USEFUL TO THE MICROSCOPIST 1131 



Formula rein f ing to Prisms 



Lot i == the refracting angle of the prism, <p the angle of incidence on 

 the first surface, <' the angle of refraction at the first surface, -\|/ the angle 

 cf incidence in the prism at the second surface, and \// the angle of re- 

 fraction on emergence ; then the total deviation 



D = < + ^'-i; 0' + ^ = i ill,) 



When the ray passes through the prism symmetrically the deviation 

 is at a minimum : (p = \//, <p' = ty = -, and 



a 



I 



sin 



(liii) 



by which formula the refractive indices of media can be found, because 

 both i and D are capable of accurate measurement. 



Formulae relating to Conic Sections 

 Ellipse. Let A = major axis; a = minor axis. Then 

 Focus = A 



a 



Parabola. Let A = height ; a= - base. Then 



2i 



o 



Focus = ......... (Iv) 



4 A. 



Hyperbola. Let A = major axis ; a = minor axis. Then 



Focus = - ...... (lyi) 



2 



Works consulted: Coddington, Camb. 1830; Parkinson, Carnb.; 'Ency- 

 clopaedia Britannica' ; ' Journal E.M.S.' ; Heath, Camb. 1887, &c. It will be 

 seen that several of the formulae have been entirely reset, while some 

 appear now for the first time. 



