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order. When sight is strained to a great distance the appearance of

the distant object is affected in a certain way: and the same thing

holds good here. So the reflection from the outer rainbow is weaker

because it takes place from a greater distance and less of it

reaches the sun, and so the colours seen are fainter. Their order is

reversed because more reflection reaches the sun from the smaller,

inner band. For that reflection is nearer to our sight which is

reflected from the band which is nearest to the primary rainbow. Now

the smallest band in the outer rainbow is that which is nearest, and

so it will be red; and the second and the third will follow the same

principle. Let B be the outer rainbow, A the inner one; let R stand

for the red colour, G for green, V for violet; yellow appears at the

point Y. Three rainbows or more are not found because even the

second is fainter, so that the third reflection can have no strength

whatever and cannot reach the sun at all. (See diagram.)



5



The rainbow can never be a circle nor a segment of a circle

greater than a semicircle. The consideration of the diagram will prove

this and the other properties of the rainbow. (See diagram.)

Let A be a hemisphere resting on the circle of the horizon, let

its centre be K and let H be another point appearing on the horizon.

Then, if the lines that fall in a cone from K have HK as their axis,

and, K and M being joined, the lines KM are reflected from the

hemisphere to H over the greater angle, the lines from K will fall

on the circumference of a circle. If the reflection takes place when

the luminous body is rising or setting the segment of the circle above

the earth which is cut off by the horizon will be a semi-circle; if

the luminous body is above the horizon it will always be less than a

semicircle, and it will be smallest when the luminous body culminates.

First let the luminous body be appearing on the horizon at the point

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