674 Prof. B. M. Sen on the Kinetic Theory of Solids 



Table I. 



Metal <? 



Density 



Atomic 



1ST 



1 



M. wt. 



a } coeff. of 



c compres- 





D. 



weight. 







of mol. 



expansion. 

 16-7XlO" H 



sibility. 

 ■74 xlO- 12 



Ou 



8-93 



63-57 



8-64 X10 22 



226 xlO" 8 



103 XlO" 22 



Ag 



10-5 



107-9 



5-97 „ 



2-55 „ 



1-75 „ 



18-8 „ 



'92 „ 



Pe 



7-86 



55-84 



8 67 „ 



2-26 „ 



0-91 „ 



102 „ 



•63 „ 



Zn 



71 



65-37 



669 „ 



246 „ 



106 „ 



26 





Pb 



1137 



207-2 



3-38 „ 



309 „ 



336 „ 



27-6 „ 



20 „ 



Au ... 



19-32 



197-2 ,6-05 „ 



2-55 „ 



3-19 „ 



139 „ 



0-60 „ 



Pfc 



21-50 



195-2 678 ., 



2-45 „ 



3-17 „ 



8-9 „ 



0-41 „ 



Sn 



7-29 



118-7 |3-78 „ 



2-98 „ 



1-93 „ 



21-4 „ 



1-9 



Al 



2-7 



27-1 



6-16 .., 



2'5o ,, 



0-44 „ 



25-5 „ 



133 „ 



2. Arrangement of molecules in an isotropic body. 



To find the number of molecules which can be arranged 

 about a central one at a distance I from it and from one 

 another. The problem is the same as the determination of 

 the number of tetrahedrons having all their edges equal to I 

 and having one vertex at the centre which can be fitted 

 inside a sphere of radius I. For every tetrahedron we have 

 an equilateral triangle of side I having its vertices on the 

 sphere. If a, b, c be the sides of the spherical triangle so 

 formed, 



a = 6 = c = 60°. 

 /. CosA=i, and A = 70°. 



,". the spherical excess = 30°. 



4"7r 

 The total number of tetrahedrons = — -7= 24. 



7T/0 



For each tetrahedron there are three molecules and each 

 molecule comes in -j7r, or about live times. The number of 

 molecules, therefore, is about 14. 



3. Rough working model. 



It is not geometrically possible to have an arrangement of 

 molecules on a sphere so that the spherical arc between any 

 two adjacent ones is 60°. Bit in a rough model form 

 these 14 may be supposed to be arranged as follows : — The 

 centres all lie on a sphere of radius I. Two may be fdaced 

 at the two poles which may he arbitrarily chosen. Three 

 meridian circles are drawn making an angle of 60° with 



