266 Mr Galbraith on the English Arc of the Meridian. 



2. Mudge's base, on Hounslow Heath, at 62° Fahr., 100 feet above the 



sea, in feet, 27404.3155 



By Ramsdcn's sealc, of which the logarithm is 4.4378190 



Reduction to imperial standard, ... + 300 



Reduction to level of the sea, .... — 21 



Log. of true length of base (1791), . . 4.4878469 



Which gives, imperial feet, . . . . 27406.076 



3. Mudge's base, on Salisbury Plain, 690 feet above the level of the 



sea, at the temperature of 62° Fahr., was . . 36576.4 feet. 

 Of which the log. is ...... 4.5631891 



Reduction to imperial standard, ...-}- 300 



Reduction to level of the sea, .... — 143 



Log. of true length of base, .... 4.5632048 



Which gives, in imperial feet, . . . 36576.723 



4. Mudge's base, on Mistcrston Carr, 85 feet above the level of the 



sea, at 62' Fahr., was in the same standard, .^6342.712 feet. 



Of which the log. is 4.4206605 



Reduction to imperial standard, . . . + 800 



Reduction from 35 feet to level of sea, . . — 7 



Log. of true length of base at sea, . . . 4.4206898 

 Which in imperial feet is 26344.491 



Hence we have the whole of these four bases all in imperial 

 feet, with their corresponding logarithms, ready for the ulte- 

 rior calculations, though the two bases on Hounslow Heath 

 disagree more than is generally believed ; because, instead of 

 being, as usually supposed, in terms of the same scale, they 

 are essentially different, and their lengths ditfer by 1 foot 4| 

 inches. 



Spherical Excess. 



In computing the spherical excess, I employed the formula 

 e" = ^ sin 1" X 2 «/-. In which a is the area of the triangle 

 in square feet, / the factor to convert feet into arcs for 

 X (jjf-i' j^ ;") = L, the mean latitude of the three angular points 

 of the triangle at an angle a of 45° with the meridian. My 

 results correspond nearly to those in the Survey, with one or 

 two exceptions. That in which the error is greatest is the 

 triangle Castle Ring, Bardonhill, Orpit. In this triangle, the 

 spherical excess is 4".06 instead of 2".85, as stated in the 



