relation to the Constitution of the Earth's Crust. 21 



have to be accounted for. So that the theory of hydrostatic 

 equilibrium in this instance may be considered a not unsatis- 

 factory explanation of the phenomena. 



To understand what has been done, we observe that the 

 calculated effect of the local attraction of the parallelepiped is 

 absolute, not relative, supposing that there would be no local 

 attraction at the mean sea-level of a continental land-surface. 

 It ought therefore to be compared with an absolute quantity. 

 The 23*57 swings, given in column 7 of our Table, being the 

 difference between the effect due to height and mass at More 

 and that due to height alone, is also absolute. If, therefore, 

 we take the parallelepiped to roughly represent the plateau, 

 23-57— 4*15 = 19-42 is the absolute difference between the 

 effect of the plateau considered as supported by an excessively 

 rigid crust and by hydrostatic equilibrium. Thus far observed 

 vibration-numbers are not involved. 



When we consider these, we see that there were 1*67 more 

 swings at More than at Punnae. But without knowing what 

 the effect of local attraction is at Punnae, we can have no exact 

 knowledge of that which exists at More. If the number of 

 swings of a given pendulum at the equator at the surface of the 

 sea (but not subjected to the local attraction of an insular mass) 

 was known, knowing the number at Punnae, we could deduce 

 the absolute attraction there, and consequently at More also. 

 Here, however, we are at fault. 



Colonel Herschel has treated this question very fully in the 

 second Appendix to the i Account, &c.,' explaining that he 

 has adopted a novel method ; for, whereas local variations of 

 gravity had previously been treated by the method of least 

 squares, as if ihey were errors of observation, he has regarded 

 them as having a real existence ; and has obtained his equa- 

 tions for finding the vibration-number of a given pendulum 

 at the equator from the numbers observed at known stations, 

 on the two suppositions (1) that the mean of all observed 

 local variations should be zero, and (2) that the mean of those 

 in one narrow zone of north latitude should be equal to the 

 mean of those in the corresponding zone of south latitude. 



But, seeing that the local variations are calculated subject 

 to the attraction of the masses, and that the masses give very 

 different attractions according as they are treated as if sup- 

 ported by excessive rigidity of the crust, or by hydrostatic 

 equilibrium, it appears that the resulting equatorial mean 

 vibration-number obtained on the one supposition is not likely 

 to agree with that obtained upon the other. 



Colonel Herschel (Appendices, p. 45) makes local attraction 

 at Punnae = —4*2 swings. But if, by way of illustration, the 



