210 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1931 



For the sodium lines the calculated number is only one nine- 

 hundredth as great, thus supporting Lockyer's old conclusion. 



For the thousands of fainter lines similar measures would be 

 very laborious and of doubtful value, since a number of other in- 

 fluences, solar and instrumental, produce a small widening of the 

 lines. A recent admirable investigation of the green magnesium 

 lines by Prof. H. H. Plaskett, of Harvard (and soon of Oxford), 

 shows that the prediction of dark solar lines is a much more com- 

 plicated aifair than is supposed in the simpler theory already 

 mentioned, and that exact calculation of the number of atoms active 

 in producing them is very difficult. Some other line of attack is 

 to be desired, and one is opened by the modern theory of spectra. 



Most spectroscopic terms are nmltiple, with from two to seven 

 components. Combinations between two such terms give rise not 

 to single lines but to groups of from 2 to 19 lines, called multiplets. 

 Some lines in such a group are much stronger than others, and their 

 relative intensities — that is, the relative number of atoms engaged 

 in their production — can be calculated from the quantum theory, 

 independently of the temperature, pressure, and other conditions. 



We may now have (for example) 2 lines in the same multiplet, 

 of which the stronger has the intensity 4 on Rowland's arbitrary 

 scale, and the weaker intensity 1, while the formulae indicate that 

 40 times as many atoms are at work on the first as on the other. 

 Another pair of lines with the same Rowland intensities may give 

 the theoretical ratio 25, another 50, and so on — for Rowland's esti- 

 mates are rather rough. But great numbers of lines are available, 

 and the average of all gives a good determination of the relative 

 number of atoms which produce lines of various intensities on Row- 

 land's scale. In this way Doctor Adams, Miss Moore, and the writer 

 have calibrated Rowland's scale. The same difference in his inten- 

 sities corresponds to a greater difference in the numbers of active 

 atoms for lines in the violet than in the red ; but this can be allowed 

 for. With the aid of the strong lines which have been individually 

 measured, the actual number of atoms which are at work in pro- 

 ducing a solar line of given intensity may be found. 



For a line of Rowland's intensity — just well visible with ordinary 

 high dispersion — there are about 10" atoms at work per square cen- 

 timeter, or enough to make a layer of gas, under standard conditions, 

 a little over a ten-millionth of an inch thick. The faintest lines of 

 all require about a twentieth as much. 



We may now find how many atoms of each element are engaged 

 in producing each one of its observable lines. To find the total 

 number of atoms of this element, in the solar atmosphere, we must 

 allow for those which give lines in the infra-red and ultra-violet, 

 which we can not observe. This can be done if we can get at all the 



