310 G. H. KNIBBS. 
indicates that they are to be preferred under certain circumstances. 
In order to attain to the ultimate degree of precision possible 
with this method, and to form a just estimate of its value, it is 
necessary to eliminate at least every source of systematic error, 
and to have regard to conditions of accuracy generally. These 
last, vary with changes of the sun’s declination and with its 
altitude, and are moreover different in different latitudes. Is is 
proposed therefore to develope rigorously the theory of the subject, 
because the rigorous theory will not be without utility in attempts 
to perfect the method. 
2. Instrumental Theory.—An observation for the determination 
of the meridian line, consists essentially of a measurement of the 
direction or azimuth, and of the altitude, or of its complement the 
zenith distance, of the celestial object selected for the purpose. 
The result is consequently affected both by instrumental and by 
astronomical conditions. The former involve an investigation of 
the particular instrument used, and the application of the general 
theory of corrections for the errors of instruments. The principles 
of the investigation of the first element have been elsewhere 
discussed,’ and are outside the scope of this paper. 
The only corrections to be applied to observations besides that 
for the index or constant error of the zero of the vertical circle, 
are those for the collimation and level errors.? If ¢ denote the 
angle between the sight line of the telescope and the plane at 
right angles to its rotation axis—considered as positive towards 
1 By Bessel, C. A. F. Peters, Hansen and others. The theory of the 
errors of instruments is admirably treated in Chauvenet’s Spherical and 
Practical Astronomy, Vol. 11., Philadelphia 1863. See also Clarke's 
Geodesy, London 1880. The Surveyor, Sydney, Vol. 1., Nos. 2, 4 10, 
1888-1889. On the rigorous examination and use of transit theodolites 
by G. H. Knibbs. Also the theory of the repetition of angular measures 
with theodolites—Journ. Royal Society, N.S.W., Vol. xx1v., pp. 87 - 106, 
1890, by the same author. 
2 Errors of eccentricity are eliminated by taking the mean of the read- 
ings of the microscopes, dividing the graduated circles into equal - 
Corrections to particular graduations would be also applied if an investi- 
gation had revealed their existence. 
