475 
A PENDULUM FOR THE REDUCTION TO A VACUUM. 
and a proper correction has, in each case, been applied to the arc for the pro- 
portion which this distance bears to the distance of the telescope from the pen- 
dulum. The values in the Table are the readings thus corrected. 
All the pendulums have been reduced to a common standard of temperature, 
which I have assumed equal to 62°. As I had no means of determining the 
expansion of the different metals, I have adopted such as I have considered 
most worthy of confidence. Any error arising from this source can be but 
trifling ; as no considerable change of temperature has ever occurred during 
any two consecutive experiments. In the suspension by the iron and silver 
wire, I have taken into account the small piece of brass rod (about 1^ inch,) 
attached to the knife edge, and also the radius of the sphere. The following- 
are the assumed rates of expansion for 1° of Fahrenheit’s thermometer : viz. 
Iron wire, &c. = '000006666 
Iron bar = *000006850 
Copper bar = *000009444 
Brass bar = *000010000 
Silver wire, &c. = *000010600 
The rate of expansion being denoted by e, the formula for the correction of 
the number of vibrations, on account of the temperature, will be 
N X Ae(*°-62°) 
where f denotes the mean height of the thermometer, during the interval of 
the coincidences. The mercurial pendulum (No. 39,) and the wooden rod 
pendulums (No. 40 and 41,) being compensation pendulums, do not require 
any correction for temperature. 
For determining the temperature I have always used two excellent standard 
thermometers, made under Mr. Troughton’s immediate inspection. These 
are placed inside the vacuum apparatus*; one of them on a level with the axis 
of suspension, and the other on a level with the centre of oscillation of the 
inclosed pendulum : the lower one can be read through the glass window of 
* In a few of the experiments, before I had contrived a method of suspending the lower thermo- 
meter in the inside of the tube, it was placed in a similar position (as to the centre of oscillation) on 
the outside. The inner thermometer however has, in all such cases, been used in the reductions ; 
adding - 05 to the mean height : this being half the quantity by which the outer thermometer ex- 
ceeded the other. 
