202 On the Arcs 'perpendicular to the Meridian, 



three chronometers, A, B, and C ; A and C keeping true 

 time, B intermediate between the others, gaining five seconds 

 in the 24 hours : suppose, further, that the three first signals 

 given on any particular night are the only ones seen by A and 



B, and that in like manner these signals only are seen by B and 



C, but that those signals are the three last given on that night ; 

 the number of signals in each night being ten, the interval 

 between each ten minutes, and the signals between B and C 

 given always five minutes later than those between A and B. 

 In this case, the comparison between B and C takes place 

 one hour, fifteen minutes after that between A and B, B having 



gained intermediately on each of its neighbours — ^^ = o',s. 

 Now the sidereal time arriving from one extremity of the line 

 has to be conveyed to the other extremity, by being successively 

 transferred from A to B and from B to C, by means of their 

 respective differences. But the difference between B and C, 

 taken 1 hour 15 minutes after the comparison of B with A» 

 differs 0',3 from what it would have been had the comparisons 

 been simultaneous. The sidereal time will, therefore, be re- 

 peated from C, charged with the whole of the error arising 

 from the rate of B in the interval of comparison, unless a cor- 

 rection, proportioned to the rate and interval, be applied to the 

 differences. The rates of the chronometers adopted in this 

 illustration are such as actually did exist in the operations 

 between Paris and Greenwich ; and but for the corrections ap- 

 phed, would have introduced a considerable error. 



We consider, therefore, that Mr. Herschel has rendered a 

 valuable service to those engaged in operations of this nature, 

 by giving a short and easy method, whereby the result of such 

 a broken series may be computed, Avith a due consideration of 

 the respective rates and intervals, and without rejecting any 

 observations but such as, having been seen only at a single 

 post, must of course be wholly useless. 



From the 120 signals given in 1825 between Paris and Stras- 

 bourg may be derived 35 results, either of complete trans- 

 missions, or from signals, between which the intervals were so 

 small as to admit of their being combined, to represent complete 

 transmissions. The mean of the 35 results is 21' 35",4. View- 



