S58 Mr. Mbbil oH FtesheVs liJory of Doiible Refhtctibri. 



ances. The motions will depend upon the extent to which we 

 suppose the forces are sensible. Suppose the only particles 

 w^hose forces on A are sensible, to be B, C, D, E, F, G (omit4 

 ting those in the same line, as their attractions are equal and 

 in opposite directions); and suppose them to be attractive, and 

 as the inverse square of the distance ; and the absolute force 

 of each = m. The whole force to pull A downwards is 



§ni)njf^^ + (^ + tt.^^^i)«^*3fi5|Ag H«(^i«etoi^*^ gnrlBluDlcD 

 nsrfw n, m{h-u + u,) ^ mjh + u-u') ^ ^^^^j^ 



" Expanding these fractions and neglecting powers of m — «, 

 and M— V aboyja l^e. first, tbefor^e tepdiog^o^i«i«w^ i^iStd 

 JO .*J09(dLre air. i^ajli d:^w oJ wa] Jobxs iib dJiw baJnieup 

 3f IT .Q^bij I oi^ *L 1^ j , fp (2,ttl + ^jowinf^ riaua 'Xo xliiow adj 

 -ns oJ loiab Jacui ; 2* ' ,(,q jjininjemdi srii "io noiaauDaib 

 Puttmg for «i, ^ ^ ^^ ^ ^^ .yjin«.l'iQqqo ladio 



U — -j-h + -V— 2 '§^<'I ,8 wdmavoVI ,!ooqi9viJ 



and for «?^- JOHoupa^no - ■ ' lo ovbonoa oj \?.m si 3l * 



-niad oi3(li lo xiilidiaaoq ^ „ d^uh^ '■ "M^ixm eaaJnoa I Jud ;noi^ 



-lol 'jn9i{(j<! B io lBdi--lfet^.,-^.A -ir.rT^ .■!=■» oidiy Ifsaiavensii lo ■i^\»irft b 

 7o» ,Bo 9bnj3 oJ ^golsne on fMLlia biftnbaftJaiJa n lo asBo adT .alqrasxa 

 iN$(fifi# ^' ,3Jfi3V3 J!b jA .noijorn 9/Ii In ,tnii- itIH -^dl ni ?\ aaiw sdj ai^riJ 

 »iom rioum 97Bri Jeur^^ljKuurtj. ?5i ; J \ rrtd^U '''' k^iSTenCTno afea/Ji 

 -io Idlnicq iKoin 9d'l--=-J«rialHl *w;-;j I XT~2» '^^H" bawoJead :>dguodJ 

 arij 31 ,^(io3dj '(loisbSferadl Id- (loJ^ig'^'' "^ "i^diiw LsJoonnoo sonBlamuD 



an eqaation of exactly the same form as^^h^t'ror TO^tfifeifi^is- 

 sion of sound. The solution therefore has the same form; 

 and therefore the transversal motion of particles supposed here 

 follows the same law, that is, it follows the law of undula- 

 tion." And moreover, if the above were correct, the velocity 

 of the luminous wave would be proportional to the square 

 root of the force of elasticity in a direction transverse to the 

 direction of the course of the wave. 



Whether the above illustration — for at best it would be no- 

 thing more — is due to Fresnel or Mr. Airy himself^ I am not 

 aware : but the whole is erroneous from beginning to end. 

 The mathematics not only fail to meet the case under con- 

 sideration, but there is a palpable mathematical error in the 

 process, which, even admitting the data, completely vitiates 

 the result. I need but advert to the circumstance, that in the 



