VARIATION OF RATE IN A TIME-PIECE* 27' 3 



inftrument, to exprefs the force of condenfation over and above 

 the common atmofpheric preflure; which force is (ignified in 

 the inftance above, by the fraction T T T , unity being the atmo- 

 fpheric preflure. If we denote the atmofpheric preflure by 30 

 inches of mercury, or 32 feet of water, then the force ^ in the 

 above example, will be exprefled by 2.727 inches of mercury, 

 or 2.9 1 feet of water ; and the like for any other inftance. 



If a mercurial inftrument of the above conftru&ion be pre- If mercury be 



ferred, it becomes neceflary to add the height of the mercurial ufed » lts denfitjs 



J ° . muftbeconfi- 



column to the force found as above : thus, if the condenfation dered in the 



of air be from 12 into 9 inches, then the addition to the force fhort inftru- 

 of the internal air in the tube is equal to -j-, or 10 inches of mer- 

 cury, to which muft be added the three inches raifed in the 

 tube, and the whole force will be 13 inches of mercury, exclu- 

 five of that of the atmofphere. 



This fort of inftrument or gauge ferves equally well for find- General apply- 

 ing the expanfive force of any kind of elaftic fluid, as for mea- tl0n t0 a11 safes * 

 furing the velocities with which they iflue out of the place of 

 their confinement. It may be applied to all kinds of bellows, 

 to condenfed fteam, and to the air pump. 



XII. 



On the Variation of Rate in a Time-Piece, as indicated by ths 

 Changes in the Arc of Vibration. In a Letter from Mr. 

 Ezekiel Walker. 



To Mr. NICHOLSON. 



S I R, Lynn, July 20, 1802. 



J? ROM what I have already mentioned in a former paper *, Expediency of 

 it follows, that in clocks ufed in making aftronomical obferva- frc q uent obfer 



rr r * m r va t ,Q n of the < 



tions, it is neceflary to oblerve the arc or vibration very fre- f vibration 

 quently, and when it is found different from that generally de- clocks « 

 fcribed by the pendulum, the rate of the clock muft on this ac- 

 count be corre&ed. 



To determine this correction, let x denote the time which a Rul . e for de * 

 pendulum, vibrating in an arc exceedingly fmall, will lofe ationln time"* 

 when made to vibrate in a larger arc of the fame circle, T the from' that of the 



arc. 

 * See pa. 76 of this vol. 



Vol. II.— -August, 1802. T number 



arc, 

 in 



