526 Mr. A. E. Oxley on an Apparatus for the. 



If now A' is to be -=-, where n is an odd integer, then the 



real part of the expression on the R.H.S. will be zero. This 

 gives the following equation for cj> : 



(sin 4 <j> . cosh 4 7j — 6 sin 2 </> . cosh' 2 rj . cos 2 </) . sinh 2 rj + cos 4 </> . sinh 4 rj) x 

 (sin 2 </V . cosh 2 rf — cos 2 </>' . sinh 2 rf) ■+■ 8 . sin cf> . cosh rj . cos <j> . sinh rj . sin <j>' 

 cosh?;' .cos <j>' . sinh^' (cos 2 cj> . sinh 2 ?;— sin 2 <j> . cosh 2 w) = 0, . ..." • ( 



where , sin d> , , sin 6' 



cosh 77 = , cosJi >y = — — , 



and , 6' it 



This is an equation of the sixteenth degree in sin <f>, i. e. of 

 the eighth degree in x. An approximate solution has been 

 found by trial' and error, and taking fi D =1*5035, the value 

 of $ is approximately 73° 48'. From the relation 



we get f = 57°36 / . 



As a test of the accuracy of these values of </> and </>', the 

 equation (4') was used to find A' lor angles of incidence <f> 

 and <//. If we call the relative phase-differences 6—^6 > and 

 6' — o in accordance with the notation on p. 525, then from 

 the equation 



cos A= T 2 , ] 2\ ..■■•■• --r 



we find, <9 -B = 9r— 23° 40''21 



^-8' = 77-42°42 , -2J 

 which gives 



2(0-o) + (<9 / -S')=27r + S9°57'-4. , 



A still more accurate value of cf> was found as follows. 

 ■Taking -#=73° 49', the total phase-difference for the three 

 reflexions calculated as above is 



2 Jft- S). + {$' - 6') = 2tt + 90° 2j:Sr. " 



Taking #=73° 48', it may be shown that 



2(0-8)+ '(0'-8') "rB.27T4-.S9 57'-4. 



