53 
at the total solar Eclipse in 1882. 
To find the succeeding values of A let us take A 1 and A 2 . A x is 
evidently equal to CBB x and to CAA , ; therefore 
tan A x = 
B X C 
CB 
and these are known from the coordinates of the given point B x , 
therefore A x is known and the values of i x and m x follow as above. 
Through B 2 draw B 2 D X at right angles to A l B 1 and cutting it at D x . 
Then D X B 2 
and 
Then 
tan A 
sm ^ 1 , 
D X B X = m x cos i x . 
CB, + D X B, 
AC — (D X B X + A 2 B 2 ) 
CB X + m 1 sin i x 
AC-AB 
m 1 cos ^ 1 
whence A 2 is found. 
The values of i 2 and m 2 follow as before, and we have 
, A CB X + m, sin i x + m 2 sin i 2 
t&D A T) • ~ j 
Ab — AB — m x cos i x — m 2 cos i 2 
whence A s is found ; and by thus proceeding step by step the 
elements of all the mirrors in the series are easily obtained. 
The diagram (Fig. 6) was actually constructed on the following 
numerical data : — 
AB = 30 millimetres, BC = 20 millimetres, 
and CB X = 25 millimetres ; 
and the values of the different elements as calculated are collected 
in the following table. It is to be remembered that tan^L is 
00 
always the quotient - of the coordinates of the point A, and that 
y 
the values of y change sign at the origin. Thus for A x , 
for A 2 , 
for A 3 , 
y x = o 0 — 30 = 20 ; 
y 2 = 50 -11*25 -30 = 8-75; 
y 3 =50 -1125 -24 66 -30 = 
and so on. 
15*91 
In order to make the table complete the specifications of the 
metal bands for the mirrors are added. 
