Figure y Rotation, and PrejeSlton of tht Earth. 39 



XII. 



ExtraEis from the Syfeme dti Monde of M. La Place *. 



J. H I S work of La Place explains the leading points of the fyftem of the world. It is 

 as it were an abllraft of a large work, in which this profound geometer propofes to treat 

 the fame objcfls by the principles of the moft fublime geometry, and which he promifcs 

 foon to publifh. I fliall copy fome of the refults of this author. 



" The degree meafured at the Cape of Good Hope in 37" fouth latitude f, is found to 

 be 307999,8 feet, which is very nearly the fame as the degree of France, under the parallel 

 of 50", and greater than that which was meafured in Pcnnfylvania, at the latitude of 43° 56, 

 of which the length is no more than 307195,2 feet. The degree of the Cape is alfo 

 greater than the degree meafured in Italy in the latitude of 47'' 80, which was found to be 

 307680,6 feet. Neverthelefs it ought to be fmaller than every one of thefe degrees, if 

 the earth were a regular folid formed by the revolution of a meridian perfectly alike on 

 each fide of the equator. Every fa£t leads us to conclude that this is not the cafe." V9I. I. 

 page 105. 



He concludes, that the terrcftrial meridian is a line of double curvature. 



" Terreftrial bodies fituated under the equator defcribe, by virtue of the rotation in each 

 fecond of time, an arc of 40" 1395 of the circumference of the terreftrial equator. The 

 radii of this equator being 19634778 feet very nearly, the verfed fine of this arc is 

 0,0389704 feet. Gravitation caufes bodies to fall at the equator through a fpace of 

 1 1,23585 feet in one fecond. The central force neceffary to retain bodies at the furface of 

 the earth, and confequently the centrifugal force arifing from its rotatory motion, is to gra- 

 vity at the equator in the proportion of i to 288,3. The centrifugal force diminifhes the 

 weight, and bodies do not fall at the equator but by virtue of the difference of the true 

 force. If we therefore ufe the word gravity to denote the total weight which would take 

 place, exclufively of the diminution it undergoes, the centrifugal force at the equator is 

 extremely near -j^?*^ P'*'"' ^^ gravity. If the rotation of the earth were 17 times more 

 rapid, the arc defcribed in a fecond at the equator would be 17 times greater, and its verfed 

 fine would be 289 times more confiderable. The centrifugal force would then be equal to 

 gravity, and bodies would ceafe to prefs or weigh towards the earth at the equator."^ 

 Page 263. 



•• To explain the double motion of rotation and progreflion in the earth, it is fufficient 

 that the fuppofition be admitted of the primitive impulfe having been given at a fmall 

 diftance from its centre of gravity -, which diftance, fuppofing the planet to be homogeneous^ 

 muft have been nearly the -rs-d'h part of its radius." Page 299. 



" The probability is infinitely fmall, that the original projedionof the planets, fatellites, 

 and comets, ftiould have pafled through their centres of gravity. All thefc bodies muft 

 therefore have a rotative motion. From a fimilaf reafon, the fun, which turns on its axis,, 

 muft have received an impulfe, which not having pafled through its centre of gravity, car-^ 



* Expofition du Syftcme du Monde, par Pierre Simon La Place, de I'lnilitut National de France et du Bureau 

 dcs Longitudes, z vol. in Svo. A Paris de I'lmprimeric du Cercle Social, Rue du Theatre Franjois, No. 4, — I 

 have not the work, but tranflate from Dr. Lametherie, in the Journal de Pbyfique, Auguft 1794. 



'jr The autUer divides tJK circle into 400 parts. 



ties 



