502 Prof. Q. Majorana: Theoretical and 



difficulty of calculation ; moreover, for a first research of 

 the kind, it may be permitted. I shall suppose the leaden 

 mass in, weighing 1274 gr. concentrated in one point ; I 

 shall suppose, moreover, the mass of mercury, weighing 

 104 kg. transformed from cylindrical to spherical shape, 

 though containing still concentrically the V sphere (fig. 3) . 

 The radius of the mercury sphere so resulting will be equal 

 to 12*35 cm. Finally, the thickness of mercury crossed by 

 the single gravitational actions that the lead puts forth (or 

 receives) can be rated, always in rough approximation, as 

 equal to the difference between the radius of the mercury 

 sphere and the sphere V. This corresponds to 12*35 — 3*95 

 = 840 cm. Consequently we have in the formula (10) : 



e = 9*8. 10- 7 gr. ; m u = 1274gr.; S=13*G0 ; r = 8'40; 



and hence 



9 10 _1 



L— = 6*73.10- 12 . 



1274. 13*60. 8*4 



The order of magnitude in this determination coincides 

 with the one predicted. 



Application of the experimental result to the Suns case. — 

 The results already obtained are based chiefly upon the 

 hypothesis that the sun's astronomical density, called here 

 apparent, may be inferior to another density : the true 

 density. Making always the simplification, deriving from 

 the hypothesis of the constancy of the sun's true density, it 

 can be considered as determined by the experiment described 

 above. Let us call E fi the sun's radius, 8 rS9 8 as , its densities 

 (apparent and true). Putting j» = BJEL = R/iS, we have for 

 the sun 



p s = hS vs R s . 



To p/s value corresponds a determinate value ^jr s of the 

 t|t function, which might be deduced from fig. 2, if S vs were 

 known to us. Now, from (7), we have 



VS ~ir s ; 



. 



p s yjr s = hU s 8 as . 





' cm. B as = l'4:l ; 



A = 6*73.10- 12 ; 



therefore 



Since R s = 6*95 

 w T e have further 



p s f s =Q-lS . lO" 12 . 6*95 . 10 10 . l-41 = 0-660. 



This condition must be satisfied. Considering the curve 

 in fig. 2 we note that for the point p = 2'0, ^ = 0*433, and 





