INTENSITY AND DIRECTION OF THE FORCE OF GRAVITY IN INDIA. 293 



TABLE II. 



EXPLANATION OF TABLE II. 



Given the amount of matter in tlie crust at a stauJaril station, we wish to find from pendulum observations, the excess or deficiency of matter 

 underlying any other station ; from observation we find ilrj, the local variation of gravity from the normal, and we wish to determine the mass 

 whose attraction at sea-level is equivalent to dg. From its attraction only we cannot determine both the height and density of a hidden mass, 

 but If we assume that the density is equal to 2 '8, the normal density of surface rocks, we can then ascertain the height; by this assumption we. 

 mean that the density of a hidden disturbing mass is 2 -S in excess of the normal density of the surrounding crust . The problem to lie solved is, 

 therefore : given a small attraction dij, what is the height of the attracting mass, its density being 2-8? 



It is necessary to consider how dij is obtained ; by observations taken at a station of height H we find the value of gravity to IK; y. To oblain 

 the corresponding value of gravity at sea-level, <7 , we have firstly to correct for the amount H, by which the distance of the station from the 



centre of the earth exceeds the earth's radius, 2l' = 



fj 



R- 



= ij (\ + \. 

 \ R / 



This correction would be sufficient if the obser\ ing station were in mid-air and over the wean, but when we observe at a station on land, wr 

 have to consider the attraction of that portion of the crust that lies between sea-level and the station ; this attraction tends to increase Un- 

 observed value of g, and the correction for it is ncgat ive. The attraction of a horizontal plateau of height H and density S upon a pendulum 

 situated at the centre of its upper surface is A = 2*611. The force of gravity at sea-level is g = JirRA, where A is the mean density of the earth. 



Then if y a " be the value of gravity at sea-level corrected Iwth for height of station and for the attraction of the intervening mass, we get the 



well-known formula of UOUGUEK, y a " = y a A = ij ( 1 + - ^-|f ). (/" gives then the obsen-eit value of gravity at an ideal station, situated upon 



\ R 4 K / 



a continent, whose surface is level with the sea. 

 Now <tg = g a " fa, where / is the theoretical value of gravity. To lind the height of a plateau whose attraction would be sufficient to 



increase the observed force of gravity by 0-001 centim., we have . . y = dg = O'OOl. II = O'OOl x ; x . Assuming the earth txi be a 



4 K y 



sphere with a mean radius of 6367000 metres, and the mean value of the force of gravity to lie 980-0, we get II = O'OOl x J x ** l( _ _ = S'S573 metres. 



The attraction thus of a plateau of height 8 '6373 metres wilt increase the observed value of gravity by O'OOl, and vice versa ; if the observed value 

 of gravity at sea-level differs from the theoretical value by -t-'O'OOl there is an excess of matter in the underlying crust equal to a disc 8 '6573 

 metres thick of a density 2 '8. 



If we imagine that from the surface to a depth 1), the density of the crust underlying the station is less by 2 '8 than the normal surface 

 density, then D = - (#," - yj 8 '8573 metres. The visible excess of matter will be equal to H (see fig. 1), the hidden deficiency will be equal to D 

 (see fig. 2), and the actual disturbing mass, shown in the section of fig. 3, will be (H D). 



Prom Table II. it appears that at MorA the value of g a " is '518 less than y ; therefore the hidden deficiency = D = 518 x 8 '573 = 4484 metres 

 (fig. 2). The height of the visible mountain at Mor6 is H = 4696 (fig. 1) ; the actual excess of matter in the crust at More = (H - D) = 212 

 metres (fig. 3). 



At Dehra Dun <y " - y u > = - 0'224, hidden deficiency = D = 224 x 8-8573 = 1939 metres (fig. 2). The altitude of Dehra Dun is S3 metres 

 (fig. 1) ; at this station, then, the hidden deficiency exceeds the visible excess, and the resultant is (H - D) = 683 - 1939 = - 1256 metres (fig. 3). 



At the important station of Kalianpur (</" y a ) = '042, the hidden deficiency = D = 42 x 8 '6573 = 364 metres, the visible excess at 

 Kalianpur = H = 538 metres. There exists, therefore, at Kali:in pur a resultant excess of matter in the crust equal to a disc of density 2 '8, and 

 pf height 174 metres. The existence of this excess has been questioned, and the calculation is therefore giren in detail. 



