Mr. Ivory on the Figure of the Earth. 4 IS 



able quantity, as usually assumed, but a quantity decreasing 

 gradually from the pole to the equator. As this inference 

 which M. Biot has drawn from a comparison of the experi- 

 ments is opposed to the usual theory, and would lead us to 

 entertain new notions concerning the figure of the earth, it 

 seems important to examine the grounds of it with attention. 



In what follows I shall use the lengths of the pendulum in 

 M. Biot's paper without reducing them to EngHsh measures. 

 This will save calculation, and besides it has this advantage, 

 that all the pendulums are reduced to the level of the sea by 

 one uniform rule. If A denote the length of the equatorial 

 pendulum, and I the length at any latitude \, we shall have, 

 by the usual formula, 



I = A X (1 +/sin'x); 



from which we get, 



^ A sin2 X 



Now, having assumed some known value for A, if we begin 

 at the greatest north latitude, and substitute for I the succes- 

 sive observed pendulums, we shall obtain a series of values of 

 f which will show whether that coefficient is constant or vari- 

 able in the supposition of the assumed equatorial pendulum. 

 The formula must not be applied to latitudes less than 45°: 

 for in such cases, the difference of the pendulums in the nu- 

 merator is sensibly affected by the errors of observation ; and, 

 the effect of these being increased by the small divisor sin % 

 the results would be too irregular to lead to any certain con- 

 clusion. But we shall be able to form an opinion respecting 

 the new system advanced by M. Biot without going to lati- 

 tudes less than 45° ; because the whole decrease of the coeffi- 

 cienty from the pole to the equator attains half its magnitude 

 at the parallel of 45°. 



The last four columns of the following Table exhibit the 

 values of y for all the observed pendulums between the pa- 

 rallel of 45° and the pole, on the supposition of four different 

 equatorial pendulums, denoted by L, L', L", L'". Of these 

 L = 990"^"^-B^16 is the observed pendulum at Maranliam, re- 

 duced to the equator by a small deduction; L'= 990™™-9466 

 is the observed pendulum at Ilawak on the equator ; L" = 

 991'"'"*0270 is the mean equatorial pendulum adopted by 

 M. Biot; and L"'= 991'""'-1106 is the observed pendulum 

 at St. Thomas, on the equator. 



Table. 



