PEN 



3. To correct the going- of a clock. 



Let L present length of the pendulum, t" No. of seconds gained 

 or lost in the time T", jc quantity by which the pendulum must be 

 altered ; then 



-f- 2 L t" 

 A- = - ; - nearly. 



5. Let .r height of a mountain upon which a seconds pendulum lose-s 

 n" per hour ; then 



x n + TJ- miles nearly. 



6. If the force of gravity be slightly altered, to find the number of 

 seconds gained or lost in a day by a seconds pendulum, 



Let g force of gravity when pendulum vibrates seconds, 



N No. of seconds in a day, 



g (1 4. h) force of gravity when slightly increased, 

 t = seconds gained in consequence, then 



7. Given the number of vibrations (??) of a pendulum in air, to find th 

 number V in a vacuum. (Galbraith.) 

 Let in be the spec. grav. of the pendulum, that of air being 1 j then 



S. If n' be the number of oscillations performed in 24 hours by the ex- 

 perimental pendulum, n the true number, e the expansion for a change 

 of 1 Fahrenheit, t the standard temperature, and t' the observed j then 

 n n' + l / 2 n' e (t 1 t) 



9. To reduce the length of the pendulum from any height to the level 

 of the sea, the true length being denoted by I, the observed by /', the 

 .height above the sea by a, and the radius of the earth by r ; then 



Some allow one-third for the 'effect of the dense strata iimuediateh 

 under the pendulum, in which case 



4 a /' 



In a similar manner v ~ V -| -- o~r'- 



