60 



H. JACOBT, 



those of dp and d$, and equations (22) those of dj; and d n Y] . Equations (16) 

 will then make known the theoretical probable errors with which we deter- 



mine the quantities u -+-p <d Q A' and v-t-pd^ provided we know those of 



£'' and £' . But we already know from the solution of equations (17) the 



o,» 



probable errors of A B f' and A n C n ,. Those of £ and £ 0j$ are obtained 

 from these by the relations : 



t, , -n n ytr Prob. Error of A n C"«, « 



Prob. Error of X, # = . "■» _"»£ 



Prob. Error Of f ; = Prob. Error of A„ ^ 



The foregoing investigation has lead us to a method of studying the 

 motion of the pole which is undoubtedly subject to systematic error on ac- 

 count of the two assumptions we have been compelled to make. Possibly the 

 following considerations will set this matter in a clearer light. Let us sup- 



l 



pose that the pole actually moves in a curve which we will call Q. Then on 

 account of our assumption concerning the rotary component of the motion ? 

 we can always find another curve Q^ such that both curves will give the 

 same residuals for the observed positions of the stars on the plate. The que- 

 stion now is: will the curve of the form (22) resulting from our least square 

 adjustment be an approximation to the true curve of motion Q, or to the 

 false curve Q\ ? Evidently we shall approximate to that one of these curves 

 which most nearly resembles equations (22) in form. But there is an over- 

 whelming probability that the true curve Q will not differ very greatly from 

 some simple curve. If proper precautions have been taken to make the tele- 

 scope stand still, we might almost expect it to approximate more or less 

 closely to a straight line. In that case, our solution by the aid of equations 

 (22) would certainly lead to the true curve Q, and not to the false curve Q'. 

 So far, then, as we may accept probabilities, we may conclude that a system 

 of stellar coordinates obtained by the present method would possess a freedom 

 from both systematic and casual errors greater than the existing system 

 enjoys. Such a system would therefore be better suited for a determination 

 of the constants of stellar astronomy. 



3. Example of the Reduction of a Trail Plate. 



As an application of the methods developed in the foregoing, we shall 

 give here the details connected with the reduction of an actual trail plate. 

 The negative discussed was very kindly made by Prof. Donner, with the 

 photographic telescope of the Helsingfors Observatory, 1896 Nov. 10. It is a 



$H3.-MaT. CTp. 60. 20 



