494 



seas, there must be corresponding hollows in the solid crust below 

 filled up by the lava, and this would point out a law of varying 

 thickness in the crust which no process of cooling could well pro- 

 duce. 



3. The author considers, however, that if there be a compen- 

 sating cause it must lie in this direction ; and he puts forth the hy- 

 pothesis of deficiency of matter in a new form. He supposes that 

 the mountain mass has risen up in consequence of a slight expansion 

 of the solid crust below through many miles of thickness, producing 

 a slight attenuation from a considerable depth. He calculates for- 

 mulae and reduces them to tables to find the effect of this atte- 

 nuation, and shows that the mountain attraction, modified by this 

 attenuation, if it extend down through 100 or 300, or 500 or 1000 

 miles (the attenuation being uniform along each vertical line), will 

 produce the following deflections : 



At Kaliana. . . . l"-538, or 6"'872, or 10"'912, or 16"'779. 

 Kalianpur. . 0"' 064 0"'369 2"'425 4"'661. 

 Damargida 0"'065 0"'076 0"120 1"'570. 



4. These four sets of deflections are then applied to correct the 

 amplitudes of the two portions of the arc, and by their comparison 

 to find the ellipticity, which is shown to be, in the four cases, 



J_ _L J_ 1 



216' 280' 286' 8 385' 



So that although the hypothesis, if the depth of attenuation be 

 about 100 miles, greatly reduces the deflection, it does not reduce 

 the ellipticity to the mean value, which is attained only if the depth 

 be somewhere between 500 and 1000 miles. There is little or no 

 ground, therefore, for working with a mean ellipticity as is done in 

 the Great Survey. 



5. It is next pointed out that this theory will not explain the 

 peculiarities of the Indian Arc under consideration ; in which (ac- 

 cording to Colonel Everest: see his volume for 1847, p. clxxvii), 

 the upper portion has an excess in its amplitude, geodetically deter- 

 mined, of 5"-236, and the lower a defect of 3"' 789. The presence 

 of other disturbing causes near Kalianpur or Damargida, or both, 

 is indicated by this ; either in visible masses above, which ought to 

 be accurately surveyed (as even small masses, if near enough, will 

 produce the effect) ; or in invisible defects or excesses of matter 



