118 Winterhalter — Personal Equation Machine. 



ing breaks the current successively for each artificial transit. 

 It can be so set that the machine's break and the observer's 

 break shall differ by a constant amount, allowing them to 

 appear in succession on the chronograph sheet and be recorded 

 by one pen. 



The motor used was the clock-work of a Hipp chronograph. 

 On one end of the horizontal axis of the telescope the two 

 halves of a wheel are clamped. This wheel has a double row 

 of teeth, one row gearing into the chronograph-train used as 

 the motive power, the other into the connections for moving 

 the ocular. At the latter, the arrangement contemplates, by 

 means of the raising of a cam, the alternate engagement of a 

 pinion in upper and lower racks for motions forward and back- 

 ward. This change of direction can be made without the eye 

 leaving the eye-piece. By combining wheels of different num- 

 bers of teeth, a large number of different speeds can be given 

 to the clock-work. 



I pass over a number of interesting experiments, such as 

 those with a flat platinum-point for slow motions and a fine one 

 for fast motions, experiments with various insulating substances 

 for filling the grooves representing the wires, and will mention 

 that the application of the apparatus to the Cauchoix instru- 

 ment in question restricts the motion of the telescope through 

 116° of the 360° of a complete revolution, of which only about 

 26° are above the horizon. This facility of movement enables 

 the observer to take up any desired position on or off the 

 observing-couch. Designed for a new instrument, still more 

 ample motion might be secured. The motive power should 

 impart a regular motion and should be capable of regulation 

 without the insertion of various wheels. 



The author gives the results of numerous observations made 

 for the determination of his personal error, using the equation 



a) -=^. 



where x is the absolute personal error ; a, the difference taken 

 from the chronograph record between the machine's and the 

 observer's breaks for motion in one direction ; b, the same foi 

 motion in the opposite direction. All instrumental inaccura- 

 cies are eliminated, as may be seen from the two equations (a), 

 (b), from which (1) is derived : 



(a) a = x + c-hd+f, for forward motion ; 



(b) b = x—6=pd—f, for backward motion ; 



where, in seconds of time, 



c is the error introduced by a slight eccentric displacement of the 

 image produced by the motion of the ocular; 



