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 and the eye of the spectator, (Fig. 210.) the radius of any arc of which $A$ is the highest point, is equal to the sum of its altitude $AOh$, and that of the Sun $SOH$, or $hOS$. We have therefore only to take with a sextant, or other equivalent instrument, the greatest height of any arc above the horizon, and add that of the Sun, to obtain the radius of the arc.

183. It is sometimes required to determine, from observations on the rainbow, the ratios of refraction, for the different kinds of coloured light, between air and water.

Suppose that we have found the value of $θ$, or $2φ′−φ$ for an arc of the primary bow.

We saw that in this case

From this equation we must find $tan(2φ′−φ)$, and from that by a table $=$ and $A$: then dividing $tanφ′$ by $=$, we shall obtain the particular value of $t$ required.