# Majoranas Analysis and Experiment

In his second series of experiments concerning the absorption of gravitation, Majorana tried to decide whether gravity was due to something emitted from the Earth (his own hypothesis), or something coming to the Earth from space (such as Le Sage's corpuscles). He supposed that in the first case the weight of the test body would be decreased by a screen placed between the Earth and the test body, but not if the screen were placed above the test body. In the second case, the converse would be true.

Let us suppose two bodies A and B attracting each other. According to the first model [Majorana's hypothesis], when one puts a third body C between them, the original attractive force would be diminished, because some of the particles travelling between A and B would be absorbed by C. In the case of the second model [Le Sage's hypothesis], the attraction of A towards B is explained as the reciprocal protection or shielding action of these masses against the collisions of the energetic particles that come from distant places of the universe, from all directions. If the third body C were a shield external to both masses A and B, it would produce a reduction of the attractive Fig. 1 - When the Earth B attracts a test body A placed between two thick plates C and C' the weight of this body should decrease, due to gravitational absorption. Majorana claimed that, according to Le Sage's hypothesis (gravitational rays coming from space) only the plate above the test body should produce gravitational absorption, and that, according to his own hypothesis (gravitational rays emitted by the Earth) only the plate below the test body should produce gravitational absorption.

Fig. 1 - When the Earth B attracts a test body A placed between two thick plates C and C' the weight of this body should decrease, due to gravitational absorption. Majorana claimed that, according to Le Sage's hypothesis (gravitational rays coming from space) only the plate above the test body should produce gravitational absorption, and that, according to his own hypothesis (gravitational rays emitted by the Earth) only the plate below the test body should produce gravitational absorption.

force between them, because some of the particles would be captured by C. One may also see that even when the shield is not closed this reduction would occur, although in a lesser measure. Therefore, according to Le Sage's hypothesis, even putting the three bodies in the order A B C, this would engender a diminution of the attractive force between A and B; however, this diminution would only occur, according to the first model, if the three bodies are placed in the order A C B (Majorana, 1921-1922, p. 78).

Majorana attempted to choose between the two hypotheses by comparing the weights of a test body when placed above and below a massive lead shield.

Suppose that B is the Earth and A is a test body (Fig. 1). According to Le Sage's theory, the gravitational force acting upon A is produced by gravitational rays coming from all directions of space. The Earth reduces the flux of upward gravitational rays reaching A, and the excess of downward gravitational rays produces the resultant force acting upon A—its weight.

According to this hypothesis, we would expect that a thick material plate C put above A, besides attracting A, will also reduce its weight because it will act as a gravitational shield, reducing the flux of gravitational rays coming from space and pushing A toward B. On the other hand, according to Le Sage's hypothesis, we would expect that a similar plate put in position C', between A and the Earth, will attract A and increase its weight, but will not decrease the force produced by the Earth, because it will not reduce the flux of gravitational rays coming from space and reaching A.

Conversely, according to Majorana's hypothesis, we would expect that when the plate is put between A and B (position C') its gravitational absorption will decrease the force produced by the Earth upon A, but no effect should exist when the plate is in position C.

Fig. 2 - In his attempt to choose between Le Sage's and his own hypotheses, Majorana compared the weight of a test body in three positions: at the centre of a lead cube (1), below the cube (2) and above it (3).

To check the hypotheses, Majorana measured the weight of a small test body when it was (1) at the centre of a lead cube; (2) 5 cm below the cube; and (3) 5 cm above the cube (Fig. 2).

The test body was a lead sphere weighing 1.274 kg. The sides of the lead cube, built of lead bricks, measured 95 cm, and its weight was 9,616 kg. In a series of ten measurements, Majorana observed that when the test body was at the centre of the lead cube its weight suffered a reduction amounting to 0.00201 mg, with a standard deviation of 0.00010 mg (Majorana 1921-1922, p. 144). Notice that the standard deviation is about 10-10 of the mass of the test body. Majorana was unable to measure the mass of the sphere with this precision. He could only measure very small mass changes.

The gravitational attraction of the lead cube, computed according to the Newtonian theory of gravitation, was about 0.217 mg—that is, about 100 times the weight change observed when the test body was at the centre of the cube (Majorana, 1921-1922, p. 222). Therefore, if there were no gravitational absorption, the test body would suffer equal weight changes when it was placed above and below the cube: its weight would increase by about 0.2 mg above, and would decrease about 0.2 mg below the lead cube.

When Majorana put the test body above the lead cube he observed a weight increase of about 0.2 mg, and when the test body was below the lead cube there was a weight reduction of about 0.2 mg. The two changes were not exactly equal, however. Comparing eight series of measurements, Majorana arrived at the result that when the test body was below the lead cube its weight change was about 0.004 mg larger than when it was above the cube (Majorana, 1921-1922, pp. 223-5, p. 343). That difference was twice the weight reduction of the test body when it was at the centre of the lead cube (0.002 mg).

Majorana's conclusion was that the first hypothesis is the correct one, that is, gravitation is produced by gravitational rays emitted by the attracting bodies, and not by rays coming from space (Majorana 1921/22, p. 79). This experiment is inconclusive, however. Indeed, according to both hypotheses, the change of weight of the body below the cube should be greater than its change of weight above the cube. This can be shown by the following argument.

According to Majorana's own hypothesis (gravitational rays emitted from the Earth), when the test body is above the lead cube (position 3), its weight W would increase by F (the attraction of the cube) and would decrease by f (the absorption of gravitational attraction of the Earth). When the test body is below the lead cube (position 2), its weight W would decrease by F (the attraction of the cube).

According to Le Sage's hypothesis (gravitational rays coming from space), when the test body was above the lead cube, its weight W would increase by F (the attraction of the cube). When the test body was below the lead cube, its weight W would decrease by F (the attraction of the cube) and would decrease by f (the absorption of the gravitational attraction of the Earth).

 Test body above the cube Test body below the cube Majorana's hypothesis W + F - f Le Sage's hypothesis W + F W - F W - F - f Suppose that F = 200 / g and f = 4 / g, as this case, the changes of weight would be: in Majorana's experiment. In Test body above the cube Test body below the cube Majorana's hypothesis 196 Le Sage's hypothesis 200 -200 -204

In both cases, therefore, the change of weight with the test body below the cube should be greater than with the test body above the cube. Majorana's test could not distinguish between the two hypotheses.