STATIONS NEAR THE NORTHERN BOUNDARY OF OHIO. 253 



;i 



^ 



s ^^ 



7. 



^ 



SECTION VII. 



In order to deduce the final correction of /' in Table I., let ■^, t^', 

 V and ' denote for the European observatory values corresponding re- 

 spectively to t^t\n and 0, for a western station. Eflfecting the inter- 

 polation by means of the same values of «, 5, c, &c. : a, /y, y, &c. ; and 

 with constant values of X, X', &c., for the known value of T, or lon- 

 gitude of each observatory from Greenwich, we derive for the longi- 

 tude of the western station, independent of the stars' and moon's right 

 ascensions in the N. Almanac, 



T = t -\-v («o + T— '0^o + ^>-Hg — ^_^^ ) 



Also calling W the weight of each result, and yi the probable error 

 of a transit over a single wire (assumed equal + 0.2 sec), and mak- 

 ing o' = ([iH-ju'-t-^"4-, &c. we have, after Gauss's method, quoted 

 above, 



W = ^ ^ 



(;i + G ) n n 



Probable error of final result for each station = 



V S 



2, a 



(/i -\- a ) n n 



The values of T, for the several Stations, are given below. The 

 weights of the Cambridge and Edinburgh observations are computed on 

 the supposition that the moon and stars are observed on five wires, as 

 this number is not stated in the lists of moon culminations published in 

 Mem. Royal Astron. Soc. When both limbs are observed at the same 

 culmination, / or /' is the sum of the wires for both limbs. The re- 

 sult of a single comparison of a western station has the weight w. 

 The result for each day has the weight W computed by the above for- 

 mula, making a' and /' equal to the sum of all the wires on which the 

 moon or a star was observed at all the European observatories. 



