CHAP, xm.] OBSERVATIONS FOR ERROR 307 



or last of a set, when the set will become one with an even 

 number of observations, and to get elapsed time we must, 

 instead of the central observation, take the mean of the two 

 times corresponding to the two central observations. 



Four sets of eleven observations each, half upper limb and Personal 

 half lower, ought to give accurate time ; but it must be under- ^^l^ ^°^ 

 stood that equal altitudes do not eliminate personal errors, nated by 

 only instrumental and atmospherical ones. It is evident that, Altitudes, 

 if an observer is, for instance, habitually too slow in recording 

 his contacts, the resulting middle time will be so much after the 

 true time of transit. Taking the case of an observer recording 

 the time of contacts of opening limbs correctly, and of closing 

 ones habitually too late, the middle time will still be in. error. 

 It is only when the observer records opening limbs in error one 

 way, and closing in error in the contrary way, that these 

 personal errors can be eliminated. This is, of course, not 

 likely to happen with many people, and we must consider the 

 time resulting from any observer's sights as being ah\ays in 

 error by the amount of liis personal equation. 



In running a meridian distance, however, this personal error, Dis- 

 supposing it to be tolerably constant, will disappear, as his Meridian" 

 time being equally in error, and in the same direction (either Distance, 

 too fast or too slow) at both places, the difference of time, on 

 which alone longitude depends, wiU not be affected. From 

 this it results that in rumiing a meridian distance, the same 

 observers must always be employed. 



The formula for finding the equation of equal altitudes is as 

 follows : 



Equation = A + B. Formula 



1 c elapsed time ^°^ Equa- 



A (in seconds of time) = x -Tan lat x Cosec ^°^ °^ 



15 2 2 Equal 



Altitudes. 



1 c elapsed time 



B( do. ) = - X Tan dec x Cot 



15 2 2 



c 

 where - is half the change of declination in the elapsed time, 



or, as we use it in the computation, the change of declination 

 in half the elapsed time. 



The rules for noting the algebraic signs of A and B will be 

 given hereafter. 



20—2 



