OF ARTS AND SCIENCES. 401 



XVI. 

 OPTICAL NOTICES. 



By Wolcott Gibbs, M.D. 

 Presented, April 13, 1875. 



I. — ON A NEW OPTICAL CONSTANT. 



When a plate of glass with plane and parallel surfaces is placed in 

 the field of the spectroscope in such a manner that one half of the 

 bundle of rays incident uj^on the first surface of the prism passes 

 through the sflass, a series of interference bands will be seen in the 

 spectrum, known from their discoverer as Talbot's bands. When the 

 mean index of refraction of the glass plate is less than the mean index 

 of the prism, the plate must be so placed as to receive the rays which 

 fall upon the prism nearest its refracting edge ; in the opposite case, so 

 as to receive the rays which fall ujDon the prism nearest its base. A 

 plate of any transparent medium not doubly refracting may be made 

 to exhibit similar bands in the spectrum. Doubly refracting plates 

 produce two sets of bauds, corresponding respectively to the ordinary 

 and extraordinary rays. In any isotropic substance, the number of 

 bands, t, between any two lines in the si^ectrum the indices of which 

 are ti.^ and n^, may be found from the expression. 



= ^{("-^)l,-('^-^)^} 



in which d represents the thickness of the plate, and X.^ and 1^ the 

 wave lengths in air of the two rays corresponding to n^ and n^. 



The formula which I have given is familiar to all who have paid 

 attention to the beautiful and fertile theory of interferences. It forms 

 the starting-point of my investigation. 



If we take d as unity, the formula 



will give the number of dark bands for a plate having the unit of thick- 

 ness, which, if l.^ and ^ be expressed in fractions of a millimeter, will 

 VOL. X. (n. s. II.) 26 



