Winterhalter — Personal Equation Machine. 119 



d, the time by which the machine's break occurs earlier or later 



than the transit ; 

 f, the time by which the machine's break precedes the transit for 



all threads, by reason of the adjustment of the platinum-point ; 

 rfc, prefixed according as the machine's break occurs e "ie c r r than the 



corresponding transit of the artificial star. 



The time elapsing between a transit and the corresponding 

 automatic break must be the same for both directions of the 

 motion of the ocular, which must be assured by the use of a 

 uniformly acting clock-work. A table is computed to show the 

 small influence of irregularities in the performance of the driv- 

 ing clock, provided only the ratio — is confined within narrow 



limits ; in this, t represents the amount in seconds by which the 

 automatic break precedes or follows the actual transit ; T, the 

 time, in seconds, occupied in the forward motion of the ocular, 

 T±d being the time for backward motion. 



The observations made by the author with this apparatus are 

 exhaustive and may be divided into two principal groups : the 

 first, consisting of three divisions, in each of which the rate of 

 motion of the star remained unchanged, while the telescope 

 was made to assume five typical positions ; the second, in which 

 the position of the telescope and rate of motion were uniformly 

 changed, so that the artificial star should have that speed of 

 transit corresponding to the observation of an actual star in 

 transit in that position of the telescope. 



In observing, the artificial star was allowed to run over the 

 whole field and the transits over 21 threads were noted, giving 

 21 values for the personal error, each depending on two transits, 

 for forward and backward motions of the ocular. • The means 

 which I have collated below are formed from those of several 

 series on a number (usually five) of days. The author uses in 

 his notation the expression, 



Actual transit — observed = personal equation. 



So that the result is the correction and has the sign with 

 which it is to be applied to an observation. 



First Group. 



4. 



+ S -519 

 + -477 

 + '323 

 + -410 



+ 1 '772 



In this table, the first column indicates the position of the 

 telescope, counting from the horizon, + above it, — below ; 



1. 



j 



1 





3. 



+ 90° 



— s 



•190 



-0 s 



•013 



+ 45 



— 



•178 



— 



■020 







— 



•207 



— 



•046 



-45 



—0 



•127 



+ 



•041 



— 90 



+ 



•140 



+ 



•497 



