Diamond with Theoretical Carbon Atoms. 265 



We have, therefore, to calculate the z component forces 

 for five different sets of coordinates only : first, the force of J 

 in plane +1 j and, second, the force due to 20 in plane -f 1, 

 which, multiplied by 6, gives the z component of the whole 

 hexagon 20-25 inclusive ; third, the force of 29 in the base 

 of the tetrahedron, which is to be multiplied by 3 ; and, 

 fourth, the force of 33 in the same plane — 1, which is to be 

 multiplied by 3 ; and, lastly, the force of 36, which is to 

 be multiplied by 3, for the lower triangle in fig. 4. The 

 results are as follows : — 



Plane. Atoms. 



-f 1 J F,= +~- j-10-66666P 2 /3|/- 4 + 142-2222 fe 2 m 2 V 6 |(l) 



+ 1 20-25 F,= 



, {- 0-67830 



>) 



+ 1-17036 



95 



}(2) 



-1 29-31 F*= 



, {- 1*97531 



59 



+ 117-6348 



?? 



}(3) 



-1 32-34 F,= 



, {- 0-59008 



59 



- 2-4363 



5? 



}(*) 



-3 35-37 F,= 



, {- 1-8121 



99 



- 5-757 



99 



}(5) 



Total . F 2 = 



„ [-15-7225 



99 



+ 252-83 



99 



}<6) 



K is the specific inductive capacity of the medium ; a^ the 

 radius of the orbit in centimetres of the single electron in 

 the hydrogen atom ; /3 # the ratio of its linear velocity to 

 that of light; co^ its angular velocity ; c the velocity of 

 light ; P the number of electrons in the carbon atom ; 

 Sim 2 the sum of the squares of the radii of the orbits of 



¥ 



each olectron in the carbon atom ; and I the length of the 

 edge of the elementary tetrahedron in the diamond, measured 

 in a* units, a^, /3^, and a> # are constants whose values have 

 been previously f determined. 



£.= g^-» = ° 207 * 1 f " * f ° * 10 " = 0-00103 . (7) 



G o X J-U 



c _ 3 x 10 — O'xIO- 8 . (81 

 o). - 15-0 x 10'» - U " X lU W 



For the carbon atom the number of electrons is 12, and 

 P = 12. The determination given later of the distance I ill 

 diamond gives 2'528 x 10~ 8 centimetre, which is equivalent 

 to 122,100 a m units. That is to say, the edge of the tetra- 

 hedron is this number of times greater than the radius of the 



t Loc. cit. pp. 772, 773, equations (63) and (68). 



