25 



Fig. 1. 



llie space 0^ 35 r x e.^ sin. 2 0, In consequence of this the circle re- 

 volves round its vertical diameter, and the deviation of its telescope 

 from the meridian at an altitude a is as cos. a x sin. (2 a — a), a 

 being the altitude at which the deviation in azimuth vanishes. The 

 same reasoning applies to the transit instrument, and the errors aris- 

 ing from this cause may be easily ascertained and corrected. Besides 

 this, the centre of the circle is also transported horizontally through 

 a space bearing a constant ratio to the motion of the pivot ; and 

 this constitutes what I have called variable excentricity, different in 

 no respect as to its influence on the measurement of angles from the 

 permanent kind. 



To determine what this is, let DB be an ex- 

 centric circle, whose divisions are read by a mi- 

 croscope at B ; while the circle is turned through 

 the angle DC'B the arc DB passes before B, cor- 

 responding to DCB, less than the true angle 

 DC'B by C'BC. Now sin. B : sin. CC'B : : 

 CC : CB ; or putting CC -4- CB = e, DC'B 

 = 6, arc DB =: R and the angle B = z, we have ■ 



* = R -^ z, sin. z=e sin. (R -\. z) 



If e be so small that its powers above the first may be neglected, 

 the second equation becomes 



zz=e. sin. R. 



Now let there be applied several microsscopes distant from each 

 other by arcs = a. 



In fig. 2. Let Cm be the radius passing- 

 through the centre of rotation, and Cw the line 

 drawn from this through zero of the divisions ; 

 let B be the w"* microscope, A the first, then 

 A« is the arc corresponding to AC'n or 6, at A, 

 Bn' at B. Both extremities of these arcs are 

 effected by excentricity, therefore we must apply 



VOL. XV. E 



Fig. 2. 



