[ 217 ] 
XII. On the Cause of the Discrepancies observed by Mr. Baily with the Cavendish 
Apparatus for determining the mean density of the Earth. 
By George Whitehead Hearn, Esq., of the Royal Military College, Sandhurst. Com- 
municated by Sir J. F. W. Herschel, Bart., F.R.S. 
Received February 11, — Read March 11, 1847. 
In the Fourteenth Volume of the Transactions of the Royal Astronomical Society 
will be found a full account of the Cavendish apparatus, and of the mode of expe- 
rimenting followed by Mr. Baily. It v/ill therefore not be necessary for me, in this 
place, to enter into any detail as to the different parts of the instrument, and the 
various precautions adopted in order to avoid that singular source of error c currents 
of air in the torsion box arising from unequal temperature,’ which had been disco- 
vered by Cavendish. It will be sufficient for me to state that all the arrangements 
are of a highly satisfactory kind, and that I am of opinion that no aerial currents 
could have existed in the torsion box. 
The deduction of the mean density of the earth from the observed vibrations of 
the balls influenced by the torsion force and the attraction of the masses, is founded 
on a mathematical theory of the motion of the balls given by the Astronomer Royal, 
Mr. Airy ; and as this theory is certainly insufficient to account for the discrepancies, 
it will here be necessary to give a brief sketch of it. 
The momentum of attraction of the masses and planks on the torsion rod and balls 
supposed to be in the zero position, is calculated. The weights or masses are all 
represented in grains, and one inch is taken as the unit of length. The momentum 
is called E. In deducing it, the portion depending on the attraction of the planks is 
obtained by supposing the masses of such planks to be collected in their axes. The 
moment of inertia is then found and called F. A modulus of attraction k is then 
^ x E 
assumed, so that — p— is the impressed angular accelerating force on the rod and 
balls in the zero position. 
The distance from the centre of motion to the centre of the balls is denoted by c, 
so that, if 6 be the very small arc described, cO is the space described in inches. 
Let m 2 d denote the force of torsion which is known to be proportional to the angle 
described, supposing the apparatus in a normal state ; or if we suppose it slightly 
out of order so as to rest at an angle a from the zero position when the masses are 
removed, m 2 (Q—a) will denote the force of torsion ; and it may also be conceived that 
the small force of attraction of the torsion box, &c. is included in this. 
2 F 
MDCCCXLVII. 
