of the Pendulum made hy Capt. Kater, M. Biot, ^c. 21 



correction to be applied for a variation in the lenofth of the 

 penduhim of one-tenth of an inch, or when it is increased from 

 39 to 39*1 inches; and is always to be added. By means of 

 these it is hoped the length of the pendulum can with suffi- 

 cient accuracy be more easily obtained than by using the la- 

 borious process of the squares of the numbers of oscillations, 

 as may be seen by the following examples. 



Capt. Kater found that his experimental pendulum at 

 London, in latitude 51° 31' 8" N., alter the proper reductions 

 made 86061*52 oscillations in a mean solar day at 62° Fah- 

 renheit ; while at Unst, in latitude 60° 45' 28" N., the same 

 pendulum, at the same temperature, made 86096*90 oscillations. 

 Required, the length of the seconds pendulum at Unst, that at 

 London being 3913929 inches? 



Number of oscillations at Unst . . . 86096*90 

 at London . . 86061-52 



Difference more 35^38~ 



Hence the seconds pendulum must be longer at Unst, and 

 the general correction must be added. 



Now by formula ( 1 ) A L = -7^- , which by substituting 

 the proper quantities stated above becomes 

 , 39-13929 X 35-38 



+ — 435i8i5— = +0-03216697 



Correction from table, col. 2, for 30°'- —470 

 Prop, part for 5°'-38, col. 3, . . . —197 

 Equation for 2d difference, foot of table, + 13 

 Correction for +0-13929, col. 4, — 2 



Amount —656 QSQ 



Total correction to be added . . . . + 0-03216041 

 Length of seconds pendulum at London . 39-13929 

 Length of the pendulum at Unst .... 39-17145 

 differing only one unit in the fifth decimal place from the de- 

 termination of Capt. Kater. 



In the application of the corrections of the formula, the 

 equation of second difference and that from column 4 are ap- 

 plied as they ought to be to the first part of the correction 

 from column 2, with contrary signs. Indeed, it is unnecessary 

 to carry them further than about five or six places of decimals, 

 being more than even the best observations can warrant, as may 

 be readily seen by comparing those of Kater and Biot at the 

 same place; as for example, at Leith or Unst. In fact, with- 

 out the small corrections, the formula in this case would have 

 given Kater's determination exactly. 



Again: Capt. Hall found that an experimental pendulum, 



