OF THE VIBRATIONS OF AN INVARIABLE PENDULUM. 231 



pressure of the gas was 30.120 inches : bemg a difference of 1.95 vibration per 

 diem, corresponding to a barometric difference of 29.248 inch, of hydrogen 

 gas : the temperature of the gas being 39°.75 in the compressed, and 40.72 in the 

 rarefied state. 



We have in this and the preceding experiment, data for deductions on three 

 distinct points : 1st, on the retardation occasioned by an atmosphere of hydro- 

 gen gas : 2nd, on the retardation occasioned by an atmosphere of common air : 

 and 3rd, on the comparative retardation in air and in hydrogen gas. 



1st. From the results of Exp. VIII, we have 1.95 vibr. per diem, correspond- 

 ing to 29.248 inches of the barometer of hydrogen gas ; whence 2 vibrations 

 per diem is the reduction to a vacuum for hydrogen gas of 40° under 30 inches 

 pressure : and the number of vibrations per diem of the pendulum in a vacuum, 

 derived from the vibrations in hydrogen gas, is 86316.95. 



2nd. We have the vibrations in a vacuum 86316.95, — the number in atmo- 

 spheric air 86306.39, = 10.56 vibrations per diem ; which is therefore the reduc- 

 tion to a vacuum for 30.1 13 inches of air at 41°.25. \ 



3rd. We have the ratio of the retardations occasioned by air and hydrogen 

 gas, both at 40° and under a pressure of 30 inches, as 10.55 : 2. 



Combining the Vllth and Vlllth Experiments, we have corroborative results 

 on the 2nd and 3rd points, from the vibrations in air and hydrogen gas on 

 the 9th and 10th of February. The pendulum in Exp. VII. made 86314.085 

 vibrations in hydrogen gas of 39°.32 under 30.192 inches pressure; equivalent 

 to 86314.085 -f- 2.01 = 86316.095 in a vacuum. The vibrations in atmo- 

 spheric air in the same experiment were 86305.57 ; Barom. 30.193 ; and tem- 

 perature of air 38.1 : whence the reduction to a vacuum for air of that tem- 

 perature, and under that pressure, is 86316.095 — 86305.57 = 10.525 vibra- 

 tions per diem. And tlie ratio of the retardations in air and in hydrogen gas, 

 both at 40°, and under 30 inches barometric pressure, is as 10.41 : 2. 



Bringing together the two results in regard to this ratio, we have 10.55 : 2 ; 

 and 10.41 : 2. Or generally, the retardation in air, is to that in hydrogen gas, 

 as 5| : 1 . Now the ratio of the densities of air and hydrogen gas being about as 

 13 : 1, if the resistance of the elastic fluids to bodies falling through them were 

 simply as the respective densities of the fluids, the retardation occasioned by 

 air should be 13 times as great as that occasioned by hydrogen gas. The dif- 

 ference of this ratio from that shown by experiment is greater than can well be 



