346 G. H. KNIBBS. 
at the commencement and close of the observations. A similar 
procedure, in regard to the index error of the vertical circle, will 
reveal any change which may have taken place in the axis of the 
level attached to the alidade. 
(v) Uncertainty in the assumed value of the latitude may be 
eliminated by combining observations symmetrically situated with 
respect to the meridian line, that is at equal intervals of time 
before and after apparent noon. 
(vi) Even where it is intended to employ the method of equal 
altitudes, the observations should be so made as to permit of their 
reduction as altazimuth observations, because of the uncertainty 
of obtaining satisfactory observations on the other side of the 
meridian, 
(vii) The barometric and thermometric readings should never 
be neglected, even for the method of equal altitudes, since the 
fore and after noon differences are usually quite appreciable. A 
difference of pressure of +0:1 inch is equivalent to about - 1° : 
Fahr., the amount of the refraction being increased by either 
change by 3}5, or about 2” for an apparent altitude of 5°: 
(viii) The advantage of securing a small azimuthal component 
in the sun’s apparent motion by observing only at great zenith 
distances may be even more than abolished by the greater un- 
steadiness of the image near the horizon, and by the greater 
uncertainty in the absolute value of the refraction. In this con- 
nection it may be observed that the extraordinary variations of 
terrestrial refractions, and the systematic difference in the refrac- 
tions across the sea and land, are a sufficient indication of the 
great uncertainty in the celestial refraction of rays nearly tan- 
gential to the earth’s surface. Observations at a less altitude 
than say 10° should be made only under exceptional circumstances, 
especially when the azimuthal component of motion, compared 
with the vertical, is relatively large. 
19. The method of equal altitudes.—If the directions of the 
sun’s centre could be directly observed when at equal apparent 
