THE RELATIVE FORCE OF GRAVITY AT KEW AND GREENWICH. 
557 
tlie vibration-nmnbers for Kevv and Greenwich which have already been })resented ; 
but it would not affect the differences between those numbers, which are what is 
really wanted, to a degree that is at all comparable with the errors to which 
pendulum observations are liable from other causes. 
Reduction to the Sea-level. 
The pendulums were swung at an elevation above the mean sea-level of about 
15 feet at Kew and 157 feet at Greenwich. The vibration-numbers must be 
correspondingly increased. 
The well-known formula for the correction for height is 
Correction = V -, 
r ’ 
V being the vibration-number, h the height, and r the radius of the earth. Dr. 
Young has suggested that account should also be taken of the continental mass 
which is situated between the level of the sea and that of the station of observation, 
in increasing the force of attraction and consequently the vibration-number. Thus, in 
accordance with his views, the usually-accepted correction takes cognisance of both 
height and )Dass, and is 
Thus for these pendulums, when h is expressed in feet, we have 
Correction for height only 
Correction for height and mass = 
391 ‘ 
It is now, however, very questionable whether any reduction for mass is allowable. 
The pendulum operations in India have thrown much light on the constitution of the 
earth’s crust, and shown that there is a marked deficiency of density under the 
Himalayan mountains, and an increase of density under the bed of the Indian Ocean. 
Thus continental matter above the sea level may be conceived as appertaining to the 
strata underneath, immediately below the sea level, which are correspondingly 
attenuated. In this case, the excess of matter above would probably compensate for 
the deficiency of matter below, and would not form an attracting force to be 
independently allowed for while no cognisance is taken of the deficiency below. 
If the vibration-numbers at Kew and Greenwich are corrected for height only, the 
correction to be applied to their difference will be 
whence we obtain 
15 - 157 
213 
0'58, 
Kew^—Greenwich — 1'22 — 0‘58 = 0'64 
as the result of the revisionary operations. 
