138 



EOGEES AND McLEOD ON THE 



[5] 

 [0] 



C. — G" 



+ 



+ 



a — c" 



a-\-c 



[7] = 

 [8] = 



A 



C, — C" 

 C, - C 



A' -A' 

 + z z. « + c 



+ 



0, -C 

 A, — A" 



C" 



a-{-c 



Referring to equations (10), the values of a and c will be best determined from equa- 

 tions [4] and [3], if it can be assumed that there is no peculiar personal equation for stars 

 observed at the lower culmination, and if these observations have approximately the same 

 precision as corresponding observations at the upper culmination. For the remaining 

 equations, the order of ]3reference will be : 



[6] [5] 



[8] [7] 



[1] [2] 



Thus far we have considered the equations as referring to observations of single stars. 

 If, however, the time stars are divided into groups in which each star observed has nearly 

 the same declination, the mean of the several equations which compose a group may be 

 taken as representing the passage of a fictitious star which has for its declination a value 

 corresponding to the mean value of the azimuth. In this way considerable freedom from 

 accidental errors may be obtained for the known terms of the equations. 



If there are observations of several polar stars there will be a series of equations of the 

 forms 



[3], [4], [5], [6], [7], [8], 



and the means of the separate groups of equations may be regarded as mean equations for 

 the better determination of a and c. 



It is to be noted that in the formation of unknown terms of equations (10), the clock 

 is supposed to have a zero rate. If the hourly rate is appreciable, it must first be deter- 

 mined approximately and the observed times T must be reduced to an assumed common 

 instant for each star. The advantages of the arrangement indicated above may be stated 

 as follows : 



(a) "Without any previous knowledge of c, one can, with one or two substitutions of 

 assumed values of c in equations (10) determine the A'alue which will nearly satisfy all 

 of the equations, since under perfect instrumental conditions and with perfect observations 

 the A^alue of a should be the same from each eqtiation. 



{b) "While it cannot be expected that equations [1] and [2] of series (10) will yield very 

 precise values of a and c, and while the direct solution is impossible ; indirectly a very 

 precise check upon the true value of c may be had by a comparison of the computed value 

 of a for an assumed value of c with the corresponding values of a derived from the 

 remaining equations. 



(c) A check upon the assumed value of c will be had, first by a comparison of the 

 separate values of a, and secondly by a comparison of the valvies of a for stars at opposite 

 culminations. 



(d) A bad observation can be easily detected by an insi)ection of the separate values of 

 /IT for the time groups and of a for the polar group. 



