AT THE SURFACE OF THE EARTH. 



683 



16. Now the most obvious cause of irregularity consists in the attraction of the land lying 

 between the level of the station and the level of the sea. This attraction would render the 

 values of g sensibly different, which would be obtained at two stations only a mile or two apart, 

 but situated at different elevations. To render our observations comparable with one another, it 

 seems best to correct for the attraction of the land which lies underneath the pendulum ; but then 

 we must consider whether the habitual neglect of this attraction may not affect the mean values 

 from which G and e are to be found. 



Let g = g: +g', where g is the attraction just mentioned, so that g^ is the result obtained by 

 reducing the observed value of gravity to the level of the sea by means of Dr. Young's formula*. 

 Let h be the height of the station above the level of the sea, a the superficial density of 

 the earth where not covered by water; then by the formula for the attraction of an infinite plane 

 we have g = Zircrh. To make an observation, conceived to be taken at the surface of the sea, 

 comparable with one taken on land, the correction for local attraction would be additive, instead of 

 subtractive ; we should have in fact to add the excess of the attraction of a layer of earth or rock, 

 of a thickness equal to the depth of the sea at that place, over the attraction of so much water. 

 The formula g' = 2irah will evidently apply to the surface of the sea, provided we regard A as a 

 negative quantity, equal to the depth of the sea, and replace cr by cr - 1, the density of water being 

 taken for the unit of density ; or we may retain o- as the coefficient, and diminish the depth in 

 the ratio of cr to cr - 1. 



Let p be the mean density of the earth, then 



§■' = 2 irah 



O 7 = G- 



i-TTf 



2 pa 



If we suppose a 



o\_ 



p = 5^, a = 4000 miles, and suppose h expressed in miles, with the 



I 



understanding that in the case of the sea k is a negative quantity equal to f^ths of the actual 

 depth, we have g' = .00017 G/j nearly. 



17. Consider first the value of G. We have by the preceding formula, and the first of 

 equations (27), 



G = m (g,) + G x .00017 m (A)- 



According to Professor Rigaud's determination, the quantity of land on the surface of the 

 earth is to that of water as 100 to 276■^. If we suppose the mean elevation of the land -J tli 

 of a mile, and the mean depth of the sea 3 ^ miles, we shall have 



f X 3| X 276-1 X 100 

 m (/i) = - ^ ^ — g — 2 = - 1.49 nearly ; 



so that the value of G determined by g, would be too great by about .000253 of the whole. Hence 

 the mass of the earth determined by the pendulum would be too great by about the one four- 

 thousandth of the whole ; and therefore the mass of the moon, obtained by subtracting from 

 the sum of the masses of the earth and moon, as determined by means of the coefficient of lunar 

 parallax, the mass of the earth alone, as determined by means of the pendulum, would be too 

 small by about the one four-thousandth of the mass of the earth, or about the one fiftieth of 

 the whole. 



18. Consider next the value of 

 stituting g, for g in (27), and let 



Let £| be the value whic 



he di'liriiiined by sub- 



* I'hi/. Trans, for IKlii. Dr. Young's formula in Ijasttl on the 

 principle of taking into account the attraction of tlic table-lantl 

 exiHting between the .station antl the level of the sea, in reiiucing 

 the ohnervation to the sea level. On account of this atlrsction, the 



— J which gives the correction for elevation alone 



must be reduced in tlic ratio of I to 1 



, or 1 to .&') nearly, if 



ff = 2j, ^ = 5J. Mr Airy, observing that the value it i a j is n 

 little too snuill, and (J.. (IJ a little loo grcvt, has employed the 

 factor .(!, instead of .(III. 



t Ciiiii'iriih/r 1'hilo.miMeill yn/luv/ffio;!., Vol. vi. p. '.",1". 



