On Refraction. 393 



dy — V 



dr ps 



V* = a* — u^ ; rdv =3 xd.r — udtf 



dv xdx udu .r a- 



dr vdr vdr inpsi/ ' mpsy- 



j dv dx xdv , 



Q — - = — i- — du 



dr vipsy mpsy- 



ddi) _ V , XV V , 



■ — + — V ; or =1 only- 



a/» 7njrs-y^ mph^y^ vip'fy^ 



^ ddt; _ dv __ 2vdy 



dr' mp-fy'' ?np^s''y^ 



d^v 1 u , 2v- 



+ 



dr^ iirp^s^y-i mp'^shj- riip-^s-'y^ 



, d^v _ — 3dy 2udy 4 vdi; _ Gv^dy 



dr-' m^p^s'^y"^ mp's^y-^ mp'-^s-^y-^ mp^s'^y* 



d*v 3u 2tiv , Av Auv 



dr* m-p^s^y* vip^s^y^ m^p*s*y* jnp^s^y'-^ 



, 6v^ 7 V 6uv , 6v^ 

 + =r — + __ — _ 



+ 



mp^s^y^ rn-p*s*y* mp-^s^y^ mp-'s'y 



dr* \mpsy psy J7np-^s'y^ \7npsy 



24r3\ dy 



psy J mp-^s-^iy 



dr^ \ inps ps J \nrp*s*y* mp'-'s-^y^ .' 



+ (l^-lSs + ^.^\ _ll_. 

 \mpsy psy J inp*s*y* 



We shall find no difficulty in substituting for the coefficients 

 of these formulas the numerical values employed by Laplace, and 

 quoted by Mr. Ivory, that isp = .000293876 and 1 =.00125254 ; 



whence i = 3403, J- = 4.2624, _L = 18.168,_L = 

 p mp mY mp' 



14505, _L_ =61820, -L_ = 49360 700, and _L- = 

 OT»p3 mp^ m'p* 



210 395 000. 



dw 7"' d'u 7'^ 



The formula h s A // = vr + __.-—+ -t", . .tt, + ' • * 

 ' •' dr 2 dr 2..< 



will then become 



Vol. Xll 2D 



