284 PROCEEDINGS OP THE AMElilCAN ACADEMY 



XXI. 



ON A METHOD OF DETERMINING THE INDEX ER- 

 ROR OF A MERIDIAN CIRCLE, AT ANY INSTANT, 

 DEPENDING UPON THE OBSERVED POLAR DIS- 

 TANCE OF POLARIS. 



By "Wii.liam A. Rogers. 



Presented May 9th, 1883. 



The three methods which are commonly employer! in the determina- 

 tion of the index error of a meridian circle are the following : — 



(a.) The reading of the circle for the nadir point determined by 

 the coincidence of the real and the reflected images of the central 

 thread of the transit-reticule formed by reflection from the surface of 

 mercury. This reading, which is a function of the latitude, will give 

 the index error under the name of the "zenith-point correction." 



(5.) The mean of the observed zenith distances of fundamental stars 

 situated symmetrically with respect to the zenith, when compared with 

 the corresponding tabular zenith distances, will yield the zenith-point 

 correction independent of the refraction of the stars observed, since, 



For stars south of the zenith, z= (cj) — 8) — Refraction, 

 and 



For stars north of the zenith, 2 = — (4> — S) -f- Refraction. 



(c.) A comparison of the observed with the tabular polar distances 

 of fundamental stars symmetrically distributed in declination from the 

 pole to a point as far south as the refraction can be securely deter- 

 mined, will give the index error under the form of a polar-point cor- 

 rection. The index error determined in this way, however, involves 

 the systematic errors in declination of the fundamental system through 

 which the observations are reduced. On the other hand, if the funda- 

 mental system is really free from this class of errors, this method fur- 

 nishes the data for an approximate determination of the periodic 

 errors of the circle. 



