196 PROCEEDINGS OF THE AMERICAN ACADEMY 



The wearing of the piv'ots of a transit instrument. Employing a per- 

 son to note time for the observer proper. 



Negligence in determining the zero-points ; too great trust in the Nau- 

 tical Almanac in comparison with immediate observation. 



The employment of two observers of very unequal skill upon the same 

 work. The employment of a careless or ignorant person to direct 

 good observers. 



In all these cases, some one cause of larger error than is unavoidable 

 is brought into the work, and manifests itself by larger discrepancies 

 than the theory of probabilities indicates. In some old series, several 

 such causes are visible : the effect of tliese is to produce much larger 

 errors. Now-a-days an observer may be called upon to use an old and 

 poor instrument upon distant service, and runs the risk of unusual dis- 

 crepancies thereby. 



So far with regard to the errors of single observations : I come now 

 to the smaller errors of series of observations. 



If a star's place is determined hy four observations of equal value, it 

 will be affected with but one-fourth the sum of all the individual errors ; 

 and its probable error, the so-called internal probable error, will be but 

 one-half that of each observation. But there will be new errors intro- 

 duced, tending to slightly increase this. The skill of the astronomer is 

 shown in making these as small as possible : first, by giving all the 

 parts of his instrument as many reversals as he can, without affecting 

 the stability, reversing his axis end for end, interchanging objective and 

 ocular ; or else by making his observations more strictly differential. 

 The former is best, when fewer objects are to be observed ; the latter, 

 where the mass of work done is more important than its strict inde- 

 pendence. 



Now I wish to notice that the errors of uniform star places will be 

 more exactly distributed according to the law of probabilities than 

 those of the single observations from which they are formed. For, in 

 the first case, the sources of error are more mmierous, and more 

 exactly uniform in their action ; while the resulting errors are more^ 

 infinitesimal ; provided, that is, due care is taken witli the elimination 

 of constant error. 



On the other hand, if one star be observed twice, and its neighbor, of 

 just the same importance, twenty times, it will be difficult to bring the 

 piobable errors of the results under any general rule. 



