and Energy Distribution oj Diffraction Gratings. 543 



Plate for No. 1 , PI. JgT) There is almost no central image 



with the grating No 7, so we are justified in assuming that 



there remains none o£ the original surface, i. e. the grooves 



c 

 join on, point to point. This establishes the ratio j , and c may 



be computed, as b is known,' being the value of one space of 

 the grating. Since the true value of the angle A is not 

 necessarily 19° the grating was mounted in the fixed colli- 

 mator apparatus with the direct-vision spectroscope, and 

 using this method the angle was found to be about 23°. As 

 confirming this result, reference to the curve for wave-length 

 4*65 /a for this grating will show that when the second order 

 is located about 23° out from the central image, the orders 

 on either side of this order are most symmetrically arranged. 

 Neither of the two observations are sufficient alone, but 

 agreeing as they do, we are justified in taking the angle 

 as 23° approximately. All the elements of the groove are 

 now known and are given in fig. 4 b. 



The series of observations for both the Wood grating No. 7 

 and the Brackett grating No. 10 show conclusively that the 

 assumption by Messrs. Wood and Trowbridge that the energy 

 diffracted appears in the direction in which it would naturally 

 be reflected is completely justified. There remains, however, 

 the consideration of the weak orders, which are particularly 

 noticeable in the curves for the Wood grating No. 7. 



§6. 



It is well known that with an ordinary grating in which 

 the element is composed of equal reflecting and non-reflecting 

 parts, the even orders are missing, due to the fact that in 

 the position where these orders would naturally occur, the 

 retardation over the reflecting portion of the element is such 

 that the effect from each element destroys itself, according 

 to the elementary theory of diffraction from a slit. The 

 curves for the Wood grating No. 7 show quite a number of 

 instances of weak orders, and we now propose to consider 

 this phase of the subject. 



The form of the groove for this grating was established 

 in § 5 (fig. ib), It will be seen from this that the narrow, 

 steep plane of the groove is not in such a position that it 

 reflects very much energy for the angular settings at which 

 the' grating is used. Further, it is not placed so that it 

 cuts off any energy reflected or diffracted from the main 

 plane of the groove. An expression very nearly rigorous for 

 the retardation over the whole element may be found by 



