396 R. Hooke — Law of Densities of Planetary Bodies. 



To determine the value of the surface density of the earth 

 and moon from their mean densities and diameters, we have, 

 according to the indicated law of density, the following equa- 

 tions : 



Make P the surface density of the earth and of the moon. 



X the difference between the mean and surface density of 



the earth. „ 



Y the difference between the mean and surface density of 



the moon. 

 P+ X the earth's mean density. 

 P+ Y" the moon's mean density. 

 D the earth's diameter. 

 d the moon's diameter. 

 And k the difference between the mean and surface density of a 



planet of unit diameter, and we have 



k _P±X-{P±Y) 



L - ~b^t (1) 



and P=P-\-X-DJc=P+Y-dlc. (2) 



If we have another planet of the same class as the earth and 

 moon, whose diameter is DJ, and whose mean density is P+Z, 

 we have, according to the law of density, 



P+Z=P+D'k. (3) 



Substituting the proper numerical values in equations (1) 

 and (2), and making the unit of diameter a mile, we get 



£=•000389, and P=2"58. 



Dk and dk in equation (2) represent respectively that part 

 of the earth's mean density, and that part of the moon's mean 

 density, which is due to compression, and their numerical 

 values are as follows : 



Dk'=3-08, and dk=0S4. 



The writer has tested the law of density by applying equa- 

 tion (3) to the planets Mars, Yenus and Mercury. The following 

 are the computed values of the mean densities of these planets, 

 on the basis of the law in question, compared with the values 

 which have been computed from the assigned values of their 

 masses and diameters. 



Mass 

 (Sun=l.) 





Value com- 



Value computed from 



• Diameter 



puted from 



assigned values of 



iD miles. 



law of density. 



masses and diameters. 



Mars 4211 



4-22 



4-17 



Venus 7660 



5-56 



5'24 (?) 



Mercury 2992 



3-74 



4-56 (?) 



30 9 350 

 1 



3 9 



1 



1500000 



