Account of pendulum experiments undertaken in the Harton Colliery, for the purpose of determining the mean density of the earth, by G. B. Airy

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                                32 <s>34</s>. The number given by this table is the logarithm of
the mean rate of the Detached Pendulum upon the Clock
Pendulum under the actual circumstances of observation.
It is next required to investigate the correction to this
logarithm depending on the <s>[?]</s> extent of the arc of
vibration: on  of the conditions of the data of he problem
being, that the <s>center of the</s> arc is observed only at
the beginning and the end of the Swing.
     In the first place, to <s>[?]</s> compute the correction
to the logarithm, supposing the arc of vibration constant.
Let the whole arc of vibration, as seen upon the
scale of inches, be I. For the pendulum 1821,
suppose the scale to be placed 1 inch behind the
pendulum, and for the pendulum 8, 1.8 inch
behind the pendulum. <s>[?]</s>
<s>[?]</s> And suppose the distance
of the object glass of the observing telescope to be 100 inches.
Then the real whole arc of vibration is I x 100/101 for pendulum 1821
and I x 100/101.8 for pendulum 8. The lengths of
the two pendulums, from the knife-edge to the indicating
point of the tail, are respectively 60.7 and 60.2 inches.
Hence the proportion of the real whole arc of vibration to
the length of the pendulum is I x 100/101 x 60.7 for pendulum 1821
                            
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Manuscript details

Author
George Biddell Airy
Reference
PT/54/5
Series
PT
Date
1855
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Account of pendulum experiments undertaken in the Harton Colliery, for the purpose of determining the mean density of the earth, by G. B. Airy, 1855. From The Royal Society, PT/54/5

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