Longitude between Melbourne and Hohart Town. 97 



COMPUTATION OF THE DIPFEKBNCE OF LONGITUDE. 



Date, 

 1875. 



Difference of 



Longitude. 



Double 



the time of 



Transmission. 



■\r.i»»^v^«- 





Hobart Town 

 Register. 



Melbourne 

 Register. 



of Cloc 

 Obse 



H 



k Stars 

 rved. 



M 



Weight. 



Jan. 30 



m. s. 

 9 25-996 



rn. s. 

 9 25-762 



8. 



0-234 



7 



8 



392 



Feb. 1 



26-084 



25-900 



•184 



6 



6 



315 



2 



25-720 



25-551 



-169 







8 







4 



26193 



26000 



•193 



6 



6 



315 



5 



25-935 



25-609 



•326 



7 











6 



25774 



25-423 



•351 



6 



9 



378 



7 



25-820 



25-577 



•243 



6 



8 



360 



The weights are proportional to the quantity found by- 

 multiplying the number of stars observed by one observer 

 by the number observed by the other, and dividing the pro- 

 duct by their sum. On February 2nd no stars were observed 

 at Hobart Town, and on February 5th no stars could be 

 observed at Melbourne, so the difference of longitude marked 

 in the columns has been found by carrying on the rates of 

 the chronometer and clock respectively ; as the combination 

 weights, however, are nothing, thej^ will not influence the 

 final results. The transmission times, however, are indepen- 

 dent of the rate of the clock, except for the few minutes 

 intervening between the receipt of the set of signals; these 

 nights, therefore, have equal weights for this purpose with 

 the others. Carrying out the combination we get 9m. 

 25-841s., from this is to be subtracted 0178s. for personal 

 equation ; we then get for the final difference of longitude 

 9m. 25'66s. + 'OGs., and for the mean time of transmission we 

 get 0'121s. Taking the length of the land lines and cable at 

 420 miles, this would represent a speed of only 3360 miles per 

 second ; the actual speed, however, must have been con- 

 siderably greater than this, for the above quantity, 0-121s., 

 includes also the armature time of the relays and repeating 

 apparatus. From some measures made of the speed of the 

 current on the land lines during the determination of the 

 difference of longitude between Melbourne and Sydney in 



