DETERMINATION OF THE PATH OF RAYS. 



I. For the optical constants : 



cj = uH' + 1 



I = u't' + 1 



k = uu't' + u + u = u'g + u 



k = t' 



23 



for which the equation 



gl - lik = 1 



serves as a check. 



II. For the cardinal points: 



The large letters here denote the abscissa-values of the corre- 

 sponding points (reckoned from any point of emergence situate in 

 the axis), that is, N, N*, those of the first and second lens- vertices, 

 JP, /*, and those of the first and last of the four principal points 

 which enter into consideration in the combination of two systems, 

 and E E*, F F* those of the resulting principal and focal points. 



If, for example, in a given case - = 5 mm., and ~ = 4 mm., 



K K, 



then the first focal point F lies 5 mm. before the first lens- vertex, 

 and the second focal point F* 4 mm. behind the second. The 

 other equations are similarly interpreted. 



