DEPENDANT ON THE ARC OF VIBRATION, 275 



The ufe of this table will be eafily underftood by the follow- 

 ing examples. 



EXAMPLE I. 



Suppofe a clock goes mean folar time when the pendulum Examples* 

 Vibrates 2° on each fide of the perpendicular, what will it lofe 

 per day when the pendulum vibrates through an arc of three 

 degrees ? 



Againft 2° and 3° in the firft column, we have 6,"Q and 

 1 4/8 refpeftively in the fecond column. Then 14,"S — 6/6 

 = 8,''2 = the time loft per day. 



EXAMPLE II. 



Suppofe a clock gains l" per day, when the pendulum vi- 

 brates 1° 49' on each fide of the perpendicular, what would 

 be its rate when the pendulum vibrates 1 ° 5 1 '? 



Between 1°J and 2° in the firft column, we have /'107 in 

 the fourth column. Then 1''— ,"107 x 2 =.0/'786 = tli« 

 daily rate of the clock gaining. 



I am, with refpect, 

 Sir, 



Your humble fervant, 

 E. WALKER. 



ANNOTATION. 



The arc of vibration in clocks is likely to be affected in Whether theory 

 practice by changes in the dcnlity of the air, in its tempera- can be # a PP]. iedto 



tin engine io 



ture, and in the action of the firft mover; and thefe caufes will compounded as a 

 moft probably afford refults confiderably different from thofe clock > &c * 

 inferred from the fimple pendulum in vacuo. I take it to be 

 experimentally afcertained by the regifters of the performance 

 of aftronomical clocks very firmly fixed, that the gridiron pen- 

 dulum, with a very flexible fpring fufpenfion, is not fenfibly 

 affected during the different ftations of the barometer and ther- 

 mometer ; and I apprehend that the firft mover, if a weight * 

 muft operate either with a conftant force or with periodical 

 variations, occafioned by the train or mechanifm through which 

 its action is tranfmitted, the influence of oil, &c. which periods 

 are rendered fhorter by the well known methods of difengaging 

 the efcapement, or parts neareft the pendulum. Many other 

 confiderations will offer themfelves to the learned author, as to 



T 2 the 



