156 COSMOS. 



increase of forces of attraction (in the direction from the 

 equator to the poles) with respect to the figure of a planet is 

 dependent on the distribution of density in its interior. 

 Newton, from theoretical principles, and perhaps likewise 

 prompted by Cassini's discovery, previously to 1666, of the 

 compression of Jupiter,* determined, in his immortal work, 

 Philosophic^ Naturalis Principia, that the compression of the 

 Earth, as a homogeneous mass, was T ^-. Actual measure- 

 ments made by the aid of new and more perfect analysis have, 

 however, shown that the compression of the poles of the ter- 

 restrial spheroid when the density of the strata is regarded as 

 increasing towards the centre, is very nearly -^i-g-. 



Three methods have been employed to investigate the cur- 

 vature of the Earth's surface viz., measurements of degrees, 

 oscillations of the pendulum, and observations of the inequa- 

 lities in the Moon's orbit. The first is a direct geometrical 

 and astronomical method, whilst in the other two, we deter- 

 mine from accurately observed movements, the amount of the 

 forces which occasion those movements, and from these forces 

 we arrive at the cause from whence they have originated- 

 viz., the compression of our terrestrial spheroid. In this 

 part of my delineation of nature, contrary to my usual prac- 

 tice, I have instanced methods because their accuracy affords 

 a striking illustration of the intimate connexion existing 

 amongst the forms and forces of natural phenomena, and also 

 because their application has given occasion to improvements 



where I have shown that the opinion maintained by Delisle, Freret, and 

 Gosselin, that the excessive differences in the statements regarding the 

 Earth's circumference, found in the writings of the Greeks, are only ap- 

 parent, and dependent on different values being attached to the stadia, was 

 put forward as early as 1495 by Jaime Ferrer, in a proposition regarding 

 the determination of the line of demarcation of the papal dominions. 



* Brewster, Life of Sir Isaac Newton, 1831, p. 162. " The disco- 

 very of the spheroidal form of Jupiter by Cassini, had probably directed 

 the attention of Newton to the determination of its cause, and conse- 

 quently, to the investigation of the true figure of the Earth." Although 

 Cassini did not announce the amount of the compression of Jupiter (^th) 

 \ill 1691, (Anciem Memoires de I'Acad. des Sciences, t. ii. p. 108,) yet 

 we know from Lalande, (Astron., 3me ed., t. iii. p. 335,) that Maraldi 

 possessed some printed sheets of a Latin work, " On the Spots >of the 

 Planets," commenced by Cassini, from which it was obviofis that he wis 

 aware of the compression of Jupiter before the year Ki66, and therefore, 

 at least twenty-ona years before the publication of Newton's Principia, 



