59 



FIGURE OF THE EARTH. 



tion of density in its exterior. If Newton, upon 

 theoretical grounds, and also excited to the in- 

 quiry by Cassini's discovery of the flattening 

 of Jupiter's poles in 1666("), determines the 

 flattening of the earth as a homogeneous mass 

 at aSTf^h, in his immortal work, the Principia, 

 actual admeasurements, under the influence of 

 the new and more perfect analysis, have shown 

 that the oblateness of the earth's spheroid, the 

 density of the strata being assumed to go on 

 increasing towards the centre, amounts to 3^,^th 

 very nearly. 



Three methods have been employed to deter- 

 mine fundamentally the curvature of the earth's 

 surface : measurements of degrees, pendulum 

 experiments, and certain inequalities of the 

 moon's orbit. Thg first of these methods is an 

 immediate geometro-astronomical one ; in the 

 other two, conclusions are drawn from care- 

 fully observed motions, in regard to the forces 

 which occasion these motions, and, from these 

 forces, in regard to their causes, viz. the ob- 

 lateness of the earth in its polar axis. I have 

 here, in the general picture of nature, referred 

 exclusively to the application of these methods, 

 because their certainty reminds us forcibly of 

 the intimate concatenation of natural phenom- 

 ena in their forms and forces, because this ap- 

 plication has itself become the happy occasion 

 of improving all our instruments, whether op- 

 tical or those that are employed in the meas- 

 urement of space or of time — the very founda- 

 tion of astronomy and mechanics in reference 

 to the moon's motions, and the determination 

 of the resistance which the oscillation of the 

 pendulum experiences — and because it has even 

 served to open up peculiar and untrodden paths 

 to analysis. After the researches on the par- 

 allax of the fixed stars, which led to the dis- 

 covery of aberration and nutation, the history 

 of the sciences presents us with no problem 

 second in importance to that in which the re- 

 sult sought is a knowledge of the mean oblate- 

 ness of the earth, and the certainty that the 

 figure of our planet is not a regular one. In 

 none of the long and laborious ways by which 

 the goal is attained in scientific investigations, 

 is higher general cultivation, or more perfect 

 knowledge of mathematical and astronomical 

 science required than in this. The comparison 

 of eleven measurements of degrees, among 

 which three extra European — the old Peruvian 

 one, and two East-Indian— are included, cal- 

 culated in conformity with the severe theoret- 

 ical requirements of Bessel, has given ^^p^th 

 as the measure of oblateness of the polar di- 

 ameter of the earth('"'>). From this it appears 

 that the polar semidiameter is 10,938 toises^ 

 about 2j geographical miles, shorter than the 

 equatorial semi-diameter of the elliptical sphe- 

 roid of rotation. The bulging under the equa- 

 tor, therefore, in consequence of the curvature 

 of the surface of the spheroid in the direction 

 of gravity, comes to something more than 4f 

 times the height of Mont Blanc, only 2^ times 

 the probable height of Dhawalagiri, in the Him- 

 alaya range. The moon's equation, in other 

 words the perturbation in longitude and lati- 

 tude of the moon, from the latest researches of 

 Laplace, give nearly a similar degree of oblate- 

 ness as the measurement of degrees of the me- 



ridian—viz. 2^^th. Experiments with the pen- 

 dulum indicate a much more considerable 

 amount of flattening— viz. 2oth(^"). 



Galileo, when a boy, during divine service^ 

 and somewhat inattentive to the matter in 

 hand, as it would seem, perceived that the 

 whole height of a roof might be ascertained 

 from the dissimilar times in which chandeliers, 

 suspended at different elevations, oscillated ; 

 but he certainly did not imagine that the pendu- 

 lum would one day be carried from pole ta 

 pole, with a view to determine the figure of the 

 earth ; or rather to afford evidence of the 

 length of the seconds-pendulum being affected 

 by strata of the earth of unequal density. Theser 

 local attractions are complex, undoubtedly ; but 

 over extensive districts of country they show 

 themselves almost identical in point of amount. 

 These geognostic relations of an instrument 

 for the measurement of time; this peculiar 

 property of the pendulum to act a» a plumb-line, 

 and give us intelligence of the unseen deep, 

 even in volcanic islands('*^), and on the acclivi- 

 ties of uplifted continental mountain chains("^), 

 to indicate dense masses of basalt and melam- 

 phyx instead of caverns, combine to render dif- 

 ficult, despite the wonderful simplicity of the 

 method, the attainment of any general result 

 as to the figure of the earth from observations 

 on the oscillation of the pendulum. Even in 

 the astronomical part of the measurement of a 

 degree of latitude, the occurrence of mountain 

 masses, or of denser strata in the ground, have 

 a disturbing and prejudicial influence, although 

 not to the same extent as in pendulum experi- 

 ments. 



As the figure of the earth exerts a powerful 

 influence on the motion of other planetary bod- 

 ies, especially on that of her immediate satel- 

 lite, so, on the other hand, does the very per- 

 fect knowledge we possess of the motion of 

 the moon enable us to draw counter-conclu- 

 sions in regard to the figure of the earth. From 

 this, as Laplace(^"^) has significantly observed, 

 might an astronomer, " without leaving his ob- 

 servatory, by a comparison of the lunar theory 

 with positive observations, determine, not only 

 the figure and magnitode of the earth, but far- 

 ther, its distance from the sun and from the 

 moon ; results which have only been obtained 

 by long and toilsome journeys undertaken to 

 the remotest countries of either hemisphere.'* 

 The oblateness which has been deduced from 

 the inequalities of the moon has this advantage, 

 possessed neither by single measuremeBts oi 

 degrees nor pendulum observations, that it is a 

 MEAN applicable to the whole planet. Contrast- 

 ed with the velocity of rotation, it informs us, 

 moreover, of the increase of density of the 

 earth's strata from the surface towards the 

 centre ; an increase which the comparison of 

 the relation of the axes of Jupiter and Saturn 

 with their periods of rotation also reveals in 

 both of these great planets. In this way does 

 knowledge of mere external configuration fead 

 to conclusions in regard to the internal consti- 

 tution of the heavenly bodies. 



The northern and southern hemispheres ap- 

 pear to have nearly like curvatures under equal 

 parallels of latitude(^°*) ; but pendulum experi- 

 ments, and measurements of degrees of the 

 meridian, give such different results in refer- 



