52 
Transactions of the Royal Society of South Africa. 
(presumably) gave rise to it. For example, if we confine our attention to the 
band of second highest wave-length, we find that the fluorescent light has a 
wave-length which is 1'14 times the wave-length of the second line in the 
absorption-spectrum, and this figure holds for all the substances. For 
uranyl nitrate the fluorescent line is \ 535 and the absorption line \ 470 ; 
for basic uranyl acetate the respective figures are X 536 and X 471 ; for 
autunite the figures are A 554 and X 485 ; for uranyl bisulphate they are 
X 541 and x 475 ; and for the metaphosphates (acid and sodium) the ratios 
are 542/475 and 562/492. These ratios vary only between 1*139 and 1-142,. 
which is purely experimental error. 
Again, if we confine our attention to the first band in each substance, the 
constant ratio for all the substances is again met with, but this time it is 
1'150 : the particular cases are : uranium nitrate 560/486, uranium bisulphate 
565/492, autunite 575/500, uranyl acid metaphosphate 566/492, the variation 
in the ratio being from 1'149 to 1*151. 
For the third band there is again a constant ratio, the value of which is 
about 1*119, and for the fourth band, which is, however, not accurately 
observable, the value of the constant ratio is about 1*110. 
The fact that these four ratios should themselves be so close together and 
yet be undoubtedly different for each of the four corresponding lines is in 
itself very remarkable. At first sight one would suppose that the ratio 
represents the ratio of two adjacent natural numbers, e. g. 8/7, on the suppo- 
sition that the fluorescent light is the seventh harmonic of a fundamental of 
which the absorbed light is the eighth harmonic. As will be seen above, the 
fluorescence phenomenon is independent of the size of the molecule, the ratio 
being the same for all the substances. It may next be noted that the change 
in ratio from the fourth to the first line is about 1 part in 29, whereas the 
corresponding change in wave-length, e. g:S7b to 500 in autunite, is about 1 
part in 7, so that it appears that the value of the ratio varies according 
to the fourth root of the fluorescent wave-length. Thus 1*15 1*11 = 
Again, the values for the other 
It becomes thus possible to show that 
any fluorescent line can be directly calculated from an observation of the 
position of any other fluorescent line along with an observation of the 
corresponding absorption line. 
The equation = (fr) holds true for all the lines, in which A„ and 
F„ are corresponding wave-lengths in the absorption and in the fluorescent 
