340 G. H, KNIBBS. 
the system ot wires to which reference has been made: z should 
preferably be the apparent zenith distance of C, not of I.’ 
The correction for the difference of altitude between I and the 
point o in Fig. 3, may be supposed to have been ascertained by 
previous investigation. Let it be denoted by i: the position of 
- the image of the sun’s centre will then be completely determined; 
and if 2’ denote the zenith distance given after the application of 
merely instrumental corrections, the apparent zenith distance 2, of 
C, is 
228 24 + ms X (41) 
To this must be applied the corrections for refraction, parallax, etc., 
for the result z is what would have been given had it been possible 
to have “bisected” a mark defining on its diametral plane, the 
sun’s centre. 
Let the distance of I from the vertical passing through J be 
denoted by j as before, see (v): then A’ being the corrected instru- 
mental record, the true direction A = the image of the sun’s centre 
will be 
A= A's (j+Y) cosec z (42)? 
z is the apparent zenith distance of the sun’s centre, as found by (41) 
15. Elliptical image of the sun tangent to perpendicular and 
horizontal diaphragm wires.—When the sun is so observed as to 
1 Strictly the almucantar should start on NC at a point vertically 
elow J, see . 8: or else a line should be drawn from C perpendicular 
to the almucantar, and the difference between its length and that of Cm 
taken as the aaa m. By using » instead of 2’ see (41) hereafter, 
the correction becomes very nearly exact: practically however, either 
may be employed, since the altitudes in the case considered are ad 
: site sare z is 45° the difference can amount only to 0°02. 
2 This formula is of course not strictly exact: j ought to be multiplied 
by the cobesaut a the zenith distance of J: the error however is quite 
papal And again the substitution of an expression of the form 
= kb, instead of the proper spherical formula tan o = k tan b, k being 
cosec # and b,j + Y, is also theoretically defective. The equivalent of 
the proper formula is 
b [1- 4b? (k? -1) ete.], 
but the error committed is easily seen to be quite insensible. 
