454 



MEMOIRS OF THE AMERICAN ACADEMY. 



DUXBURY. 



Date. 





a 



1869. 



Dec. 



14 



u 



14 



u 



15 



u 



15 



u 



23 



u 



23 



u 



9 



31 



a 



31 



1870. 



Jan. 



3 



a 



3 



it 



4 



u 



5 



ii 



5 



it 



7 



M 



8 



44 



9 



44 



11 



II 



16 



ii 





a 



<i 



44 



44 

 44 



18 

 19 

 21 

 22 

 23 

 26 

 26 

 28 

 28 



0.367 

 0.262 

 0.278 

 0.168 

 0.241 

 0.320 

 0.087 

 0.081 



0.232 

 0.122 



•0.098 



+0.038 

 —0.184 

 0.117 

 0.089 

 0.478 

 0. 1 80 

 0.121 

 +0.013 

 +4.234 



0.340 

 0.139 

 0.309 

 0.082 

 0.102 



■0.192 

 0.196 

 0.373 

 0.015 



c 



0.472 



0.472 

 0.261 



0.015 

 0.015 

 0.015 

 0.015 



0.010 

 0.010 

 0.032 

 0.023 



A'J\ 



Hourly Kate. 



0.034 

 0.051 

 ■0.076 

 0.046 

 0.037 

 0.151 

 0.198 



0.065 

 0.074 

 0. 1 00 



0.085 



13.548 ± 0.042 

 13.868 ± 0.026 

 2.482 ± 0.021 

 3.132 ± 0.031 

 2.343 ± 0.013 

 2.143 ± 0.016 

 4.328 ± 0.015 

 4.361 ± 0.024 



6.627 ± 0.019 

 6.806 ± 0.021 

 7.433 ± 0.015 



7.786 ± 0.032 

 7.951 ± 0.030 

 7.532 ± 0.027 

 7.343 ± 0.015 

 6.584 ± 0.020 

 6.607 ± 0.025 

 6.163 ± 0.026 

 + 9.462 ± 0.034 



026 + 0.023 



Number of Stars 



0.160 

 0.1 60 



0.180 



•0.001 

 0.001 

 •0.000 



+10 



+11 



+12 

 +15 

 +16. 

 +18. 



+1 



± 0.023 

 ± 0.027 

 ± 0.022 

 ± 0.016 

 ± 0.018 

 ± 0.016 



0.040 

 0.040 

 0.030 

 0.030 



0.030 

 •0.030 

 0.025 

 0.000 

 0.045 

 0.010 

 0.045 

 0.012 

 0.000 

 +0.000 

 —0.015 

 0.018 

 0.030 

 0.030 

 0.040 

 0.045 



5 



8 

 10 



7 

 19 



11 



13 



7 



16 



8 



9 



4 



10 



7 



11 



10 



18 



9 



7 



17 



0.040 



2.256 ± 0.021 

 2.117 ± 0.024 

 2.298 ± 0.026 



0.000 

 0.000 

 0.000 



6 



3 



12 



10 

 9 

 8 

 6 

 7 

 4 



After the instrumental and the clock corrections have been found, the difference of longitude is computed 



in the following manner : 





dT x 



T x is the mean of the recorded Brest clock times of sending a set of westward signals. 

 T t ' is the mean of the recorded Duxbury clock times of receiving these signals. 

 ~ is the mean of the recorded Brest clock times of receiving a set of eastward signals 



is the mean of the recorded Duxbury clock times of sending these signals. 

 T Y ' is the mean difference for the westward set. 

 is the mean difference for the eastward set. 



T 2 < 



T' 



J TJ is the difference of the clock corrections at Brest and Duxbury, when the westward signals 



were sent. 



J To 



JTJ 



* 



is tbe difference of the clock corrections at Brest and Duxbury, when the eastward signals 



were sent. 



x is the mean transmission-time of signals 

 X is the difference of longitude. 

 A and x are computed by these two formulas. 



(2.) 



2A 

 2x 







When signals are sent in only one direction, 



+ 



JTA 



+ 



(JT, 



A TO 



ATA 



(3.) 

 (4.) 





{T x 



(T 2 



') + 



*Ti) 



+ 



or 



x 



In using the formulas (3) and (4), we must adopt an assumed value of *, and this assumed value may be 

 the one computed from the perfect sets of signals of the same class exchanged on the same night, or the more 

 general mean derived from the perfect sets exchanged on all the ni-hts. 



