Rev. W. Scoresby on some remarkable Rainboios. 239 



the bow from the direct rays was less than a semicircle* And 

 all these circumstances^are found to be realised in the phenome- 

 non described. 



Moreover, in proof that this was the real origin of the verti- 

 cal spectra, I may mention the exact coincidence of the two 

 bows on the line of the horizon — the similarity and order of the 

 colours, and the peculiar position and curvature — with the whole 

 of which particulars a bow produced by a reflected sun, would, 

 under the circumstances, exactly correspond. 



This is clearly shewn by the figures and diagrams. Fig. 1, 

 already referred to, is the appearance of the various arcs, as 

 drawn and registered at the time when they were seen. Fig. % 

 is the form and appearance, which, on the same scale of curva- 

 ture, these arcs, according to theory, would assume, — «, 6, the 

 primary and secondary bows being drawn from a centre 74° be- 

 low the horizon (equal to the supposecl altitude of the sun), and 

 c, rf, the bows of reflection from a centre lh° above the horizon. 

 The resemblance, it is evident, is as near as could be desired. 

 Had the arcs been complete, the form would have been accord- 

 ing to the dotted lines. 



From hence we derive an explanation of the causci of the in- 

 verted rainbow, described by some authors; a phenomenon^ 

 however, of rare occurrence, and requiring, on this principle, a 

 variety of accommodating circumstances for its production. In 

 respect to this phenomenon, many philosophers have either 

 doubted its reality, or have considered it as an optical deception* 



* The centre of the common rainbow being in a straight line continued from 

 the sun, through the eye of the observer, as far as the base of the iris (when it ap- 

 pears to terminate at the horizon), that centre will evidently be just as much be- 

 low the horizon as the sun is above it. But the bow of reflection has its centre 

 just as far above the horizon. For the angles of incidence and reflection being 

 equal, the image of the sun, that gives rays to the bow of reflection, will be at an 

 angle, just as much below the horizon as the sun is above it, and consequently the 

 centre of its concentric bows will be exactly at the same altitude above the hori- 

 zon as the sun is. Hence, whatever portion the bow of reflection exceeds a semi- 

 circle, in consequence of its centre being above the horizon, the direct bpw will 

 want of a semicircle, by its centre being equally below the horizon- Consequent- 

 ly, the chord of each arc at the horizon will be equal ; and, therefore, if placed 

 together, their feet or bases will correspond. And hence, the direct and reflected / 

 bows, as regards the portion above the horizon, and terminated by it, would, if one 

 of them could be turned downward, exactly complete the circle. 



