34 
ARCHDEACON PRATT ON THE EFFECT OF LOCAL 
be concluded that the true cause is error in the amplitudes, or in the latitudes of the 
stations terminating the several arcs. And as these latitudes have been deduced 
from the most careful observations, it must be inferred that the errors arise from 
local attraction affecting the plumb-line. 
6. An examination of the values of A deduced above will serve to show where the 
chief sources of attraction lie. 
If the elements of the mean meridian of the earth be taken (as laid down by 
Mr. Airy in his Article on the Figure of the Earth) to be 
a=209237l3 feet, £=^^ 1 : 8 ’ 
then the formula for A in art. 3. leads to the following values of A for arcs with their 
middle latitudes the same as those of the subdivisions of the English arc under con- 
sideration [the calculation is given in the Appendix] : — 
1st arc, value of A=0’00986402 . 
2nd arc, value of A=0'00986300 
3rd arc, value of A = 0 00986238 
4th arc, value of A = 0'00986104 
5th arc, value of A=0'00985911 
If we take the differences between these and the values before deduced, we have 
1st arc, defect of A below the mean =0*0000929 
2nd arc, defect of A below the mean =0*0001450 
3rd arc, excess of A above the mean =0*0000946 
4th arc, excess of A above the mean =0*0001220 
5th arc, excess of A above the mean =0*0000676 
If these are multiplied by the lengths of the several arcs, the results will be the 
errors in the amplitudes ; that is, on the supposition that the ellipticity of the arc is 
the same as the mean ellipticity of the whole earth, and that the discrepancies in the 
amplitudes arise from local attraction alone. 
The results are as follows (see Appendix): — • 
// 
1st arc, amplitude is in defect 2*914 
2nd arc, amplitude is in defect 1*926 
3rd arc, amplitude is in excess 1*323 
4th arc, amplitude is in excess 5*491 
5th arc, amplitude is in excess 2*748 
From this it appears that the local attraction is so distributed as to make the observed 
zeniths of Dunnose and Greenwich, and also of Greenwich and Blenheim, to approach 
each otlier, and those of the extremities of the other three arcs to recede from each 
other ; and that in the degree marked by the above angles. 
7 . In the following diagram I lay down these angles (on an exaggerated scale) in 
