«^^,^ 112 '^^ 



His autem adeo determinatis, expHcitain, ex qua re- 

 fracflones determinentur, quae in horizontis valeant viciniis, 

 ita eruemus formulam. Sit q deQnitn, quce daloe cuilibet 

 conveniat a vertice distantioe 6, refractio; q -\- t autem in- 

 definita, quae indefiuitae conveniat distantiae p 4- '. Atqu« 

 cum sit Sin (6 -^ y . q) =2 (l — z_) . Sin 6, et 



Sin (S -4- / — V? — vO = O — 's) ' ■^'« (6 -ir Vf 

 fiet, per differentiationem ita institutam, ut < et x solas pro 

 variabilibus habeantur 



(dt - vds) . Cos(& ^ t- vq - ysj zn - Zj dt . Cot (6 4- tj, 

 hoc est, si brevitatis causa suraamus ' 



p z=z 6 + t — vq — vx, 



fiet dp .Cospz^O^ ^) '^^ • Cot C^ -h 



et inde, per diflferentiationem ulterius continuatam, 

 d^p Cotp — dp"^ Sinp z=: — (t — zj df* . Sin (6-^0, 

 d'pCotp- sdpd^ p Sin p - dp'' Cotpx=a- (i-z) dt » . Cot (6 4- 1). 



i^pCo,p-4ip'"p Si.p-3d'p' ^■•"''U (,.,)„. «„(« + ,;, 



- ^dp*d^p Cosinp +• rfp* Sinp ) 



d^p Cosp — Sdpd^p Sin p 



- lod^pd^p Sinp - tsdpd-p^ ^°'^l = (,- 2)rf/» Cox (9 + /). 



- lodp'^ d*pCotp-i-iodpU^p Sinp ' 



-J- flfp * Cosin p 



