for determining the difference of meridians, ^c. 105 



Statement of the method of combining and calculating the Obser- 

 vations, and obtaining the Rates of the chronometers. 



Previous to stating the result of these observations, it will 

 not be irrelevant to explain the method pursued in reducing 

 them, and the principles on which the calculation has been 

 made ; and it may be here remarked, that the brevity and 

 facility of the computations which will appear to be required 

 for this purpose, is not the least recommendation of the 

 method itself. 



Suppose A and Z to be the two extreme points whose 

 difference of longitudes is to be determined, and at each of 

 which the true sidereal time is supposed to be known by 

 transits of well determined stars and registered by exact 

 clocks, or carefully compared chronometers. Intermediate 

 between these, suppose two, or any number of stations, 

 B, C, &c. chosen, at each of which are placed observers fur- 

 nished with telescopes and good chronometers ; and again, 

 intermediate between these, and in the order 



A, a, B, 6, C, c, Z, 

 let posts or stations a, b, c, be selected, at which signals are 

 made, by the explosion of gunpowder, the discharge of 

 rockets, the extinction of lamps, or otherwise, at regular 

 concerted times, and so arranged that the signals at a shall 

 be visible from both A and B ; those at b from both B and C ; 

 and those at c from B and Z. Now let a signal be made at 

 a, and observed both from A and B, and the moment of its 

 happening noted at A by the sidereal clock, and at B by the 



MDCCCXXVI. P 



