284 Mr. A. A. Michelson on the Application of 



the surface of the plane parallel plate Gi*. Here it divides, 

 part being transmitted to the fixed plane mirror M, and part 

 reflected to the movable mirror M 2 . These mirrors return 

 the light to the silvered surface, where the first part is re- 

 flected and the second transmitted ; so that both pencils 

 coincide on entering the observing-telescopef . 



A little consideration will show that this arrangement is, 

 in all respects, equivalent to a film or plate of air between 

 two plane surfaces. The interference phenomena are, there- 

 fore, the same as for such an air-plate. 



The theory of these interference-bands has been given in 

 an article entitled " Interference Phenomena in a new form 

 of Refractometer," Philosophical Magazine for April 1882. 

 As is there shown, the projections of the bands are, in general, 

 conic sections, the position of maximum distinctness being 

 given by the formula 



P=r^r taut oos*0, 



tan 9 



in which t is the thickness of the equivalent air-plate, where 

 it is cut by the axis of the telescope, <f>, the inclination of the 

 two surfaces, 6 and i, the components of the angle of inci- 

 dence parallel and perpendicular respectively to the inter- 

 section of the surfaces, and P, the distance of the plane of 

 maximum distinctness from the surfaces. If be small the 

 variations of P with 6 may be neglected, and we have then 



P=7^-7 tan i 



tan</> 

 or with sufficient accuracy, 



P=H 

 9 

 From this it will be seen that the focal plane varies very 



* The light entering the telescope is a maximum when the thickness 

 of the silver film is such that the intensity of the transmitted light is 

 equal to that of the reflected light. The silvering has another important 

 advantage in diminishing the relative intensity of the light reflected from 

 the other surface. Indeed, for this purpose it is advisable to make the 

 film heavier ; even so thick that the reflected light is twice as bright as 

 the transmitted. This does not affect the ultimate ratio of intensities of 

 the interfering pencils — for what is lost by transmission on entering the 

 plate G x is made up by reflexion on leaving it, the effect being simply to 

 diminish somewhat the whole intensity. Another advantage of the 

 thicker film is that it can be made uniform with far less difficulty than 

 the thin film. It may be mentioned that with this form of instrument 

 the interference-fringes in white light present a purity and gorgeousness 

 of coloration that are surpassed only by the colours of the polariscope. 



t The second plane parallel plate Gf 2 is made of the same thickness as 

 the first, and is required to equalize the optical paths of the two pencils. 



