at the total solar Eclipse in 1882 355 



Join AA. 2 and produce it to a point B 3 , so that A 2 B 3 = AB. 



Join B Z B 3 ; then R 2 B 3 is the line which represents in section 

 the second mirror of the series. 



Through Z? 3 draw O 3 P 3 parallel to OP, and on it lay off 

 B 3 A, = ffA. 



Join AA 3 and produce it to a point B 4 , so that A 3 B^ = AB. 



Join B 3 B t ; then Z? 3 Z? 4 is the line which represents in section 

 the third mirror in the series ; and so on. 



It is evident from the properties of parallel lines that the 

 angle which the incident ray makes with the outer extremity 

 of any one of these lines is equal to the angle made with it 

 by the line connecting that point with the upper extremity 

 of the focal line. Therefore all the rays parallel to the axis 

 which strike the outer extremity of a line of section are 

 reflected upon A, the upper extremity of the focal line. In 

 the same way all the rays parallel to the axis which strike 

 the inner extremity of a line of section are reflected upon B, 

 the lower extremity of the focal line. Consequently all the 

 rays parallel to the axis which fall upon intermediate points 

 in the line of section are reflected upon the corresponding 

 points between A and B on the focal line. Therefore all the 

 rays parallel to the axis which strike the reflector are reflected 

 and condensed on the focal line AB. 



If the graphic construction is effected on the natural scale, 

 all the measurements, both linear and angular, can be taken 

 from it directly with sufficient exactness to enable the reflector 

 to be constructed. On the other hand, the geometrical con- 

 struction is so simple that there is no difficulty in arriving at 

 all the values by calculation. It will be apparent from the 

 diagram (Fig. 6) that most of the elements of each section 

 are contained in an isosceles triangle A n B n B n + l . In it the 

 angle A at the apex of one triangle is derived from the data 

 of the previous triangle. The angle of inclination to the axis 

 of the mirror is 



and the length of the base or width of the mirror is 



in = 2 A B cost. 



232 



