450 Transactions. — Miscellaneous. 



Art. LXIII. — On Rainbows caused by Reflection in Still 

 Water, and on Elliptically -generated Rainbows. 



By Major-General Schaw, C.B., E.E. 



[Read before the Wellington Philosophical Society, 18th January, 1893.] 



Plates L. and LI. 



There are two ways in which, under special conditions, the 

 phenomenon of the rainbow may be produced by reflection 

 from the surface of still water : — 



1. By the reflection of the sun itself, which forms a virtual 

 image of the sun at the same angle of depression below the 

 horizontal as the angle of elevation of the sun above it. The 

 rays from this reflected image of the sun act on the raindrops 

 in the same way as the direct rays from the sun, and produce 

 an image in the observer's eye of another rainbow at a higher 

 altitude than the rainbow produced by the direct rays of the 

 sun. Such rainbows have been observed not unfrequently. 



2. Although I have not been able to trace any record of its 

 having been actually observed, yet undoubtedly under suitable 

 conditions the reflection of a rainbow might be seen on a 

 reflecting surface of still water — not the reflection of the rain- 

 bow seen by direct vision, but that of another rainbow which 

 would be visible on the rain-cloud to another eye in another 

 position. 



Before entering on any explanation of these special cases 

 it will be desirable to rehearse succinctly the causes and modes 

 of production of the ordinary rainbow. 



The essential conditions under which the rainbow-image 

 can be formed in our eyes are the following : — 



1. The sun shining clearly behind the back of the observer, 

 and low down — i.e., at an altitude of less than 40°. The 

 nearer the sun is to rising or setting the larger the visible bright 

 arc of prismatic colours. 



2. A sheet of falling raindrops in front of the observer, 

 with rain, cloud, or other dark background behind it. 



3. Moonlight under the above conditions will also produce 

 a rainbow, but owing to the feebleness of the light the colours 

 are rarely distinguishable, and it appears as a w r hite rainbow 7 . 

 "White rainbows also may be produced by sunlight if the rain- 

 drops be very fine, or if the sun be partly obscured by thin 

 clouds : in either case so many spectra are produced that they 

 overlap and neutralise one another. 



Under the conditions 1 and 2 a rainbow will be seen which 

 will be more or less brilliant as the sheet of falliug rain is 



