On the Extra- Meridian Determination of Time. 215 



In other words, if <, does not agree with t-^' the difference must be 

 divided proportionally to Tj and r,'. In the same manner the differ- 

 ence between t^" and t^'" must be divided proportionally to r," and 

 t/". Finally the clock correction is to be derived from the formula 



t = ^ {t,J^t.^') -f- 0-000038 {t—t^') (Z" Z'"— Z Z'), (44) 



the last term of which is an exceedingly small quantity, and although 

 easily computed, it may generally be neglected, if the collimation is 

 small and a little care is taken to select stars which will give Z" Z'" ap- 

 proximately equal to Z Z'. In fact it may readily be seen that for 

 h" — h = <^'-66, and for stars within 20° of tTie zenith the last term of 

 (42) can never exceed 0^01. 



If the observer sweep in altitude and azimuth until Polaris is near the 

 center of the field of the telescope, and the latitude and time be ap- 

 proximately known, approximate values of r — m, m and t may be 

 readil}- obtained for each star from auxiliary tables; these will be 

 found convenient for setting purposes and for the determination of »,. 

 Such tables have been kindly prepared for me by Mr. Howe. 



A portable transit is often used in a fixed observatory for the deter- 

 mination of time, and since it ma}^ be kept nearlj' in the meridian, n^ 

 may be assumed equal to zero, and the differences between t^ and t-^' or 

 <i" and t^'" divided proportionately to tabulated values of tan d — tan <p. 



