402 PROCEEDINGS OP THE AMERICAN ACADEMY 



If, then, we put 



\ = the wave-length of the initial line J* 



and X, = the wave-length of a line whose reading upon the 

 scale is a;, 

 we shall have 



X, — \^=x p 



where p is a constant factor (the equivalent in wave-lengths of one 

 division of the scale), which must be obtained from the lines of known 

 wave-length (i. e., X^ given), by the relation 



Xa \ 



or, putting for convenience 



we have p 



AX 



X 



and A X = X p. 



For the determination of p I have used the wave-lengths of all 



o o 



lines given by Angstrom, except b^ and b^, and for these Angstrom 

 gives but a single value, 51G4.59, which appears to be about their mean 

 wave-length. The mean of fifteen values of p thus obtained is 



p = 0.85476 log p = 9.93184 



How nearly this value satisfies each of the lines by means of which 

 it was obtained, may be seen by comparing the last two columns in 

 the table upon page 403. 



Having found p, the wave-length, X^.^ of any unknown line is readily 

 determined, for we see 



or K = '\ + A X. 



This last quantity, X^ -f- A X, is found on page 403, and the corre- 



o 



spending "X" of Angstrom's lines are given in the next column. All 

 wave-lengths are expressed in " tenth-metres," a tenth-metre being 



■rrrrr of Si mctrc : for instance, the wave-length of i^ is 



0.00000051 61G2 metre. 



Taking for abscissas the readings, x, of the scale, and for ordinates 



o 



the wave-lengths of the corresponding lines as given by Angstrom, a 

 " curve of wave-lengths " was drawu through the points found. The 

 wave-lengths thus graphically deduced were found to agree closely 



