of the Figure of the Earth, 413 



= 1— 3G( ^— y? ), neglecting small quantities of the second 



order. 



Hence 3G is the quantity which measures the ratio in which 

 gravity is diminished between the equator and the poles by this 

 change of distribution. 



7. Suppose the earth's mass to be divided into five portions, 

 viz. four shells each 800 miles thick, and a central nucleus of 

 800 miles radius. I will proceed to find the numerical value of 

 3G for each of the three shells between the outer shell and the 

 central nucleus. 





2 a 5 



Substituting in this the values found in paragraph 5, and put- 

 ting e= ^q7 (the value given in the volume of the British 



Ordnance Survey) and m= jr^r, we have for the first shell 



G = 0-00053, for the second shell G = 0-00018, for the third shell 

 G = 0-00003. Thus the three values of 3G in these three cases 

 are 0-00159, 0*00054, and 0*00009. 



The increase of gravity, in the actual state of the earth, in 

 passing from the equator to the poles is 0*00518*. Hence the 

 change of distribution of the materials in the above three cases 

 would produce a decrease of gravity in passing from the equator 

 to the poles, bearing the following ratios to the actual and known 

 increase of gravity : — 



0-00159 0-00054 0-00009 



0-00518' 0-00518' 0-00518' 



or T %ths, yLth ; and g^th. 



The highest northern station at which pendulum experiments 

 have been made is Spitzbergen. There 214 more vibrations are 

 made by a seconds' pendulum in 24 hours than at the equator)". 

 In the three cases under consideration these would be diminished 

 by 64, 21, and 3J vibrations in the course of the day. The first 

 and second of these would be very easily detected, though per- 

 haps not the third, at so great a distance as Spitzbergen is from 

 the equator, considering the difficulty of comparing the pendu- 

 lums at the two places or transferring the pendulum from one 

 place to the other without injury. The first and second, 

 however, fully answer my purpose. They show how' sensible 

 a change would be produced in the variation of gravity by 

 the slight alteration which I have suggested as a first test. 



* See Humboldt's ' Cosmos/ vol. iv. part 1, p. 4G8. 

 t Ibid. p. 469. 



