1858.] and the Figure of the Earth. 209 



it bad attained the height Bn = 99 feet, and over A the height 

 Am = 271 feet — these being the heights found by Mr. Tennant on 

 using iny formula of attraction. Cum (and not CBA) is the curve 

 along which the spirit-level would move, as this is the curve which 

 cuts all the plumb-lines at right angles. In ordinary cases the 

 curve which cuts the plumb-lines at all stations on the meridian at 

 right angles is the curve of the arc. This would be the case in this 

 instance also, were it not for H. If H did not exist, Cnm would 

 coincide with CBA, Now if mountain-attraction is not taken 

 account of, it is the same as supposing that H does not exist : in 

 which case while the calculation of the Great Survey is being made 

 in reality (because H does exist) for Cnm, the calculators imagine 

 they are making it for CBA. They come to some station, B sup- 

 pose, on the arc itself, having well calculated the distance from C ; 

 they apply the spirit-level, find that Bb' is the vertical, and think 

 that CB is the arc they have calculated in fathoms, whereas it is 

 Cn', that arc along the upper curve which comes to the same plumb- 

 line. This arc is shorter than CB by nn' ; and therefore by that 

 quantity is B placed in the map too much north, in consequence of 

 neglecting mountain-attraction. And this is an error wholly inde- 

 pendent of the particular curvature of the meridian and therefore 

 it affords an additional argument to show the necessity of calculat- 

 ing and allowing for deflexion. 



9. Mr. Tennant's next calculation shows that the effect of even 

 much smaller masses than the Himalayas may be of importance 

 and may disturb the local form of the curve cutting the plumb-lines 

 at right angles, which, as I have said, is the curve to which the 

 Great Survey calculations refer. The derangements of the curve 

 may be only local in this case ; but if any one or more of the 

 stations used for finding the astronomical amplitude be situated in 

 these localities, the effect may be of serious importance. The effect 

 of these comparatively small masses I have also shown in a paper 

 on the English Arc printed in the Philosophical Transactions for 

 185(5. This only aggravates the uncertainty caused by attraction, 

 and increases the doubtfulness of results arrived at without a 

 complete knowledge of the disturbing causes — at least as far as 

 those results are supposed to have an extreme accuracy. 



2 E 



