356 G. H. KNIBBS. 
With perfect adjustment in both cases this correction, viz. (59), 
therefore becomes exactly the same as (52). 
These last three formulee serve for the correction of observations 
of the type 3, see both the representations of Fig. 4. - 
20. The method of altazimuths.—The altazimuth method of 
solar observation has the advantage that each observation affords 
data by means of which the direction of the meridian can be 
deduced. Where the field of the telescope is sufficiently large, it 
is generally desirable to employ the double tangency method 
represented both in Fig. 3, and in observations of type 3 in 
Fig. 4; because this method yields accurate data both in respect ~ 
of the altitude and azimuth at the moment of observation. If 
the direction of motion be sensibly vertical, however, the single 
tangency method type 2, Fig. 4, is to be preferred, because in that 
case a small error of altitude cannot sensibly influence the result, 
and the tangent point will be more perfectly determined than is 
possible when the two tangencies have to be simultaneously 
observed. The criterion for determining the selection of either 
method may be derived by a process analogus to that indicated in 
§ 18 for the choice between observations of the type 1 and 2. 
The reduction of the results may be made by means of one oF 
other of the formulz (38) to (44) or (46) §§ 14, 15; so as to obtain 
the apparent direction and altitude of the sun’s centre at the 
moment of observation. This altitude when corrected for refrac- 
tion and parallax, the latitude of the point of observation, and the 
polar distance of the sun deduced from the recorded time at which 
the observation was made, are the data from which the azimuth 
or the hour angle of the sun’s centre may be computed. 
The influence of slight defects in the measurement of the 
positions of the diaphragm wires, of imperfect determinations of 
the collimation and level constants, and of rotational movements 
of the stand, may be minimised by taking a series of observations 
similar to those indicated in the preceding section, with similar 
reversions of the face of the vertical circle. Thus if the real 
