108 PROFESSOR AIRY ON THE CALCULATION OF 



rr,! /. , •! i- • •^ IT a' + b' a'x' 



1 he first consideration gives vis j— = - . — rrr ' x = -; — rt ; 



^ h\ \ a'b' af + b" 



"^aX ''^ «'6'X y ^ b'{a' + b')\' ^ a\ ^ a'b'X ' 



and the second consideration gives 7 = e; S = ^; whence 5 — 7 = ^-c. The 

 first set of equations, reduced, are 



6 = ^' + 



1 1 *,OaA ^./l 'aA 



a\/ - = tj'S/ J- — y' \/ jn\ whence (/3 — a) v - = — >?; and w= — V- 



The purport of these equations, in common language, may be stated 

 thus : 



If in Newton's method light pass through a rectangular hole whose 

 horizontal breadth is /3 — a, and through a slit whose horizontal breadth 

 is 5-7, at the distance a from the former, and fall finally on a screen 

 at the distance b from the slit: 



And if in Fresnel's method light pass through a rhomboidal hole, 

 with two vertical sides, at the distance a' from the Sun's image; and 

 fall on a screen or eyepiece at the distance V from the hole, so that 

 1 1__ 1 

 a'^ b'~ b' 



And if the length of the vertical sides of the rhomboid be \/- x 



til 



the horizontal breadth of the external hole in the first case (or /3 — a); 

 and the horizontal breadth of the rhomboid be equal to the horizontal 

 breadth of the slit in the first case (or 5 -7); and the tangent of the 



angle made by the sides of the rhomboid be \/ j, (the acute angle of 



the rhomboid being on the side where x is negative and y positive). 



