In _Nature_ for March 5 (p. 408) Prof. Mayer suggests an improvement in
our method of determining the mean density of the earth, from which it
appears that our plan has not been properly understood. This
misunderstanding, no doubt, has arisen from the incomplete description of
our method given in the _Nature_ (Jan. 15. p. 260) report of the
_Proceedings_ of the Berlin Physical Society, which report was probably
the only source of information accessible to Prof. Mayer. We are led
therefore to give a short description of our method.
Let H I K L represent a section of a cubical block of lead, about two
meters in the edge, and weighing 100,000 kilos. The balance, A B C, is
placed in the middle of the upper horizontal surface. It bears the
scale-pans, D and E. Under these scale-pans the block is bored vertically
through, and two other scale-pans, F and G, are suspended below the
block, attached to the balance by means of rods passing through these
openings.
A weight D is brought into equilibrium by weights in G. The weight in D
is acted upon by the earth's attraction + that of the block, and that in
G by the earth's attraction - that of the block. The weights in G are then
greater than that in D by twice the attraction of the block. The weight
in D in now removed to F, and counterbalanced by weights in E. The weight
in E will be less than that in F by twice the attraction of the block.
The difference of the two weighings gives therefore four times the
attraction of the block. A correction must be introduced for the
variation in the earth's attraction due to the different heights of D, E
and F, G.
[Illustration]
In order to obtain as great a deflection of the balance by the method
suggested by Prof. Mayer, each of the mercury spheres must exert the same
attraction as our lead block. This would require spheres having radii of
about one meter. The length of the beam of the balance would be
necessarily at least two meters. Besides, each mass of mercury, would
exert some attraction on the weight on the other side, and thus lessen
the deviation of the balance.
The method given by Prof. Mayer, except for the suggested employment of
mercury, is then no improvement on ours. If we should use mercury, we
would construct a cubical vessel to contain it, and use it as we propose
to use the lead block. The advantage of using mercury is, however,
counterbalanced by the difficulty of obtaining it in such large
quantities as would be necessary.