On the Length of the Seconds Pendulum. 257 



conrormity with the theory of gravity, evidently indicates in the 

 terrestrial strata, a harmony which they conld only have acquired 

 in a state of primitive fluidity, a state which heat only could 

 have given to the whole earth. 



The difficulties which present themselves in the measurement 

 of the pendulum disappear, for the most part, when the same 

 pendulum is transported to diflerent points of t'ne terrestrial 

 surface. It may he said, indeed, that we thus obtain onlv the 

 relative lengths of the seconds pendulum in these different places; 

 but it is sufficient, in order to determine the absolute lengths, to 

 measure its length with care in one of these places. 



Of all t!ie measures of absolute length, that which we owe to 

 Borda appears to me to be the most exact. The little difference 

 Avhich the result of twenty observations offers, leaves no doubt 

 of the exactness of their mean result. By applying to them my 

 formula of probabihtv, I found that an error of a hundredth of a 

 millimetre wou'd iie an extreme improbabihty, if we were cer- 

 tain that tliere existed no constant causes of error. 



In examining with attention the ingenious apparatus of Borda, 

 a circumstance mav be noticed, the effect of which, although 

 very slight, is not to be overlooked in so delicate an inquiry. 

 The pendulum is suspended from a knife, the edge of which rests 

 on a li )ri/,ontal plane. It has been supposed, in calculation, 

 that the edge of this knife around wliich the instrument oscil- 

 lates, is of infinite fineness ; hut on examining it with a iiiicro- 

 scojje it presents the form of a demi-cylinder, the radius of which 

 exceeds a hundredth of a millimetre. One might at first be led 

 to believe tliat it would be necessary to add this radius to the 

 length of the pendulum ; but on reflection it may easily be'per- 

 ceived that this addition would be erroneous. The oscillation 

 takes place every instant around the point of contact of the cy- 

 linder with the plane, and this point varies incessantly; it is only 

 necessary therefore to make a calculation of the force which the 

 pendulum experiences from the action of the weight, and from 

 the friction of the knife upon the plane, in order to know the 

 correction due to the radius of the cylinder or edge of the knife. 

 In making this calculation, on the supposition that the knife 

 does not slide upon the plane, I come to this singular result; that 

 in place of adding the radius of tiie cylinder to the length of the 

 pendulum, it is necessary to subtract it. This correction is less 

 sensible, on the length of the pendulum, the longer the oscilla- 

 tions of the pendulum arc. In the experiments of Borda it is 

 reduced to a fourth of the radiu-* of the cylinder, while it exceeds 

 that radius in those of Messrs. Bouvard, Biot, and Mathicu, who 

 for this reason nuist have found, and did actually find, a length 

 of the seconds pendulum two hundredths of a tnillim'jire greater 



Vol.4y.No.228. >^/)n7 18l7. H than 



