At THE MADPvAS OBSERVATORY. 301 



graduated (as has been stated higlier up) at the temperature of 61"; 

 whereas the mural scale was constructed at that of 82° ; and for this 

 difference of 21°, we have on one foot 0.0025977, and for the length / 

 (= 36.6981) we have to add 0.00779 &c. 



so. To proceed, we had the length of the pendulum on a mean 



...... = ..... - ..,_ = ...... 39.6981 



Correction for temperature 4. 0.00779 



Corrected length of I. 39.70589 



Diameter of the ball ; d. . — 1.35692 



Length of the string / 38.34897 



Senli-diameter of ball ;r ....0 = .....- . ..... 0.6784,1 



Corrected length 7+ r 39 .OgZiig 



Hence expounding the formula, we have 



fll = . . . . 983.4091 

 3 ,. • ^ 



W. /+Th = 5701510.0 

 2r^= , . . . 0.1841 



Sum 57023'23.59S2 log. = 6.7560G607iS 



lii = . . . 38.4665 

 2 



W. I +ir = 1 46090. G0 G7. 



Sura 1461^29.0732 log. == 5.1647383975_ 



L :^ 39.023625 N. N. 1.5913276773 

 which length L is that of the simple pendulum isochronal to /. 



Sd. ■ -;.-,:;■ 



31 . To deduce, from the length L, that of a simple pendulum, striking 

 seconds of time. 



It is known to mathematicians, that if two pendulums vibrate in similar 

 arcs, the times of vibration arc in subduplicate ratio of their lengths. 

 Hence, if T = 1 ' ; t z= the time of one vibration of any pendulum ; and 

 X = tlic length of the simple pendulum striking seconds, wc have 



D 4. 



