284 Profrssor Airy on a remarkable 



only light that comes to the eye is that reflected from the metal, 

 unmixed with the other light. Beyond the polarizing angle < + <' 



is >90", tan(i + /) is negative, and a- — ' l , is positive: the two 



displacements have the same sign, and therefore are added toge- 

 ther, and the central spot is therefore bright. 



To shew distinctly that the character of the rings as well as 

 that of the central spot ought to change at the same time, it will 

 be best to take the general expression. We have to add together 



tan (« — «') . 2 ir . . 



0.7 7 A sm— {vt-x) 



tan (« + «) X 



and a . A . sin — - (v t- x — 2 T cos «' - B). 



A 



The sum is 



q f^j'-^ +^cos^.greoB.' + l?} sin ^ {vt-x) 

 \tan (i + 1 ) X J X 



2tt 



— aA. sin — .2 7' cos i+B. cos — (vt—x). 



X A 



If this be put in the form 



Psin^(vt-x-Q). 



it is easily seen that 



p* = a * panj'-O + A cos *Z .2Tcos i' + b\* + a' A' . shr ~ .2Tcosi' + B 

 Itan (« + 1 ) X J X 



„ ftan* (« — i') ., „ , 2tt —7= ; — s tan («-«')) 



= fl ! p-r^ { +A , + 2A .cos — .2T cos i+B.- — )—- /) . 



\tan 2 (< + «') X tan (t + < )J 



Now P i represents the intensity of the light in the mixture : 

 consequently the last formula will represent that intensity, or 

 the intensity of light that comes to the eye. It is easily seen 



