REVERSED AND NON- REVERSED SPECTRA. 51 



TABLE 2. Continued 



Wallace gratings 14,050 lines to inch; computed value io 3 5e=i.oi cm. per fringe. 

 io 3 Se= .22 cm. (large fringes); io 3 5e=i.35 (different *') 

 24 1.32 



.25 1-30 



23 i-35 



.23 (small fringes) 1.33 



1.23 1-33 



1.32 

 1-34 



The reason for lack of accord is given in equations (5) and (6) and table 

 i. Any wedge effect of the glass plate is probably negligible. To show that 

 the irregularity of the above results is to be sought in the accidental varia- 

 tions of the angle of incidence i at both gratings, the rough experiments in 

 table 3 suffice. 



TABLE 3. 



i, negative (less than io),l 5eXio 3 =o.77 cm. 

 Ocular drawn in, .78 



focus changing. .74 



z==tq; ocular set for ] 5eXio 3 = 1.18 cm. 



principal focal plane. Na lines ! 



in field and coincident, 1.12 



i, positive (less than lo ),"! 5eXio 3 =i.69 cm. 



ocular drawn out, / 1.66 



Thus, as equation (6) implies, small variations of i produce relatively large 

 variations of 5e, and if i passes continuously through zero, from negative to 

 positive incidence, 5e increases continually and may easily be more than 

 doubled. If the phenomenon is in focal planes in front of the principal plane 

 (ocular in), de is small, and vice versa. Moreover, this enormous discrepancy 

 is quite as marked for thin glass (2 mm.) as for thick glass plates (8 mm). 

 Again, the rather stiff screw of the micrometer, which twisted the whole 

 apparatus slightly, was sufficient to introduce irregularity. Placing the tele- 

 scope close to the grating or far off made no difference. Hence the position of 

 the optical center of the objective does not affect the result. 



An additional result was obtained by placing a plate of glass between the 

 two gratings G and G' . The effect was an unexpected enlargement of fringes, 

 increasing with the thickness of the glass plate (0.6 cm. or more). The reason 

 for this is given by equation (3), in paragraph 2, for the number of fringes 

 n' between two colors X and X', 



- xv - 



where M= i-cos0, M' = i-cos0'. Since n' is a number, the glass plate can be 

 effective only in changing 6 and 6' . As both are diminished by refraction, the 

 cosines are increased and i-cos 6, i-cos 6' are both decreased. Hence n' is 

 decreased or the number of fringes is decreased, and their distance apart is 

 thus larger. 



It is obvious that when the sodium lines are not superposed the fringes 

 can not lie at infinity, but are found in a special focal plane, depending on 



