All rainbows are portions of circles, and the eye of the observer is always opposite to the centre of the circle. The quantity of the circle seen, depends on the height of the sun above the horizon at the time ; for, as the eye of the observer is always directly between the sun and the centre of the circle, of which the rainbow forms a part, if the sun be high above the horizon, a line drawn from the sun through the observer’s eye, and so forward, would pass below the visible horizon on the opposite side, and he would see a rainbow of only a small portion of a circle, as in the lowest figure of the scene ; where, it is evident, the centre of the circle is below the horizon. If the sun be in the horizon, then a line drawn, as before, through the eye of the observer, would exactly cut the opposite horizon, and he would see a rainbow exactly equal to a semicircle, as in the upper figure of the scene. The bow represented on the right of the picture, has its centre in a line with the eye of the observer and the sun ; which must always be the case : but, in this instance, the bow appears in a different situation to the others, simply because the sun, which produces it, is situated farther to the left. The centre of every rainbow, then, is to be found in the continuation of a line drawn through the eye of the observer and the centre of the sun ; and, therefore, the appearance of every rainbow requires the circumstance of falling rain in the direction of that line.
The phenomenon of the prismatic colours, as in the rainbow, is sometimes seen in a complete circle ; but this rarely occurs, and then generally in mountainous countries.
—Charles F. Blunt: The Beauty of the Heavens a Pictorial Display of the Astronomical Phenomena of the Universe (1840)