The Total Solar Eclipse of 1900. 79 
required point, and that if a flat mirror be placed with its normal directed to N, 
and a telescope whose axis passes through the point S’ be directed upon it, the 
image formed in the focus will be so placed that the diameter ASB will be 
reflected into a horizontal position. 
The position of S’ can be very easily computed from the following formule :— 
From fig. 6 we have 
tan AM =cos € tan V. 
tan AS’ = — cot ¢ sec JV. 
Hence, we obtain 
5 
tan MS! = tan (AS’ — AM) = cos € cos 
sin V—sin 2 
and the azimuth of the point S’ is found by subtracting JS’ from the Sun’s 
azimuth (= A). 
This is the direction to which the beam ought to be reflected by the mirror. 
We have still to allow for the deviation due to the prism. If this be denoted 
by A, we have for the azimuth in which the axis of the telescope should be laid, 
A— MS' = A. 
We have also 
cos SAS’ = sin € sin V, 
and cos SiS’ = sin?AS’ cos SAS’ — cos’AS’ 
= sin ¢ (sin V—sin €) / (1 — sin Vsin Q), 
by the aid of which the angle of incidence ($ SS’) of the hght upon the mirror 
can be easily computed. 
If the observing station had been situated exactly on the line of central eclipse, 
then the position of 8’ would have been practically the same for the second and 
third contacts, neglecting the small shift due to the motion of the Sun during the 
short time for which the total phase lasted ; and in that case the same adjustment 
in azimuth would have been suitable for both phases. 
Our station was, however, situated at some little distance south of the central 
line, and in consequence the tangents at the points of second and third contact 
were no longer strictly parallel. The azimuth of the reflected beam, computed 
for the two cases by the above formule, were — 30° 7’ and — 12° 30’ respectively. 
The difference therefore amounted to only 17° 37’, and on considering the risk 
and difficulty of making a readjustment within the few seconds available for the 
purpose at mid-totality, we decided to be satisfied with a position of the instru- 
ment which would be a mean between the two positions given above. ‘The angie 
between the direction of the refracting edge of the prism and the tangent at the 
point of contact in the reflected image did not, however, even in the extreme 
cases (the first and last exposures), amount to as much as 9°. he effect of this is 
very small, and in no way detracts from the value of the photographs, while the 
