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

View transcription
                                formed of the measure of depression (including the effect
of the attraction of the water) considered as uniform.
The line of cliff may be considered as straight. Let
a be the distance from the pendulum station to the
straight line of cliff, measured perpendicularly to that
line: b the depth of the depression: let x <s>and y</s>
be parallel to a, and y parallel to the line of the cliff.
The matter d x δx x δy x b is at the distance (x<sup>2</sup> + y<sup>2</sup>)<sup>1/2</sup>
from the upper <s>and</s> station, and therefore its vertical
attraction on the lower station is d.b.c.δx.δy/(x<sup>2</sup> + y<sup>2</sup> + c<sup>2</sup>)<sup>3/2</sup> or
d.b.c.δx.δy/(x<sup>2</sup> + y<sup>2</sup>)<sup>3/2</sup> nearly. Integrating first with respect to y, from
-ꝏ to +ꝏ, we have 2d.b.c.δx/x<sup>2</sup>. Integrating
then  with respect to x, from a to ꝏ, we have
2d.b.c/a.

   These formulae will suffice for our purpose.
It is only necessary further to remark that, as
the unit of measure is absolutely arbitrary, and
as the numerical and graphical operators are a little
facilitated by using for unit the "depth of the mine",

                            
Please login to transcribe

Manuscript details

Author
George Biddell Airy
Reference
PT/54/5
Series
PT
Date
1855
IIIF
Open IIIF manifest
(What's this?)
This is a link to the IIIF web URL for this item. You can drag and drop the IIIF image link into other compatible viewers

Cite as

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

Copy

Comments

Please login to comment