REVERSED AND NON-REVERSED SPECTRA. 



59 



8 



39 



the diffracted ray b is constant and is 5=0+* in the first and second and 

 8 = 6 i in the third and fourth orders. Hence in succession 



sin (5 i) sin i = \/D sin (5 i) sin i = z\/D 



sin (5+*) +sin i = $\/D sin (5+j) +sin i = 4\/D 



from which equations the angle i may be computed. I did this with sufficient 

 accuracy graphically, and the values of i and 6 so found are given in table 12. 

 Since dB = di, apart from sign, it follows that the dispersing power is 



-d6/dK = n/D (cos i+ cos (5-*)) 



where n is the order of the spectrum and i changes sign in the third and fourth 

 orders. With the values of i given, the data for dd/d\ in the table were finally 

 computed. The dispersive power of the prism was computed as above and 

 is to be added to all the succeeding dispersive powers. Figure 39 shows the 

 relation between the dispersive pow- 

 ers and the path-difference x ^e 

 cos 8/2 computed from the observed 

 range of displacement e of the grat- 

 ing G. The largest values of x are 

 taken, as they are the most proba- 

 ble. The effect of dispersion here 

 breaks down in the third and fourth 

 orders, as already stated, probably 

 from incidental causes. For the 

 spectra themselves were still ade- 

 quately bright, but the fringes were 

 faint for some reason and I failed to make them stronger. The rate x/(dQ/d\] 

 is here about 120X10"* initially. This is larger than above, owing to the 

 differences of apparatus used, etc. 



26. Experiments with the concave grating. As there was an excellent 

 Rowland grating in the laboratory with a 6-foot radius and a grating space 

 .0=177X10-* cm., it seemed worth while to obtain the interferences with it. 

 I had hoped to doubly diffract the rays at the same grating, but there is not 

 light enough to make this method fruitful. Accordingly the device, figure 40, 

 promised the best results, where L is a convergent pencil of sunlight, 5 the 

 slit. The pencil L is carried above the grating G to the opaque mirror m, 

 whence it is reflected to the grating and diffracted into the component beams 

 a and a'. These are in turn reflected by the opaque mirrors M and N (on 

 micrometers) into the pencils b and b', nearly collinear. The latter are then 

 reflected by the silvered right-angled prism P to the common focus F, to be 

 observed with the lens T. The spectra are very bright and highly dispersed 

 and are easily made to overlap on their contiguous edges (parallel to a Fraun- 

 hofer line D, for instance) sufficiently to show the linear phenomenon of 

 reversed spectra. 







6 B 10 to 



