PROFESSOR MILLER, ON SPURIOUS RAINBOWS. 279 



According to Fraunhofer (Denkschriften der K. Akademie der 

 Wissenschaften zu Miinchen fur die Jahre 1814 und 1815. S. 214, 224.) 

 the brightest part of the solar spectrum lies between the lines D, E, at 

 a distance of between one-third and one-fourth of DE from D; and the 

 indices of refraction of water for the lines D, E, are 1.33358 and 1.33585 

 respectively. Therefore, for the brightest part of the solar spectrum the 

 index of refraction of water will be 1.33424. Hence the radii of the 

 geometrical primary and secondary bows will be 41°.53',9 and 51°.12',9 

 respectively. 



The theoretical distances of the brightest part of a bow and its first 

 spurious bow from the geometrical bow are as the numbers 1.08 and 

 3.47. In the primary bow the difference between the radius of the first 

 spurious bow and the radius of the geometrical bow is 1°.27'. Therefore, 

 according to theory, the distance of the primary from the geometrical 

 bow is 27', or the theoretical radius of the brightest part of the primary 

 is 41°.27'. The observed radius is 41°. 32'. Hence the observed place of 

 the primary is 5' nearer to the geometrical bow than its place as assigned 

 by theory. In like manner the theoretical radius of the brightest part 

 of the secondary bow is found to be 52°.6'. Hence the observed place 

 of the secondary is 8' nearer to the geometrical bow than its theoretical 

 place. 



In a second series of observations, the eyehole of the telescope was 

 covered with a red glass which transmitted light from the least refran- 

 gible end of the spectrum nearly up to the line D. The points selected 

 for observation were the dark bands and the brightest part of the prin- 

 cipal bow. The dark bars could be seen very distinctly, and were easily 

 bisected. Considerable difficulty was, however, still felt in fixing upon 

 the brightest part of a principal bow, on account of its breadth and the 

 want of a symmetrical distribution of light on both sides of the brightest 

 point. An inspection of the results will shew that the latter was sub- 

 ject to considerable uncertainty. All the observations were liable to be 

 affected by a sudden shifting of the bars, which was seen occasionally 

 to take place through a small space to the right or left. The angular 



GC2 



