ARMAGH AND DUBLIN ARCS OF LONGITUDE. 21 



of powder. The two-pounder is necessary for this, and, on sta- 

 ting my objects, a liberal supply of them was ordered by the 

 Board of Ordnance, together with tents for the firing parties ; 

 and, indeed, whatever I required was freely afforded. Without 

 dwelling on details, it may be sufficient to mention that on four 

 nights in May last, notwithstanding most unfavourable weather, 

 we obtained from seventy-four signals, forty-two good results : 

 from which we deduce our difference of meridians to be 



m s 



1 14-425; 

 only three-hundredths of a second greater than Mr. Dent's 

 chronometers had given. 



In taking this mean, it is necessary to attend to the different 

 value of the work of each night, which varies according to tlic 

 number of signals observed, and that of the stars observed for 

 time. This has been done according to the theory of probabili- 

 ties, in applying which it was found that the probable error of 

 time-determination by a star is about 0*065, and by a rocket 

 0*16. It also appears, that when several intermediate stations 

 are used, the value of the result is rapidly diminished ; so that, 

 for example, if as in Sir J. Herschel's operations between 

 Greenwich and Paris, we suppose three stations — ten signals at 

 each, and seven stars to determine time at the extremities, the 

 worth of such a result is but 0-38 of what it would be if the 

 work could be done by one signal station. If to this we add the 

 great uncertainty of perfect transmission along the line, it be- 

 comes an object to increase the extent of distance connnanded 

 by each signal as much as possible. 



To complete the result, it is necessary to know the *' personal 

 equation" of the observers, or, in language fit for the uninitiated, 

 the difference of the times at which two observers estimate the 

 passage of a star over a transit-wire, — such a difference as 

 astronomers well know almost always exists, and sometimes to 

 a startling extent. By a journey to Dublin, my assistant deter- 

 mined that he observed 0*167 earlier than the other observer, 

 and therefore the true difference of longitude is 



m s 



1 14-258 

 It is our intention next, to determine the longitude of the 

 third great Irish observatory, that which Mr. Cooper is fur- 

 nishing with instruments of unexampled magnitude and power, 

 which can be connected by one station with this and Dublin 

 simultaneously. That I hope to follow up by a similar opera- 

 tion between Armagh and Edinburgh, if, as I expect, the Board 

 of Ordnance prove as propitious to my second application. 

 Rockets of sufficient power fired on Goatfell in Arran, can be 



