ABSORPTION PRODUCED BY FLUORESCENCE. 99 



be of the same colour in the determination of a ; but in the determination of ft and 

 ft /(I + ) we are comparing the light passing through a non-fluorescing body with 

 that emitted by it directly, and the result shows that there is a difference in tint 

 between the light given out by a x and that emanating from a\. 



Substituting the values of a and ft thus obtained in ft/(l + ), we obtain 0'54, 

 which is somewhat larger than that independently determined value 0'52. The 

 difference, though only a third of the probable error of a single observation, is 

 nevertheless three times the probable error from the mean. But this, Professor 

 SCHUSTER suggests, was probably due to slight variations in the symmetry of the 

 illumination. The value of /3/(l + a) determined independently is, however, quite 

 close enough, and may for all practical purposes be considered a very good verification 

 of the accuracy of the values obtained for a and ft. 



Taking the observed values of a, ft, and ft/(l -J- a) to be 0'450, 0787, and 0'520 

 respectively, we obtain by the method of least squares* the most probable values of 

 a and ft to be a = 0'455 and ft = 0'786, which give ft/(\ -f ) 0'54 as the most 

 probable value of this ratio. 



Hence it appears that the observed values of a and ft are more reliable than those 

 of /?/(!+ a). 



*Let 



! = 1 + a, X = j + x, 



ft = ft, Y = ft + y, 



ft _Y 



71 -1+-*' *'-X' 



where X and Y are the most probable values of 1 + a and ft. y^, ft, and 7 being the observed values 

 of 1 + <*, P, and pj(l + a) respectively. 

 Then 



and differentiating, we get 



'X 3 



Y - 7l X - X 2 (ft - Y) = 0. 



Substituting for X and Y their values ( t + a') and (ft + y) and neglecting the powers of x and y 

 higher than the first, we obtain 



(1) * ia! + ft2/:=0; 



(2) y [1 + !*] + ^ y - 71 E + .ft = 0. 



Substituting for v ft, 7j, 1'45, 0'787, and 0'52 respectively, we get 



x = 0-005 ; 

 2, =---0-01. 



Hence 



X = 1-455, Y = 0-786, 



or the most probable values of and ft are 



a. = 0-455 ; ft = 0-786. 



o 2 



