mathrm {II} .$, $\mu =.0103$.

XXIX.—Method of finding $\kappa$.

In the paper on Colour Photometry which appeared in the 'Phil. Trans.,' General Festing and myself proved that a turbid medium prepared by dropping a solution of mastic dissolved in alcohol into water, obeyed Lord Rayleigh's law, as given above. If, therefore, one part of a piece of platinum paper were exposed for a certain time to sunlight after passing through a cell containing pure water, and a simultaneous exposure made on another portion of the paper with the same light after passing through turbid water prepared as above, the measures of the blackened paper would give the value of $\mu ^{\prime }$, the photographic coefficient of absorption in the formula $\mathrm {I} ^{\prime }=\mathrm {I} \epsilon ^{-\mu _{1}\gamma }$, where $\gamma$ is the thickness of the turbid medium in any unit we please. Further, if the optical values of the light transmitted were compared when passing through the same media, $\mu$ could be found and the value of $\gamma$ be reduced to atmo-