WEIGHT. 



Let L be ihe length of the pendulum at the equator ; 

 for another latitude, it will be L + a fin.' H, fo that a is 

 theexcefs of t!ie polar pendulum above the equatorial pendu- 

 lum, H being the latitude of the place. 



Let m and n be the two pendulums obferved in two very 

 different latitudes. 



m = Li -f- (7 fin.' H, 

 n = L + a fin.' H', 



- n = a (fin.' H - fin.' H') = a fin. (H - H') fin. 



(H + H') : hence a = — ■ " ~ " 



^ ^ ^ fin. (H - H') fin. (H + H')- 



If there be a greater number of fimilar equations, put in 

 each the numerical value of fin.- H, and determine the two 

 conftant quantities, L and a, by the fum of the obfervations, 

 employing, if you think proper, the method of the fmaller 

 fquares. 



Now the ellipticity is proved to be 0.00865 '-- We 



have then a value of the ellipticity, which may be compared 

 with that of the degrees. It was in this manner that M. 



Mathieu found the ellipticity to be -, by the fix ac- 



298.2 



tual meafurements of the pendulum made on the meridian 

 from Dunkirk to Formentera. So far Delambre. 



From the above equations and formula it is manifeft, that 

 if L, the length of the equatorial pendulum, and a, the dif- 

 ference between it and the polar pendulum, be known, all 

 other queftions connefted with the fubjeft may be accurately 

 determined j and hence it is, that the important problem of 



meafuring the pendulum has long engaged, and dill con. 

 tmues to command the attention of the firft aftronomers in 

 Europe. 



Laplace, in the Mecanique Celefte, gives the following 

 values of L and a; viz. o'".99o63i63i 4- o™. 005637 

 fin.' latitude, from which formula the lengths of the pen- 

 dulum may be computed in all latitudes ; but the fame 

 learned author has recently publiftied another formula in the 

 Connoiffance des Tems (1820, page 442), which is thus 

 given. 



" Mathieu, by a new difcuffion of all the obfervations of 

 the pendulum, in ufing the refults of Borda's experiments 

 reduced to the level of the fea, finds the following expreffion 

 of the length of the pendulum, 



o"". 990787 + o'".oo53982 fin.= latitude. 



" In this expreffion I have diminifhed by the two-thou- 

 fandth of a millimetre the refult of Borda upon this length, 

 for the correAion of the radius of the cylinder, which formed 

 the knife edge ; a radius which I value at eight thoufandths 

 of a millimetre. 



" The experiments now about to be made with particular 

 oare, in the two hemifpheres, will fhed new light on the co- 

 efficient of the fquare of the fine of the latitude, or on the 

 variation of weight on the furface of the earth." 



From the above formula we have computed the following 

 table, and have found the earth's ellipticity to be ~-'-j. By 

 this alfo the increafe of the weight of a body from the 

 equator to the poles is tJ-b of the whole, wherfas that de- 

 duced from the Mecanique Celefte is -rf,-, which propor- 

 tion has been adopted by Poiflbn, Biot, and other writers 

 on the fubjeft. 



Table ffiewing the comparative Weight of Bodies on different Parts of the Earth's Surface, with the proportional 

 Length of the Seconds Pendulum, and alfo its daily Number of Vibrations in each Latitude : fuppofing it corred 

 at the Greenwich Obfervatory, that is vibrating 86400 Seconds in 24 Hours. 



In 



