CHAP. XIII.] OBSERVATIONS FOR ERROR 305 



Algebraically we can express this : 



T=12-{t + e) + 2q, 



where T is mean time of first observation required. 



t is time by watch of last observation, 

 e is error of watch slow of mean time. 

 q is equation of time. 



The book in which the observations are registered should C^^^^ij'^ 

 be ruled as in annexed specimen. (See p. 306.) sight 



The first column is for the intervals between each observa- ^°°^- 

 tion of the first set of sights ; the second, the time taken at 

 those sights ; the third, the double altitude ; the fourth, 

 the sum of the seconds of the two times ; the fifth, the time 

 at second set of sights ; and the sixth for the intervals between 

 the latter. 



On next page is an example of a set of sights as \mtten in 

 the Angle Book. 



When the time-taker is practised, it is Mell for him to note Noting 

 down the interval between the sights as he notes down the ^etwee^n^ 

 time, as it enables the observer at once to know, when the Sights, 

 set is over, Avhether he has been getting good observations or 

 not, as the intervals should theoretically be precisely the same. 



We do not usually attempt to estimate time with a pocket- 

 watch to less than two-tenths of a second, so we shall not 

 find the intervals agreeing exactly, even supposing no errors 

 of observation to exist. Taking everything together, if the 

 difference in these intervals does not exceed one second and 

 a half, we may consider that we have obtained very good 

 observations. Another reason for noting these intervals is 

 that we shall see if the sun's motion is becoming too slow. 



In working out sights for equal altitudes, it is merely the Method of 

 mean of the middle times of each set that we wish to get, so ^®*^^°S- 

 that we need not mean up each column of times, but merely 

 the sum of the seconds of each corresponding times, which we 

 have in the fourth column of our Sight Book. Then, taking 

 the times of the middle observation, meaning those, and sub- 

 stituting for the seconds of this mean the mean of the seconds 

 just found from the fourth column, we shall have the true 

 mean middle time of our observations. Thus, in our example 



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