1858.] and the Figure of the Earth. 211 



tude of the middle point of the arc, and (3) the dimensions of the 

 ellipse of which it is part. The first of these is determined with 

 great accuracy by the survey, and is altogether unaffected by local 

 or mountain-attraction (see pp. 54, 55 of my paper).* The second, 

 which is not required to any great nicety, is readily found. The 

 third is altogether assumed — and here is the first source of error. 

 It has been assumed in the Great Trigonometrical Survey that the 

 great arc belongs to an ellipse of which the curvature is that of 

 the average spheroid of the earth. This is not only very far from 

 being certain, but is most probably not the case, as I have shown 

 in my preliminary remarks. Then in the determination of the 

 amplitude by observation, all the elaborate instrumental observa- 

 tions and calculations of the latitudes of the three stations at the 

 extremities and the middle of the arc in question (viz. at Kuliana, 

 Damargida, and Kulianpur near the middle) described by Colonel 

 Everest in his volume are thoroughly to be depended upon. But 

 the instruments are fixed by the plumb-line; and therefore any 

 error in this line caused by local or mountain-attraction vitiates the 

 results. Here, then, is the second source of error. Were there 

 only one source of error, the error might be determined by compar- 

 ing the computed and observed amplitudes. But as this gives 

 only one equation of condition and there are two sources of error — ■ 

 and this must be the case for each arc, so that no comparison of 

 arcs will help us — we must determine one, at least, of the errors 



* This may appear to be at variance with paragraph 8 above. But the cases 

 are different. The fact is, that the correction there pointed out is after all practi- 

 cally made during the process of the survey ; and in this way. Since B cannot 

 be seen from C, being more than 400 miles off, intermediate stations are chosen 

 for making observations and connecting B and C by a chain of triangles ; and 

 these intermediate stations are down upon the arc CB, and not on the arc Cn. 

 Of course if the spirit-level were actually used all along, and the stilting process, 

 which would then be necessary, were carried on, this would not be the case. But 

 this course is not adopted in the survey ; but, to make all the intermediate observa- 

 tions, they come down to the arc CB, and begin their curve like Cn, as it were, 

 over again at each station ; so that the height is not allowed to accumulate to Bit,, 

 and therefore the projected part of this line is not a correction wliich must be 

 applied to the length of the arc, as this correction is practically made by the 

 surveyors piece-meal, by making their observations from CB and not from Cn, as 

 they do not adopt stilts. 



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