Archdeacon Pratt on the Curvature of the Indian Arc. 341 



4. The mean elUpticity of the earth has been investigated by 

 both the Astronomer Royal and the late M. Bessel with great 

 care, by a comparison of arcs of meridian measured in various 

 parts of the earth ; and although the methods were somewhat 

 different, they arrived at the same conclusion^ one making 



the ellipticity ^ , the other ^ , the difference being in- 



appreciable. Now this is the ellipticity to which theory leads 

 us in supposing the earth to be in a fluid state, the density to 



increase gradually towards the centre by the law — [r being 



the distance from the centre, and q a constant), the density of 

 the superficial stratum to be that of granite, and the mean den- 

 sity of the earth to be what the late Mr. F. Baily made it. This 

 coincidence has been generally considered to be a conclusive 

 argument in favour of the hypothesis that the earth was once 

 fluid, and acquired its present form (at any rate its present mean 

 form) at that time, and from hydrostatic principles. 



5. These investigations, however, do not show that the whole 

 meridian through any place is exactly elliptical, nor that the 

 meridians through places in different longitudes are all alike. 

 They show merely that the mean curvature of the different parts 

 of the earth is that which corresponds with the fluid condition 

 of its mass, which is, as I have said, a very strong argument in 

 favour of the hypothesis of original fluidity. 



6. That the curvature of every meridian does not equal the 

 mean curvature can, I think, be most satisfactorily proved in the 

 case of the great Indian arc, about 800 miles long, and lying 

 between Kaliana (about 50 miles from the Himalaya Mountains) 

 and Damargida. This arc has been divided into two nearly 

 equal parts, and the lengths and astronomical amplitudes of both 

 have been determined with great precision. The astronomical 

 amplitudes, however, need correction for the attraction of the 

 Himalayas, which are found to have a sensible effect upon the 

 plumb-line. In a paper published in the Transactions of the 

 Royal Society for the present year, I have given a method for 

 calculating the effect of this attraction, and have reduced the 

 formulae to numbers. On calculating the curvature of the Indian 

 arc from the estimated lengths of its two portions, and the am- 

 plitudes corrected for attraction, I find that it is greater than 

 the mean curvature ; in fact, that the middle point of the whole 

 800 miles is raised a few feet higher above the cord joining its 

 extremities, than if it possessed the mean curvature. 



7. An hypothesis has been thrown out, since the publication 

 of my result, to show that the effect of attraction from the 

 enormous mass rising above the mean surface in the Himalayas, 



