OF ARTS AND SCIENCES. 16T 



them, but by letting them pass for what they are worth. Of course, an 

 observation must now and then be rejected. Argelander's method was 

 to scrutinize doubtful cases with much care, adopting or rejecting them, 

 and giving the results of both methods. His expei'ience in his own 

 line was so great, that he rarely missed assigning the probable cause 

 for any large discrepancy, whether it arose from errors in reading off 

 mistakes in wires, miscounting time, or imperfect hearing by the 

 recorder, where one was employed, as in the Histoire Celeste ; and, if 

 he was at fault, he would suspend judgment on the case, and not^ it 

 down for further observation. In geographical work, where the 

 observer must finish each problem in a given time, and is compara- 

 tively thrown upon his own resources for little repairs to his instru- 

 ments, and the means of avoiding their occasional great defects, natural 

 or acquired, he must proceed with double caution in making his obser- 

 vations, checking them in every way, and making enough to get his re- 

 sult in spite of any abnormal discrepancies. This is the great advantage 

 of simplicity in the field-work, and reliance upon the star-catalogues 

 (which can always be improved afterwards), for what they will give. 



The reduction of latitude observations by the zenith telescope needs 

 but little remark. Tlfe process is a simple one : the usual form (see 

 United-States Coast Survey Report for 1866) unnecessarily compli- 

 cated. 



The half-sum of declinations of the two stars can be at once com- 

 puted ; first, the mean value for the beginning of the year, i (d^ -j- d.,), 

 and then the half-sum of apparent declinations for the date : thus from 



d', = 8, + Aa', + Bb', + Cc', +- Dd', + Tfi'a 

 it follows that 



a'l + "^2 

 2 





^-^1 + ^'2 

 2 



c'l + c'^ 

 2 



d'x + d'^ 



2 



/1 + /2 

 2 



That a'j, a'g, and the rest, are only given by their logarithms, is no 

 objection to the use of this formula. The computer has simply to employ 



