Schaw. — On Bainbows. 451 



nearer or farther off, or according as atmospheric conditions 

 other than the distance, or thickness of the body of air between 

 the eye and the rain-cloud, allow more or less vivid im- 

 pressions of the rays of coloured light to affect our eyes. 

 The band of coloured light always appears to us as a curve — 

 apparently an arc of a circle ; and, although we sometimes 

 only see a small arc, sometimes a semicircle, under special 

 conditions even a complete or nearly a complete circle, and 

 although the diameter of this circle appears sometimes to be 

 greater than at other times, one peculiarity of the phenomenon 

 was noticed from very early times — viz., that the diameter of 

 the circle always subtended the same angle at the eye, and 

 this was about 82° for the middle of the coloured band (PI. 

 L., fig. 1). The colours of the primary bow are always in the 

 same order, red being outside and violet inside. This circle of 

 light is always so placed that its centre is in the production of 

 the line drawn from the sun through the observer's eye, or 

 where the shadow of his head would fall on the rain-cloud. 



It wall assist us to conceive more clearly the circumstances 

 if, as Professor Tyndall happily suggests, we imagine a cone, 

 the axis of which is this line from the sun through the head 

 and eye of the observer to the rain- cloud — the apex at the 

 eye, and the base on the rain-sheet. Such a cone, the surface 

 of which would at its base coincide with the ring or arc of red 

 light on the outer circumference of the rainbow, has the angle 

 at its vertex about 85° (twice 42i°). A similar cone having a 

 smaller angle at its vertex, of about 81° (twice 40^°), will at its 

 base coincide with the inner circumference of the rainbow of 

 violet light — the other prismatic colours being ranged between 

 them. The centre of the coloured band would coincide with 

 the base of a cone whose angle at the vertex is 82° (or twice 

 41°), as before observed. 



Now, neglecting for the moment the phenomenon of colour, 

 why is it that this luminous curved band is depicted on the 

 rain-sheet ? Why does it not reflect to us the sunlight indif- 

 ferently from all parts of its surface ? It is indeed so reflected 

 to us, or we should not see the rain-cloud and falling rain ; 

 but why this brilliant reflection on one special curved band ? 



Descartes was the first who, in 1637, solved this problem. 

 He drew the section of a globe of water, such as a raindrop, 

 though its centre, which, of course, is a circle, and by labori- 

 ous arithmetical processes he calculated the courses of 10,000 

 parallel rays of light falling on one side of this circle, being 

 refracted as they entered it, reflected on the opposite interior 

 surface, and refracted again as they emerged (PI. L., fig. 2); 

 and he found that, while most of these rays were on emergence 

 scattered in various directions, a very large cluster of rays 

 entering at the points S, S, emerged at the points e, e, parallel 



