with the Aid of a Grating, 423 



o£ the periphery are nearly the' same, or the fringes nearly 

 equidistant, the smaller wave-length will move faster than 

 the larger for a given displacement of mirror. It is at first 

 quite puzzling to observe the motion of ellipses as a whole 

 in a direction opposed to the motion of the more reddish 

 fringes when these are alone in the field. 



8. Discrepancy of the Table. — The data of Table I. are 

 computed supposing that the path difference zero corresponds 

 to the centre of ellipses. This assumption has been admitted 

 for discussion only and the inferences drawn are qualitatively 

 correct. Quantitatively, however, the displacement of about 

 AN = '003 cm. should move the centre of ellipses from the D 

 to the E line of the spectrum, whereas observations show 

 that a displacement of either opaque mirror of about 

 AN = *01 cm. is necessary for this purpose ; i. e. over three 

 times as much displacement as has been computed. The 

 equation cannot be incorrect ; hence the assumption that the 

 centre of ellipses corresponds to the path difference zero is 

 not vouched for and must be particularly examined. This 

 may be done to greater advantage in connexion with the 

 next section, where the conditions are throughout simpler, 

 but the data of the same order of value. 



Part III. — Direct Case : Reflexion Antecedent. 



9. Equations for this Case. — If reflexion at the opaque 

 mirrors takes place before diffraction at the grating, the 

 form of the equations and their mode of derivation is similar 

 to the case of paragraph 6, but the variables contained are 

 essentially different. In this case the deviation from the 

 normal ray is due not to diffraction but to the angle of: 

 incidence, and the equations are derived for homogeneous 

 light of wave-length X and index of refraccion u. 



in fig. 4, let y n and y m be the air-paths of the component 

 rays, the former first passing through the glass plate of 

 thickness e. Let the angle of incidence of the ray be I, so 

 that y m and y n are returned normally from the mirrors 

 M and N respectively, these being also at an angle I to the 

 plane of the grating. Let i be the angle of incidence of an 

 oblique ray, whose deviation from the normal is i — I = oc. 

 Let R, r, and J3 { be angles of refraction such that 



sin i = sin (I + «) = /* sin r ; sin I = /xsin R ; 

 sin (I — a) = JUL sin y5 x . 



