326 REPORT— 1881. 



of tlie measurements, since the wave-lengths of all lines are not known 

 with equal accuracy. 



If the wave-lengths are to be determined accurately to five figures, 

 it is desirable to use as reference lines those only which are found in 

 Angstrom's map, or in the B. A. map of oscillation-frequencies. 



The wave-length of the line to be measured may be calculated from 

 those of two known lines between which it falls by means of the formula : 



>. 2 ^3 — •'^1 



Aa — • 



71, — n. 



where n^ and n^ are the readings on the scale of the spectroscope of 

 the two known lines, As and Xj their wave-lengths, n^ the reading of the 

 line to be measured, and X2 its wave-length. It is desirable that the two 

 known lines should be as close to the one to be measured as possible ; 

 when sufiiciently close the above formula gives the same result as a simple 

 proportion. 



To give an idea of the accuracy of the results obtainable by use of the 

 above formula we may suppose the problem to be to determine the wave- 

 length of a certain strontium line from the wave-lengths of the following 

 three pairs of lines between which it lies. The actual wave-length of the 

 line in question, as given by Thalen (corrected), is 5533'64. The scale- 

 readings are Kirchhoffs :— 



Case 1. w, = 1274"2 A., = 5534-21 Here the formula and simple pro- 



7U = 1274'7 portion both give A.„ = 5533-60. 



wj = 1276-2 \, = 5531-77 



Case 2. w, = 1268-0 A, = 5542-10 The formula gives 553400, and a 



«., = 1274-7 simple proportion gives 5534-01. 



«3 = 1281-3 A3 = 5526-05 



Case 3. n, = 1242-6 X, = 5571-82 Here the formula gives 5533-82, 



n„ = 1274*7 and a simple proportion 



nl = 1306-7 \, = 5496-74 5534-22. 



But a far more convenient plan, and one quite equal to the above in 

 accuracy, is that of graphical interpolation, which has also the great 

 advantage of enabling us to detect at once any reading inconsistent with 

 the rest, so giving the best mean result of all the observations. 



A scale of wave-lengths is marked off along one edge of a sheet of 

 paper ruled into squares (inches and tenths or millimetres), and the edge 

 at right angles to this has a scale marked on it corresponding to the scale 

 of the instrument. The positions of as many lines as can be ascertained 

 with precision ai'e mapped on the paper, and a smooth curve is then 

 drawn through all these points, or through as many as possible, and 

 having the rest as near the curves as possible, and as many above as 

 below. In this way one observation is corrected by another, and the 

 curve is more likely to give correct results than an iri-egular line made up 

 of manj' straight portions which -would pass through all of the points. 

 The position of a line to be measured being found on the carve, will have 

 opposite to it the wave-length sought. Various devices may be employed to 

 facilitate the drawing of the curve. A smooth thin steel rule, which can 

 be bent by the hands into the curve required, will be found useful. It 

 requires, however, the co-operation of two persons — one to hold the rule 



