to be applied to the Length of a Pendulum. 359 



Let I' be the length as commonly estimated : that is, let 



Ic 



I - a + r + , . 

 a-\- r 



Then 





2ak* 



r {a + rf 



'^(V r/ r ) V r-(a + r)/ 



aTi^ k^ 



= —, — —-J nearly = -p- with sufficient accuracy for practice. 



The length of the simple pendulum which would vibrate in 

 a given observed time, is therefore greater than it is commonly in- 

 ferred from observations with tliis particular apparatus ; and con- 

 sequently the length of the- seconds' pendulum is greater than it 

 is estimated, in the same ratio. Let L be the length of the seconds' 



pendulum : then we ought to add to the estimated length „^ . 



In this investigation it will be observed that the consideration 

 of spherical form has not occurred : and that r is the distance 

 from the center of gravity to the point where the wire is firmly 

 attached to an inflexible part of the ball. If the ball be a sphere 

 of radius R, k" = ^ W, and the quantity to be added is 



25 ■ l^r ' 

 In Borda's experiments i = 12 feet = 1728 lines; R = 8 lines: 

 L = 440 lines : r was somewhat greater than R ; perhaps = 12 lines. 



Consequently the quantity to be added is about line: 



a quantity quite insensible. 



In Biot's experiments, the length of the wire was about 

 i that in Borda's, and therefore supposing the balls of the same 



