70 Davies Gilbert, Esq., on the 



tremes, they were so good as to do so ; and I learnt, with much 

 surprise, that neither at Greenwich nor at Dublin had the expected 

 variation of rate taken place. 



It has been demonstrated by Sir Isaac Newton, that small 

 changes in the resistance to oscillatory bodies do not by their 

 direct action cause any variation in the times of vibration, since 

 the ascending and descending semivibrations compensate each 

 Other ; but increased resistance reduces the arc, where the main- 

 taining power is constant; and, consequently, it reduces also the 

 circular excess, so that an increased resistance thus indirectly 

 accelerates the time of vibration. This circumstance has been 

 noticed by various writers, and had not escaped my attention; 

 but the quantity seemed so very small as to be wholly evanescent, 

 in comparison even with the minute change of time assignable 

 to buoyancy. On submitting it, however, to calculation, the result 

 proved very different. 



Let h express in barometncal inches the density of the atmo- 

 sphere. 



Then since the resistance experienced in moving through any 

 space, is proportionate to the space itself, to the velocity, and to 

 the density of the medium : and in the cycloid, or in small circular 

 arches, the space and the velocities of semivibrations are propor- 

 tionate to each other : 



If R be put for the resistance, 

 and z for the arc, 

 R = Az 2 . 



But resistance is evidently equal to the maintaining power, con- 

 sequently hz 2 is constant ; and therefore 



z 2 h s= 2hzz, or zh He 2hz, and z ie z x — - 



2/ t 



whence it appears that in different arcs the variation of the lengths, 

 occasioned by a given variation of the barometer, is proportionate 

 to the arcs themselves. 



Now the circular excess in any small circular arc is T ^th part of 

 the. arc squared. (See page 10 of the paper referred to.) Whence 

 the variation of this excess ; or the fluxion of the time (t) cor- 

 responding it h h, will be 



