. MiViAf^ ^« ^Fi'esJdel's I Theoi-if of Dijffi'tich'bh. r&l 



likewise passes through the aperture A B, which is to be 

 ccmsiderecl as a parallelogram of very small breadth. [Mr. 

 Airy does not explicitly state this fact, but the investigation 

 assumes it.] Take AH = H B, and let z be thei|wi|prt;< whose 

 41)umination is to be considered. /i .> iji; l . , . 



^bJijmizo-rfjJGsii^il T^Z^m, "(Mi^^fL; AB = ^5."^1 -V'^^' 



'U'''' i""'*"."" '■"'" "" " '"■'■' " ' '■ '■ '■■.''' .ML'f*' 



Considering each small element <^z pf A B as the origin of a 



>?idj oJ '.^djxjh-^ir !>'>,■ ■■f^.^^)i'jd/f''r\'< v/iui \ '.ii!r:fMr> 

 ft 81 in-i/ ZG^^*^ lx~'*'^ '~^™'''^ ^^«' T-^qpff -> ■ 

 "" "'/^'<^- 2% -i' • » ' ' '•'' '•■"••'fR rmitor. 



't^/— ^sin — (vt — c — zcos^) 'hlno'jil 



noij^.:^) :^' .(^^.11.^.-^.'! •-•-■';;^':- ■ ^ 2,,^ ;■ - ■ • x 



-33'+—. — -. I COS — {1)^— c— ocosS) — cos — (r'^— c + /;cos9) i 



„„. -c 2 TT cos 9 \ A ^ . -* A ^ V 



=={ — : — - sm — 7 6 cos fl . sm — (vi — c]. 



Now if this really representee! theTilfensfty at z, as Mr. 

 Airy would have us believe, it would follow, that after en- 

 tering the aperture the waves cease to be plane, and assume a 

 spherical form, having the middle point of the aperture for 

 their centre. Hence it is plain, that if the variation in velo- 

 city of the diffracted waves be an objection, Fresnel's theory 

 is as much open to it as mine*. I«,;ii»i'j 



The considerations with reference to the change in the con- 

 dition of the diffiacted waves which I have above endeavoured 

 to unfold, were suggested to me at a time when I looked up 

 to Fresnel and his theory with some portion of that respect 

 and reverence which certain teachers of the University of 

 Cambridge have so sedulously endeavoured to inculcate. 

 Neither doubting his experimental results, nor indeed his 



* In discussing the above example, I have not thought proper to advert 

 to the erronesus approximation contained in it, which 1 have elsewhere 

 sufficiently considered, and which is such as to render it totally valueless. 

 But I may observe, that not only is the formula for the intensity incorrectly 

 deduced from the premises laid down, but it is itself untrue. For, accord- 

 ing to that formula, we ought to have a series of maxima and minima in the 

 plane of the paper and nowhere else, whereas it is very certain that the 



frincipal maxima and minima would not occur in the plane of the paper, 

 t is obvious that the screen would be crossed by bands parallel to the 

 length of the aperture, and therefore in a plane perpendicular to the plane 

 of the paper, as Mr. Airy himself afterwards admits (see art. 78 of his trea- 

 tise). 



E2 



