362 Prof. F. L. 0. Wadsworth oh the Effect of 



from which we can determine x and a necessary for resolu- 

 tion for any given values of Bb. We thus obtain 



For Bb = -5754 a=i-007* 



BA = 1'3862 <7 = l-04* u 



B/^2-1972 o- = l"lla 



BA = 2-7726 o- = l-18a 



B/> = 4'6052 o-=l-54a 



B6=7-825 o-=2-56a 



These relative Aalues of Bb and a are plotted (circles) in 

 fig. 2 (PL VIII.). As is there shown, the relation between 

 these quantities can be closely represented by the dotted 

 curve, the equation of which is 



o- = * {l + -02;53 (Bb) 2 \ (18) 



an expression which is simpler and more convenient for 

 computation than the more exact formula (16). 



An inspection of the curve in fig. 2 shows that for small 

 values of Bb, i. e. for small absorptions, the actual resolving- 

 power of the instrument a is very nearly the same as the 

 theoretical resolving-power « . For large values, however, 

 it is very considerably reduced ; nearly one-third for a value 

 of Bb equal to 4. 



To obtain a better idea of the physical conditions corre- 

 sponding to the different values of Bb considered above, it is 

 desirable to express these values in terms of the intensities at 

 the centre and edges of the transmitted wave-front. We 

 have from (5) and (6) 



Since the intensities at any two points are proportional to 



the square of the amplitudes of vibration, we have for the 



centre of the transmitted wave-front a?=0, and the edge 



h . 

 x= ^j the ratio 



i 2 



i* e+ ' 



and therefore for the different values of Bb already con- 

 sidered 



