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.
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.
Berlin, Physical Institute of the University, March 15.