Vibrations of Heavy Bodies. 91 



abandoning the term Calculation, because pebbles are no longer 

 used in the operations of arithmetic. 



It may be proper for me to observe, that circular excess is 

 not noticed by Sir Isaac Newton, in the sixth section of the 

 second book of the Principia, treating De Motu et Resistentia 

 Corporum Finiipendulorum. 



And I may add that neither the resistance of media, nor 

 friction have any power to change the isochronism of an whole 

 vibration, so long as these retarding causes continue so small, in 

 comparison with the action of gravity, as to render their second 

 powers insensible ; since the lengthened time of descent will 

 be exactly compensated by the diminished time of ascent. 



But the specific gravities of media affect both parts of a 

 vibration in the same way. 



Let G =: the specific gravity of the pendulum. 



f/ = that of the medium, then -li- the loss of weight; 



G 



and since the times are inversely as the square roots of the 

 weight, the analogy will be as /i 9 : aJ I :: I : 



A/ Q 



— ^xx/Vion " ic vfrv cmi^in tn ] -J- »' 



y 



i-iL 



G 



=. (when JL is very small) to 1 + 



^ G ^ 2G 



Suppose the pendulum made of brass with a specific gravity 

 8.4, and that it vibrates in air the specific gravity of which, at a 



mean, is : then will —^^ — = , and this multiplied 



' 828 2G 13910 ^ 



by 86400, the number of seconds in 24'', will give a differ 

 ence of 6".2 between vibrations in a vacuum, and in air at the 



2 

 ordinary state of the atmosphere ; or — ths of a second for 



each variation of an inch in the barometer ; a quantity, as it 

 would seem, not to be neglected in the present highly-advanced 

 state of practical astronomy, whenever confidence is placed 

 for any considerable interval, in the steadiness of the clock ; 

 aad which, if it were carefully applied, would probably be 



