ALTAZIMUTH SOLAR OBSERVATIONS. 355 
~ In both types of observing, the declinational change to be 
allowed for, will depend upon the difference between the means of 
the times of observation. This of course is not rigorously exact, 
but owing to the fact that the declinational change is slow and 
nearly uniform, that is the change is sensibly the same in the 
afternoon and forenoon, the error can never be appreciable. 
The corrections to be applied to the mean altitude and mean 
azimuth by (12), (13) and (14)§ 5 are not required, because they 
affect the forenoon and afternoon observations by the same amount. 
Observations for equal altitude determinations of the meridian 
may also be made by the double tangency method, type 3 in Fig. 4. 
The programme would be generally similar to the preceding ones 
as regards normal and reversed positions and general manipula- 
tion. The following will sufficiently indicate it :— 
Type 3. 
Morning—1 Upper and leading limb; 2 Lower and following: 
Afternoon—3 Lower and leading limb ; 4 Upper and following. 
The means would be taken throughout as in the preceding 
instances, Rejecting negligibly small quantities, it is evident 
from (39) and (w) § 14, that the mean of the zenith distances, 
both in the fore and afternoon, require a correction of the form 
d(’ = —4(c’ ~ ¢”) 86 cosy cosecy + 45? cot z(cosec y — coty)?...(58) 
But xX and y, and 8@ will not have the same values in the after- 
noon, For brevity let us put 
G=cos x cosec y, and H=(cosec y — cot y)?...(y)' 
then the correction in zenith distance to be applied when the 
Whole correction it thrown into the afternoon observation, will be 
d¢” = —4(c" 4 ce”) (B29, — G,B,0,)+ $S? cot z(H, es H,)...(59) 
Obviously with properly adjusted diaphragm wires the final term 
would vanish, because the two values of H would be equal ; and x 
and y being complementary the value of G would become unity. 
SP apap a 
If y be nearly 90°, the y term will be very small. The expression 
may of course be written vers*y/sin?y 
