Mr. Moon on Fresnel's Theory of Double BefractiiM BBS- 

 o) ll98'^m d^K^ ' ' ' tf^Rl'ip ?^fiug¥R)J auk gi anoilBidiv 



-«oqoi. ^^'^'^J^ ^y •^; dxdz ,'xf9fIi9vo-?qoi 



,.i,Ioy,i..: _ ilR g^ + -^^ge/ + ^Iz --^ 8^«« >o'^ 



-9b i.oi^.ff - rf^^;^°^ ^ rfj/rf^*"-^ ^ rfr^.f ^r,,J,/ no" ,(£ .q 



" Now the force of restitution will be in the iAtrecfion m l^c? 

 displacement, if X Y Z be proportional to 8 a?, gj/, 8 «. Let 



ylSfi) Jtuit^ab g'djimB .iM-avig at •la'iaorf WriU 1 jfiuo33B araea 



-J<i:nJ jl3n«9i1 10 ?.92559a£)Wi^4tt>'xaxaflDJi^ oJ 93ii9i9l9-i(j fii ajgr^I 



/iun li rj/giBdw JadJ ^\ -M hi&ify^in Mni Uiw aigfaBsi ^ra gni 



tnfiBl|>i|A^^I ni gnifig 3i '\?.e9nJ3niJ«ih Inyiiiarnoag" ni Jnaw 



-iJiBq lo m^i^^ ^nBhl-dt^ luddd^ nolimqo^q orlT " 



'to anoiJDnij'K^I^ H3!riV/ ^^3 j^ '' ■'^'''*^'k'"' "« ^niJon a9b 

 -nc Jdgii Jiv-___ = A', -T—j- - B' -j— j- =s C'^jjwm ii9dJ 



.,{f f,...'>rJr,rf2«3/ dzdx dxdy ,_.,, ^^ ^^j 



and substituting in the former equations, they become >j9oi6j 



.jSjU.-vijnK. (A-s)8^ + C'8j/+B'82; = 0, -i^^^^aJ" '■ 

 fc^s'Vr^ rain. r;fg„ , m_ „>)g,, , Arg^_o -^J9cf •••l-Sf^s■^• 

 Iwvfudyi hiJ;. B'Sa- 4- A'gj/ + (C ^s)d%^ p>'' c^ f.^}, *> T^) ^ 



from which it is easy to prove, supposing ifhef'Ulidi'^ljrocess 

 correct, " that there are three directions at right angles to each 

 other, along which, if a particle be displaced, the force of 

 restitution acts in the same direction." 



But the fact is, the above process is entirely fallacious if it 

 is meant to apply to the case of the motion of a particle of 

 the aethereal medium by which light is produced. What is 

 meant by the mysterious principle, that " supposing the dis- 

 placement to be very small, the force of restitution may be 

 taken as proportional to it," I profess myself unable to com- 

 prehend ; but this I do understand, that when the co-ordinates 

 of the particle, whose motion is being considered, vary from 

 x,y.i z \.o X ■\- 8^, y -k-'ty, z -\- S.s, the co-ordinates of the other 

 particles of the medium will vary from x^y^ Sj, x^y,^ z^, &c. to 

 Xi + Sa^i, ?/i + 8?/i, 2:1 + 8 ^j, ^2 + ^^^ j/2 + ^i/25 ^2+ ^^2» &c. ; 

 and that therefore the above values (A.) tor the resolved parts 

 of the force on the particle whose motion is beinff considej^ed, 

 are entirely fallacious. '' "r.''' '"^1 - i -f •• 



^., The true valu^ ot X ni this case is. , r •, 1, 



d a^ dxdy " dxdz 



202 



