460 



MEMOIRS OF THE AMERICAN ACADEMY. x 



The 



(' 



Geodet 



. The Coast Survey Transit-Instrument at Brest stood 413.5 feet 

 c station on the St. Louis Tower. Reducing the longitudes above 

 giv«n to the Dome of the Observatory and the St. Louis Tower, we have: 



\>\ff< rence of longitude between Duxbury and Cambridge l m 50 8 .205 ± .022 



DM n-nce of longitude between Brest and Duxbury 4 h 24 m 43 8 .277 ± .047 



Difference <»f longitude between Brest and Cambridge 4 h 26 m 33 8 .482 ± .052 



In the determination of differences of longitude by telegraphic signals, a correc- 

 tion must be upplied on account of the Personal Equation of the observers in noting 

 transits of stars ; and when the signals are sent by the cable-lines, another correction 

 is required on account o£ the Personal Equation in observing and recording signals. 



1. What is called the Personal Equation in noting transits is made up of many 

 elements, some ot which are personal and others instrumental. When a star has 

 reached a wire of the transit-instrument, the phenomenon does not impress itself 



upon the eye of the obser 



ily ; then the effect upon the eye must 



be communicated to the brain ; then the will must be aroused so as to send its 

 order to the finger; and this order when sent consumes a measurable fraction of 

 time in travelling through the nerve ; there is also another delay in the execution 

 of this order by the muscles and the finger. After the finger touches the key, 

 that must move, contact must be made or broken, the disturbance must go through 

 the local circuit to the electro-magnet which works the pen of the chronograph, 

 and the magnet must act upon its armature. All these various processes require 



fraction of time, however small, and their aggregate is the Personal Equation 



The Personal Equation, therefore, depends partly on the mental and physical con- 

 stitution of the observer, and partly upon the instruments through which he operates. 

 If the delay in noting transits was the same at both stations, no error would be intro- 

 duced into the difference of their local times or into their difference of longitude. 



Even when the 



the stations are strictly the same, the observe 



different, and, therefore, the Personal Equations are different, and a correction must 

 be applied on account of the difference of the Personal Equations of the two observers. 

 If it is practicable for the observers to exchange stations with each other for half 

 of the campaign, the difference of their Personal Equations will be eliminated when 

 the separate results of the two parts of the campaign are united into a final mean. 

 Where this cannot be conveniently done, as it obviously cannot be done in operating 

 for transatlantic longitudes, the difference between the Personal Equations of the two 

 observers may be ascertained, at least so far as it is constant, by processes especially 

 devised for the purpose. 



