278 PROFESSOR MILLER, ON SPURIOUS RAINBOWS. 



secondary rainbows and of a large number of the spurious bows may 

 be seen either with the naked eye or through a telescope, forming a 

 series of vertical coloured bands, arranged in a horizontal line to the 

 right and left of the point opposite to that from which the light is 

 transmitted. A graduated circle placed horizontally with its center in 

 the axis of the cylindrical stream, carrying a small telescope parallel 

 to its plane, and having its object-end about one inch distant from the 

 axis of the circle, served to measure the angle between the line of light 

 and any one of the luminous bars. 



The diameter of the stream was determined in the following manner. 

 A lens of about 0.77 inch focal length was placed between the object- 

 glass of the telescope and the stream, at the distance of its focal length 

 from the axis of the latter, and the angle which the diameter of the 

 stream subtended when seen through the lens, measured. Next, a scale 

 of millimetres divided on glass, being placed in the focus of the lens, 

 the angle subtended by two lines distant one millimetre from each other 

 was measured. From these two angles the diameter of the stream may 

 be readily calculated. 



In the first observations the diameter of the stream was about 0.022 

 inch, and the light used was that of the Sun. The mixture of different 

 colours rendered it very difficult to fix upon the brightest parts of the 

 bars, especially of those corresponding to the principal bows. 



The mean of eight observations of the primary and two of the 

 secondary gave, 



Radius of the brightest part of the primary bow 41.32 



Radius of the brightest part of its first spurious bow 40.27 



Radius of the brightest part of the secondary bow 51.58 



Radius of the brightest part of its first spurious bow 53.57 



If 3 (sin 0) 2 = (2 + n) (2 - m), m sin 0' = sin 0, the radius of the geo- 

 metrical primary bow of the colour corresponding to the index m will be 

 40'— 20 ; and if 8(sin-v|,) 2 = (3 + /*) (3 — m), m sin ^' = sin \//, the radius 

 of the geometrical secondary bow of the colour corresponding to the 

 index n will be tt + 2\// — 6>//. 



