TABLE OF STANDARD WAVE-LEXGTHS OF THE SPECTRAL LINES 559 



are photographed side by side. Both a 10,000 and a 20,000 concave 

 were used for this work. 



Table VI gives the collection of the equations relating to the visible 

 spectrum, the final results being given in Table VII. 



The proper method of treating these twenty-six equations would be 

 by the method of least squares. But it would be so long and tedious, 

 and so liable to mistake, that I have adopted the method of starting at 

 one point and going forward until all the equations are reached. Thus 

 (Table VII), starting with an assumed value of e, we can calculate p, n, 

 1, 1c, ;', o, t. 



Using the eight values thus found once more, from p we have g, Jc, Z; 

 from n we have h, t, g; with similar results for the others. Collecting, 

 we then have e, f, g, h, j, Tc, I, n, o, p, q, t. Using these once more, we 

 have values of all the standards. We could do this any number of 

 times, keeping the proper weights, but I thought this number was suffi- 

 cient. The second calculation is done in the same manner, starting from 

 o, however, and is given in Table VIII. 



The results of the two calculations are given in Table IX. Taking 

 the mean and adding the results of local micrometer measurements, we 

 obtain the column marked " Eelative Wave-Lengths." 



Reducing these values by 1 part in 200,000, we make them agree 

 with the absolute value of the standard as before agreed upon. Thus 

 the column of standards is obtained for use in the visible spectrum. 



For ordinary interpolation with the short and imperfect micrometers 

 generally used, and working with a flat grating and a spectrum not nor- 

 mal, the standards would be too far apart. But with such a long and 

 perfect micrometer as I use, and working with the normal spectrum of 

 a concave grating, they are entirely sufficient. However, I have filled 

 in the interval from 7030 to 7621 by some extra substandards at 7230. 



The micrometer for eye observations has a range of five inches, and 

 the machine for measuring photographs of more than twenty inches, 

 both with practically perfect screws made by my process. The eye ob- 

 servations are not an interpolation, in the ordinary sense, between the 

 standards, but the whole series is continuous, the micrometer observa- 

 tions overlapping so that they join together to any length desired. By 

 measuring from the D line in one spectrum to the D line in the next, 

 and including the overlapping spectra, no further standards would be 

 necessary, as all the lines of the spectrum would be determined at once, 

 knowing the wave-length of the D line. But I usually plotted the 

 difference of the standards from the micrometer determination, usually 



