I 



LONGITUDE OF WESTERN BOUNDARY LINE. 151 



As explained in former reports, the taps were made each time at 

 five consecutive second-beats, the middle one of which is noted in the 

 first column, and the corresponding chronographic time in the fourth, 

 columns two, three, five and six containing only the fractions of the 

 seconds recorded. The eighth column serves for reducing the mean 

 time intervals of the different comparisons to one common epoch, so 

 that the figures of the last column may be viewed almost as if they 

 were different observations of one and the same middle epoch, thus 

 exhibiting an estimate of the accuracy of the comparisons. The mean 

 of these now gives the equation 



20'' 50™ 0^ chronometer =: 10'' 11™ 51^71 clock by chronograpli, 



hereto adding 



— 17™ 55^08 chronometer, and + 23M0 clock, 



as the corrections (found before) of chronometer and clock respectively, 

 we obtain 



2OI1 32™ 4^92 State Line sidereal time 



= 10'^ 12™ 14^81 Hamilton College mean time 

 = 20'' 49™ 30^51 Hamilton College sidereal time, 



and hence the difference in longitude, 



17™ 25^59, 



with the probable uncertainty of about half a second. We may add 

 hereto the, however insignificant, reduction of + 0^02 from the transit 

 to centre of dome, and further — 0^04 for wave and armature time. By 

 survey the observing station (see Plate I) was found to be situated east 

 from the boundary line 1,062 feet, which are equivalent to 14". 12 in arc 

 or 0^94 in time, — since 1^ of this parallel corresponds upon the spheroid, 

 as determined by Bessel, to 1,128.17 feet.. The final result for the 

 longitude, therefore, is : 



The Western Boundary Line of the State of New York 27™ 26^51 West of the 

 Observatory of Hamilton College ; 

 or, 



5h j^gm 3s_g3 "V^EST OP GREENWICH, 



the longitude of the Observatory being S*" 1™ 37M2 west of the latter 

 place. 



