338 Prof. F. L. 0. Wadsworth on the Resolving Power of- 



tion that the maximum practical resolving power r , which 

 has heen assumed to be equal to l*5\/&, and which corre- 

 sponds to an angle of deviation of about 90° {0 = i = 45° to 50°) , 

 can be utilized. When for any reason this is not the case, 

 whether because of the inaccuracies of ruling, the faintness 

 of the higher orders of spectra, or the character of the mount- 

 ing, a correspondingly larger aperture must be made use of. 

 If, for example, we consider the maximum angle of deflexion 

 to be 60° (which from purely mechanical considerations is 

 about the largest possible angle that can be used in the 

 ordinary Rowland mounting), we have for r 



In order to attain the same resolving powers, R, as before, 

 the apertures must be increased about 75 per cent. If we 

 assume a maximum angle of 45°, which in practice is not 

 often exceeded in our present gratings, the apertures would 

 have to be increased by over 100 per cent., and we should 

 therefore need to attain the full limiting resolving power 



For lines A\ = '01 tenth-metre, an aperture b of at least 1 metre 

 „ AX=*02 „ „ b „ 50 cm. 



„ AX = *05 „ (solar work) „ b „ 25 cm. 



Fourth Case. — In order to determine the limit of resolution 

 or the practical purity P in this, the most important case, we 

 must first determine the diffraction-curve resulting from a 

 superposition of all the elements of the slit, each one of which 

 has a dispersion-pattern similar to those represented in full lines 

 in fig. 5. If, as before, these elements are equal in intensity, 

 i. e., if the illumination over the whole width of the slit is 

 uniform, the intensity-curve of the diffraction-image will be 



J +0-/2 

 ^i(?-7, ™, ")^=^//(>, 7,^"), • (28) 

 -<t/2 



where 



J- £<»-*>] 



as derived from (19) and (21). 



Since: the function fc is not known in Hnite terms, ^r n can- 

 not be directly found. We may, however, approximate very 



