540 Mr. E. J. Kendtorff on 



which gives us the original order. (This is given with the 

 wrong sign on p. 350 in the paper by Prof. Brace.) If "01 

 of a band can be measured this method may be used for 

 determining the order, without any error, up to w = 25. 



For comparison of different crystals for the purpose of 

 achromatizing different combinations of plates — for example, 

 pairs of crystals for producing achromatic retardation- plates 

 — adjoining interference-spectra from each plate may be used 

 and the thickness varied until the bands coincide in any part 

 of the spectrum which it is desired to achromatize. 



Thus if 



W = T>' ne '~ n °' and N"=D"^— ^ 

 \ \ 



are the orders of each plate, then 



S(N' + N") _ A BW_ _5N" 



8\ ~°' or S\~ S\ ' 



if there is to be achromatism for any part of the spectrum X. 

 The minus sign indicates that the plates are to be placed in 

 subtr active order. 



In general such a similar disposition of the bands does not 

 obtain, but there will always be certain relative orders which 

 give the best coincidence of these bands, either between two- 

 certain periods or throughout the entire visible spectrum. 



To determine the best relative orders, the cross-hair of the 

 observing telescope was adjusted so as to coincide with the 

 position midway between the Na lines, and the crystalline 

 w r edges were then shifted until the best coincidences on either 

 side of the Na lines were obtained. If now one of the wedges 

 is shifted until the ratio of the bands between any two wave- 

 lengths is n } and if m bands have passed the cross-hair, m 

 being taken positive or negative according to the direction 



7Y17X 



of displacement, the order will be N = -z for the Na lines. 



1— n 



If the adjoining interference-spectra have the same dif- 

 ferential dispersion and are produced by crystals, one in the 

 shape of a wedge and the other a plane plate, an exact co- 

 incidence is always possible throughout the entire visible 

 spectrum, and the order of the plate may be exactly deter- 

 mined even when this order is several thousands. 



The apparatus was arranged as shown diagrammatically in 

 fig. 1. Nj K" represent thfe Nicol prisms, which are crossed 

 at an angle of 45° to the principal axes of the crystalline 

 wedges B, B. A, A are smaller wedges of the same crystal 



