270 PROFESSOR L. BECKER ON 
On p. 247 Prof. Scurrner further gives the results of his experiments on artificial 
stars produced by means of a Zoellner photometer. He finds that if the time of 
exposure be increased 2°5 times, the faintest stars recorded on the plate are only 0'7 mg. 
fainter than before, therefore b = 174. 
Let a radiation of intensity i produce a degree of blackness m, and a radiation of — 
intensity 7’ a blackness m’, both in time ¢. Let ¢’ be the time required for 2 to produce 
m’, then by (2) and (4) ! 
tate? and ¥ =i (m) , therefore 
t F(m’) 
F(m) 1\? sabe : Cine > - 
(5) Him) = (-—) for the same exposure on radiations of intensities 7 and 7’. 
m 0 
I assume that the broadening of the lines into bands is due to the same physical 
cause, and that the ratio of the intensities of the radiations at any two corresponding 
points of two bands is a constant for these two bands; therefore by (5) 
(6) a = ae = constant, and he = f “ = constant, 
where « and m are the degrees of blackness at two points of a band, and y»’ and m/ those 
at corresponding points of a second band. By means of (6) I determine the constant 
a in f(m) from the observed corresponding degrees of blackness contained in Table VI. 
The result is a= 0°04, with which I have calculated the following table. 
“Tagen NOI 
Calculated corresponding degrees of blackness for a= 0-04. 
uy AB ee 9 i 5 3 1 
11 9-2 74 57 4:0 2°3 07 
For instance, if the maximum of a band of degree 13 is reduced to degree 5 in 
another band, blacknesses 7 and 5 at other points of the band become respectively 2°2 
and 1°5, while Table VI. gives 2°2 and 1°3. The quantities in this table differ from those 
in Table VI. for all degrees of blackness greater than 0°8 by less than 0:2 degrees, and the 
average error is 0'1, but the differences increase to 0°4 for the degrees lower than 0°8. 
The function (3) therefore represents the observations satisfactorily. For a=0°03 and 
0°05 the residuals are respectively 30 and 50 per cent. higher than for a=0-04, and for 
