54 Messrs. C. and M. Barus on Interference of 



marked. In the two cases 



Be = X/2 cos i . (20') 



and 



Be = X/2 cos 0', (20'0 



so that nearly X/2 per fringe is easily attained. 



At i = 20° about, and in case of an air space, 0' is nearly 0°. 

 We suggested above that these fine fringes may be used as a 

 fine adjustment in connexion with the large fringes, on 

 which they are superimposed. In appearance these large 

 fluted fringes are exceedingly beautiful. The fine fringes 

 have the limiting sensitiveness of the coarse fringes, i.e. the 

 cases for « = 90° or 6' equal to maximum value. If in different 

 focal planes, both sets of fine fringes may be seen separately 

 for small e (air wedge). 



Equation (20) shows that for smaller grating spaces, D, and 

 consequently also in the second order of spectra, there must 

 he greater sensitiveness, cad. par. ; but as a rale we have 

 not found these fringes as sharp and useful as those in the 

 first order. 



The limiting sensitiveness per fringe, however, follows a 

 very curious rule. If in equation (20) we put { = 90°, 



2Be = \/ \'r(2-r) 



in the first order ; if r=\/D, and 



2he = \j2 s/r(l-r) 



in the second order. D is the grating space. Both equations 

 have a minimum, Be = \/2, at X/D=l in the first order and 

 \/D = 'o in the second order, beyond which it would be 

 disadvantageous to decrease the grating space. These mini- 

 mum conditions are as good as reached even when D corre- 

 sponds to 15,000 lines to the inch, as above, where roughly 

 10 6 &? = 38 cm. in the first order and 10 6 Se = 33 cm. in the 

 second order. 



To view the stationary fringes of the first order was not 

 practicable since they occurred for i = 10°, whereas the tele- 

 scopes were in contact at about 20°. In the second order of 

 spectra they may be approached more nearly, as they occur 

 when i is roughly 20°. If the distance e is made small 

 enough so that the three cases of equations (20), (20'), (20") 

 are visible, the appearance is very peculiar. The fringes of 

 equation (20) are very slow moving. They are intersected by 

 the small fringes of equation (20'), producing the fluted pattern 

 already discussed. Over all travel the rapidly moving fringes 



