NEWTON S PRINCIPIA. 377 



must therefore be divided by the quantity between the 

 brackets. 



This expression has been deduced on the supposition 

 that the point of suspension remains fixed. In the Philo 

 sophical Transactions for 1831, Col. Sabine has pointed 

 out that this is not always the case. A further correction 

 in such cases is, therefore, necessary. 



.2 The effect of the resistance of the air must be allowed 

 for ; this is called the &quot; Reduction to a vacuum&quot; This 

 will be considered in the propositions that follow relative 

 to the motion of a pendulum in a resisting medium. This 

 correction consists of two parts, that for the buoyancy and 

 that for the inertia of the air. If m be the mass of the 

 pendulum, iri that of the fluid displaced. The effect of 

 buoyancy is clearly to decrease the acting force in the 

 ratio m m to m; and the effect of the inertia is to 

 increase the mass moved by xm 9 where x is a quantity to 

 be hereafter determined. The time is therefore increased 

 in the ratio 



m + x m ^ - 



m 



Let z be the ratio of the specific gravity of the medium 

 to that of the body, and let z be very small, then the 

 above is equal to 



the observed time of an oscillation must be divided there 

 fore by this quantity. 



3. The time of an oscillation, thus corrected, enables us 

 to find the length of the seconds pendulum at the place of 

 observation. This gives the force of gravity as affected 

 by the attraction of all the irregularities of the earth s 

 surface near at hand. To render the results obtained in 

 different places comparable with each^other, we must reduce 



