302 Sir W. Crookes. [Aug. 1, 



that the sum of the errors on all the lines is a minimum, and in no 

 individual case is very great. Then, with these three corrected 

 standards, the unknown lines may be calculated with confidence to 

 seven figures. 



With few exceptions my standards are the most recent published by 

 Eowland. He has given two sets of " Standard Wave-lengths," one in 

 'Astronomy and Astrophysics,' vol. 12, p. 321, published in 1893; 

 the other in the ' AstrophysicalJournal,' vol. 1, No. 1, January, 1895, to 

 vol. 5, No. 3, March, 1897, and vol. 6, No. 5, December, 1897. Any 

 systematic or accidental error found to occur in Rowland's figures will 

 require a corresponding correction of my own wave-lengths. Assuming 

 Rowland's wave-lengths to be correct, I can follow his seven-figure 

 standards with a probable error of 0'002 at the most refrangible 

 end, and one of O'Ol at the least refrangible end. The average 

 error being O'OOS. But on the assumption that all Rowland's 

 measurements are incorrect by a variable amount, as rendered probable 

 by the recent work of Fabry and Perot,* a correction will have to be 

 made which will affect the sixth figure.! 



For the reduction of the lines 4682-149 and 4825 -896, there being no 

 well-defined iron lines suitable for measurement, I have used some 

 strong zinc and cadmium lines, which also have been measured by 

 Rowland. 



The following is the method of calculation I now employ : 



HI A! 



71 2 Ag 

 % ^3 

 71 4 A 4 



n\ and % are scale positions on the measuring machine of standard 

 lines of known wave-lengths, \\ and A. 3 . 



n<2 is the scale position of the line whose wave-length is required (A 2 ). 



?i 4 is the scale position of an additional standard line whose wave- 

 length is known. It is used for obtaining the correction to 

 apply to the approximate wave-length of A 2 . 



E 2 and E 4 are the calculated errors obtained for A 2 and A 4 , which 

 have to be added to or subtracted from A, 2 or A. 4 to get them 

 accurate. 



For the tedious calculations involved in the reduction of the wave- 

 lengths I am indebted to my son, Mr. Bernard H. Crookes, M.Sc. 



* 'Comptes Rendus,' vol. 132, No. 21, May 28, 1901. 



f Measuring a ruled glass micrometer in my measuring machine I find the 

 average of ten scale readings can be relied on as not more than 0'00002 inch in 

 absolute error on an average, with occasional errors of double this amount, and of 

 course many errors of less, or zero. The effect of an error of this magnitude 

 represents an error of 0'0025 in the wave-length at one end of the spectrum, and 

 one of O'Oll at the other end. 



