122 EIGHTH REPORT — 1838. 



the origin of the coordinates, a and h heing the general central 

 station in 4° 35' W. longitude, and 54° 16' N. latitude. 



Proceeding in the same manner for r, we have the 3 equations : 



England, + 0*575 = r -- 89 *^ — 98 y ; 

 Scotland, + 0-549 = r — 34 x + 153 y ; 

 Ireland, + 0*594 = r + 123 a? — 55 y. 



Giving the English result the vs^eight of 3, and each of the 

 others that of unity, and deducing by the method of least squares 

 the most probable values of r, x, andy, we obtain x= + '00007; 

 y = —-00013 ; and r = 0-571. at the central general station 

 in lat. 54° 16' and long. 4° 35' W. 



Whence the approximate value of r is found at any other geo- 

 graphical position in the British Islands by the formula 



r = + 0-571 +-00007 a —-00013 b ; 



the longitude and latitude of the general central station being the 

 origin of the coordinates a and b. 



The points furnished by the several observations for the near- 

 est adjacent isoclinal line, computed in the manner above de- 

 scribed, are inserted in the general table which closes this divi- 

 sion of the report. The table is in two parts ; the one con- 

 taining the observations, the other the deductions. In the first 

 part are shown the observed dip, the latitude and longitude of the 

 station, the date, the observer, and a reference to the particular 

 table in which all the details connected with the observations 

 may be examined. In the division which contains the deduc- 

 tions, are shown the dip reduced to the mean epoch of the 1st 

 January, 1837 ; the differences of latitude and longitude between 

 the station and the point furnished by it for the nearest isoclinal 

 line ; the latitude and longitude of the points, and the values of 

 u and r, employed in their deduction. 



By the method thus described, the transfer of the observation 

 to the isoclinal line involves no other material inaccuracy than 

 such as may be occasioned by incorrectness in the employed 

 values of u and r. We may, therefore, examine the probable 

 limit of the inaccuracy which may be thus incurred : — 30 mi- 

 nutes of dip is the extreme fractional amount in any case for 

 which a deduction is required : if we suppose an error in the 

 assumed value of r equal to O'Ol, which is nearly a fovu-th of 

 the extreme difference found for England, Ireland and Scot- 

 land, — the corresponding error in the geographical distance of 

 the point from the station will be less than one mile. An error 

 of 1° in the value of u, in the same extreme case of a fractional 

 amount of 30' of dip, would cause an error in the position as- 



