118 



NOTES TO PRECEDING SECTION. 



Cassini had probably directed the attention of Newton to 

 the determination of its cause, and, consequently, to the 

 investigation of the true figure of the earth." Cassini 

 Stated the oblateness of Jupiter at -^^ in 1691 (Anc. M6in. 

 de I'Acad. des Sciences, t. ii. p. 108) ; but we know, through 

 Lalande (Astronom. 3me 6d. t. iii. p. 335), that Maraldi pos- 

 sessed several printed sheets of a Latin work which Cassini 

 began, "On the Spots of the Planets," from which it is ob- 

 TJous that Cassini was aware of the oblateness of Jupiter 

 previous to 1666 ; 21 years, therefore, before the appear- 

 ance of Newton's Principia. 



100 (p. 52.) — According to Bessel's investigation of ten 

 measurements of degrees, in which the error in the French 

 measurement discovered by Puissant was taken into account 

 (vide Schumacher, Astron. Nachr. 1841, No. 438, S. 116), 

 the semi-axis major of the elliptical spheroid of rotation 

 which comes nearest to the irregular figure of the earth is 

 3272077-14 toises ; the semi-axis minor is 326113933 toises ; 

 the oblateness, ■oifoVT^' ' ^^® length of the mean degree of 

 the meridian, 5'?()l"3-l69"' toises, with an error of + 2-8403 

 toises ; whence the length of a geographical mile comes 

 out 3807-23 toises. Earlier estimates of measurements of 

 degrees vary between -^^ and -^g^iy : thus, Walbeck, de 

 forma et magnitudine telluris in'deniensis arcubus meri- 

 diani definiendis, makes it 20'^'i'6 ^^ '^^^ ' ^^- Schmidt 

 (Lehrbuch der mathem. und phys. Geographie, S. 5), 

 ■g-gny^.y^ in 1829 from seven measurements of degrees. On 

 flie influence of great differences of latitude upon the polar 

 flattening, vide Bibliotheque universelle, t. xxxiii. p. 181, 

 and t. XXXV. p. 56 ; also, Connaissance des tems, 1829, p. 

 290. From the moon's equation alone, Laplace found, first 

 (Expos, du Syst. p. 229), from the older tables of Biirg 



S^.-g ; subsequently, from the lunar observations of Burck- 

 •dt and Bouvard -^^g^W.j (M6can. celeste, t. v. p. 13 and 

 43). 



101 (p. 52.) — Pendulum experiments, as general results, 

 have given, after the great expedition of Sabine (1822 to 

 1823, from the equator to 80° N. lat.), -^^\.y ; from Frey- 

 cinet (excluding the observations of He de France, Guam, 

 and Mowi), -o^-tt ; after Foster, -o^\-j ; after Duperrey, 

 Tj^C.y ; after" Liitke, irgq-n' -A-gainst these we have the 

 observations between "Formentcra and Dunkirk (Connais. 

 des tems, 1816), according to Mathieu, -^jiV-^ ! ^^'^ between 

 Formentera and Unst Island, according to Biot, tt^V-tt- Vi^e 

 Baily, Report on Pendulum Experiments, in the Memoirs 

 of the Royal Astronom. Society, vol. vii. p. 96 ; also Bore- 

 nius, in Bulletin de I'Acad. de St.-P6tersbourg, 1843, t. i. 

 p. 25. 



The first proposal to apply the length of the pendulum 

 to the determination of mass, and to take the third part of 

 the seconds pendulum as an universal pes horarius, or 

 standard measure for all nations, occurs in Huygens' Horo- 

 logium Oscillatoriurn, 1673, prop. 25. The same wish was 

 reiterated anew in a public monument raised under the 

 equator by La Condamine, Bouguer, and Godin. On the 

 beautiful marble tablet which I found uninjured in the quon- 

 dam Jesuits' College at Quito are these words : " Penduli 

 simplicis aequinoctialis unius minuti secundi archetypus, 

 mensurae naturalis exemplar, utinam universalis !" From 

 what La Condamine says, in his Journal du Voyage a 

 I'Equateur, 1751, p. 163, of passages unfilled up in the in- 

 scription, and a slight difference with Bouguer concerning 

 the numbers, I expected to have found notable diff'erences 

 between the inscription of the marble tablet and the state- 

 ment published at Paris. On carefully comparing them, 

 however, I only found two of any importance — " ex arcu 

 graduum 3J" instead of " ex arcu graduum plus quam tri- 

 um," and for 1742 the year 1745. This last statement is 

 singular, inasmuch as La Condamine returned to Europe in 

 Nov. 1744, and Bouguer had preceded him in June, and 

 Godin in July. The most necessary and useful correction 

 in the figures of the inscription would be that of the astro- 

 nomical longitude of the town of Quito (vide my Recueil 

 d'Obs. Astron. t. ii. p. 319—354). Nonet's latitudes, cut 

 into the Egyptian monuments, afford a more recent instance 

 of the danger of all solemn attempts to perpetuate erroneous 

 or ill-calculated results. 



102 (p. 52.)— On the increased intensity of attraction in 

 the volcanic islands, St. Helena, Ualan, Fernando de No- 

 ronha. Isle of France, Guaham, Mowi, and Galapagos, with 

 the exception of the island of Rawak, perhaps in consequence 

 of their vicinity to the high land of New Guinea, vide 

 Mathieu in Delambre, Hist, de I'Astron, au 18me siecle, 

 p. 701. 



103 (p. 52.) — Many observations also show great irregu- 

 larities in the length of the pendulum, which are ascribed 

 to local attractions (vide Delambre, Mesure de la M6ridien- 

 ne, t. iii. p. 548 ; Biot in the M6m. de. I'Acaddmie des Sci- 

 ences, t. viii. 1829, p. 18, 23). When we proceed from west 



to east in the south of France and Lombardy, we find tl>» 

 least intensity in the force of gravitation at Bordeaux ; th© 

 intensity increases rapidly in places situated to the east, 

 Figeac, Clermont-Ferrand, Milan, and Padua, in which last 

 city the maximum force is observed. The influence of the 

 southern flanks of the Alps is not merely to be ascribed to 

 the general magnitude of their volume, but as M. Elie de 

 Beaumont (Recher. sur les Revol. de la surf, du globe, 1830, 

 p. 729.) believes, in principal part to the melaphyre and 

 serpentine which have raised the chain. On the flanks of 

 Mount Ararat, which with Caucasus lies as it were in the 

 centre of gravity of the old world, consisting of Europe, 

 Asia, and Africa, Fedorow's careful pendulum experiment!* 

 proclaim not hollows, but dense volcanic masses (Parrot, 

 Reisp 2um Ararat, Bd. ii. S. 143). In the geodetic opera- 

 tions of Carlini and Plana in Lombardy, differences of from 

 20" to 47" -8 were found between the immedia!e observa- 

 tions of latitude and the results of these opersitions. Vide 

 the examples of Andrate and Mondovi, Milan and Padua, 

 in the Operations g6od6s. et astron. pour la mesure d'un 

 arc du parallele moyen, t. ii. p. 347 ; Effemeridi astron. di 

 Milano, 1842, p. 57. Milan estimated by Berne, as ir stands 

 in the French trigonometrical survey, is in latitude 45° 27' 

 52" ; whilst immediate astronomical observations make it 

 450 27' 35". As the perturbations extend far to the south 

 of the Po towards Parma (Plana, Op6rat. g6od6s. t. ii. p. 

 847), we may conjecture that even in the constitution of the 

 soil of the plain, there are causes producing deviations. 

 Struve has met with the same thing in the flattest parts of 

 the east of Europe (Schum. Astron. Nachr. No. 164). Oil 

 the influence of dense masses which are conceived to lie at 

 a moderate depth, corresponding with the point of mean el- 

 evation of the Alps, see the analytical expressions (after 

 Hossard and Rozet) in Comptes rendus, t. xviii. 1844, p. 

 292, which may be compared with Poisson (Traite de M6- 

 canique, 1. 1. p. 282, 2me 6d.) The earliest indications of 

 the influence of rocks of different kinds ou the vibrations of 

 the pendulum, are those of Dr. Thomas Young (Phil. Trans. 

 1819, p. 70—96). In the conclusions, from the length of 

 the pendulum in regard to the curve of the earth, the possi- 

 bility is not to be overlooked of the crust of the earth having 

 become consolidated before metallic and dense basaltic 

 masses, forced from the interior, had approached the surface, 

 104 -(p. 52.)— Laplace, Expos, du Syst. du Monde, p. 231. 



105 (p. 52.)— La Caille's pendulum experiments at the 

 Cape of Good Hope, which were calculated with great care 

 by Mathieu (Delambre, Hist, de I'Astr. 18me siec. p. 479), 

 indicate an oblateness of q-^V-T ' ^"* ^■''°™ numerous com- 

 parisons of observations under similar parallels of latitude 

 in both hemispheres (New Holland and the Maldives com- 

 pared with Barcelona, New York, and Dunkirk), there are 

 no grounds for estimating the mean o!)]ateness of the south 

 pole as greater than that of the north pole (Biot, in Mem. 

 de I'Acad. des Sciences, t. viii. 1829, p. 39—41). 



106 (p. 53.)— The three methods of conducting the obser- 

 vations, give the following results: 1st. From deflection of 

 the plumb-line in the neighbourhood of Shehallien in Perth- 

 shire, 4-713 by Maskelyne, Hutton, and Playfair (1774— 

 1776 and 1810) according to a method already proposed by 

 Newton ; 2d. From vibrations of the pendulum on mount- 

 ains, 4-837 (Carlini's observations on Mont Cenis compared 

 with Biot's observation at Bordeaux, Efl^emer. astr. di Mi- 

 lano, 1824, p. 184) : 3rd. From the torsion balance of Cav- 

 endish, after an apparatus originally imagined by Mitchell, 

 5-48 (from Hutton's revision of the calculation 5-32, and 

 from Ed. Schmidt's revision 5*52 : Lehrb. des mathem. 

 Geographaphie, Bd. i. S. 487) ; from the torsion balance of 

 Reich, 544. In the calculation of this experiment carried 

 througk in a most masterly manner by Prof. Reich, the 

 original mean result was 5-43 (with a probable error of but 

 00233) ; a result which, increased by the quantity by which 

 the centrifugal force of the earth diminishes the force of 

 gravitation, for the latitude of Freiburg (50° 55), must be 

 changed unto 5-44. The employment of masses of cast-iron 

 instead of lead gave no difference of result that might not 

 safely be ascribed to error of observation ; there was no ev- 

 idence of magnetic attraction (Reich. Versuche iiber die 

 mittlere Dichtigkeit der Erde, 1838, S. 60, 62, and 66). By 

 the assumption of too small a degree of oblateness of the 

 earth, and the uncertain estimate of the density of the rocks 

 composing its surface, a mean density of the earth was come 

 to, as in the experiments on mountains, which was by ^ too 

 small, viz., 4-761 (Laplace, M6can. c61. t. v. p. 46) or 4,785 

 (Eduard Schmidt, Lehrb. der. math. Geogr. Bd. i. ^ 387 

 and 418). On the hypothesis of Halley, on the earth as a 

 hollow sphere — the germ of Franklin's idea of earthquakes, 

 vide Phil. Transact, for the year 1693, vol. xvii. p. 563. 

 (On the structure of the internal parts of the earth and the 

 concave habited arch of the shell.) Halley held it more 

 worthy of the Creator " that the earth, like a house of sev- 

 eral stories, should be inhabited both within and without. 

 For light in the hollow sphere (p. 576) provision could also 

 be made in a certain way." 



