ALTAZIMUTH SOLAR OBSERVATIONS. 341 
be tangent to two wires one of which is nearly vertical and the 
other nearly horizontal—see A I C, position 3 Fig. 4 hereinafter— 
the solution is simplified. It has been shewn in the preceding 
section that when the defect from verticality and horizontality is 
small, the perpendicular distance from the image of the sun’s centre 
to the wires may always be regarded as equal to the corrected 
semidiameters, viz., S and S,, and so also the lines drawn from 
that point parallel to the two wires. and x having the same 
signification as in the preceding article, we shall have 
3 = §, cos x + S, cos §........ os (43) 
= §, sin £ + §, sin x......... 
m = 4 Y? cotz (44) 
For the position illustrated in Fig. 3 the upper sign is taken in X 
and Y when the inclination of the wires is in the same direction 
as shewn in the figure. 
16. Elliptical image of the sun tangent to one diaphragm wire.— 
The observation of the sun when tangent to one wire, the inter- 
section therewith of the other wire marking the point of tangency, 
gives only one codrdinate with precision. With telescopes of high 
power, it is nevertheless the only possible method. We shall later 
return to this point. The typical positions for observation are 
illustrated in Fig. 4 hereinafter, § 18. See 1 and 2 tangent at I, 
and also 2 at J , to the line bisecting the angle EJ F. 
For the case represented by 1 in Fig. 4, the tangential point I 
is clearly similar to P in Fig. 3. Let £’ denote the error of 
adjustment of the horizontal wire, so that £” + £ = 90°, its sine 
then will be very small, hence from (37) we may write 
X = §, cos [é"(1 + ml 
»---(45) 
¥ = 8, sin [£(1 + )}--- ( 
X and Y being as before, a the vertical and horizontal 
Corrections. Y cosec x, the azimuthal correction, is of very 
doubtful value, 
For the case marked 2 in Fig. 4, the tangential point I or J is- 
cd Q in Fig. 3. will denote the angle between A B, or 
