[ 487 ] 
LIX. On the Law of the Wave-lengths corresponding to certain 
points in the Solar Spectrum. By Munco Ponton, F.R.S.E.* 
ape first attempt to find a law regulating the wave-lengths 
corresponding to definite points in the solar spectrum was 
made by Sir Isaac Newton, who chose for investigation the 
boundary lines of the seven colours, being the only determinate 
points then known. He adopted as the basis of his lawa séfies 
deduced from certain divisions of the musical chord. The same 
series, however, may be obtained in a more palpable manner 
from the following geometrical construction. 
Round the point O describe a circle, and inscribe the equila- 
teral triangle FAD. Draw the diameter A E bisecting the tri- 
angle, and perpendicular to this diameter draw another, X Y. 
Draw OB bisecting the are AY. Make AC equal to the side 
of a pentagon inscribed in the circle, and then divide the are 
A F into three equal portions by the points G and Z. 
Regarding the whole circle as divided into 360 degrees, add 
to this amount successively the number of degrees in the arcs 
AB, BC, CD, DE, EF, FG, and GA, these ares measuring re- 
spectively 45, 27, 48, 60, 60, 40, and 80 degrees, thus produ- 
cing the series 360, 405, 432, 480, 540, 600, 640, 720. Then 
divide this series by the last term, and we obtain the following: 
0'5, 0:5625, 0°6, 0°66', 0°75, 0°833/, 0°88!, and 1, a series from 
which the ratios may be deduced in reference to the longest 
wave as l. 
But it is more convenient so to alter the series as to make 
1 =the mean wave. For this purpose draw the diameter z M, 
* Communicated by the Author, having been read before the British 
Association at Aberdeen, September 1859. 
Phil, Mag. 8. 4, Vol. 19. No. 129, June 1860. 2G 
