cuid Differential Double Diffraction. 847 



plates, a change of order SN at any point in the aperture may 

 be produced by the variations found from this equation. If 

 N is the same over the entire aperture, then for any increments 

 8d x , oY/ 2 , ... . the new order will be the same over the entire 

 aperture. Such a system would be obtained by a combination 

 of wedges or wedges and plates, giving white light of uniform 

 intensity over the entire field, as in instruments constructed 

 after the manner of the colour- compensators of Bravais, Biot, 

 Soleil, and others. 



Equation (5) gives the number of bands between two 

 points in the aperture whose distance is 81 when the total 

 path varies by 8d x + 8d 2 + . . . . uniformly, and the surfaces 

 of the plates are plane and inclined, as in the case of a 

 compound system of wedges, or of wedges and plane 



parallel plates. The number of achromatic bands -^ 



visible in a unit length of the field in any direction would 



determine the total variation in the paths — ~ — : - LJ -' 



per unit distance for the entire system. If the total variation 

 in path in any direction for a unit length is given, the 

 number of achromatic bands visible in a unit distance of the 

 aperture in this direction can be determined. An example of 

 such a compound system giving achromatic bands would be 

 an optical compensator similar in construction and effect to 

 one of the forms of Babinet's compensator used with mono- 

 chromatic light. Both in the compensators with interference- 

 bands and in those with uniform field, the calibration giving 

 the value of SN (the variation in order) due either to a 

 displacement of the plates or to a change of the point of 

 reference in the field equal to 81 is obtained from equation (5). 

 From equation (2a) we have for two crystals 



Sk- 8X' (6) 



as the condition of achromatism. This indicates that if in the 

 two crystals the orders either increase or decrease with the 

 frequency they are to be crossed or placed in subtractive 

 series. If, however, in one the orders increase and in the 

 other they decrease with the frequency, they are to be placed 

 parallel or in additive series. 



This immediately suggests an experimental method of 



8\ n 8\ 

 or 



SN t «N 2 



