Compound Molecules with Theoretical Atoms. 617 



be represented by the surfaces of revolution obtained by- 

 revolving the whole figure about the ~-axis. 



The Forms of Compound Molecules. 



In giving an account of the results obtained by the use of 

 these charts in forming molecules, much of the interesting 

 detail will have to be omitted on account of its length; and 

 we will give chiefly the resulting forms of stable molecules 

 without specifying the various forces acting upon each atom. 

 These are interesting as showing which atoms are most 

 responsible for the equilibrium of any one atom. In all the 

 systems it is noticeable that the hydrogen atoms perforin 

 the function of binder to hold the system together, and the 

 carbon atoms tend to separate from each other. They are 

 prevented from so doing by the hydrogen atoms when 

 properly located. 



It was shown in a former paper that two atoms of hydrogen 

 may unite to form a molecule, the axes of rotation of each 

 being in the same line, and the distance between the atoms 

 16$'2a* units. The chart PL VIII. fig. 1 shows that three atoms 

 of hydrogen may unite into a molecule as shown in PL XII. 

 fig. 5, where the atoms H 2 and H 3 have a common axis, the 

 distance between them being 800. The third hydrogen atom 

 is situated at equal distances of 794 from the other two, or at 

 a distance of 669 from the mid-point between them, making 

 an angle of 32° 42' for the latitude of H 2 with respect to Hj. 

 In this position the .r-force of H 2 on E. x is zero, because this 

 point lies on the zero curve for the .r-force in fig. 1. The 

 same remark applies also to the effect of H 3 on H^. The 

 r-force of H 2 on Hx evidently exactly opposes that of H 3 

 on H 1? making the resultant zero. Each c-force is an 

 attraction, H 3 pulling Hj downward and H 2 pulling it 

 upward. In the third direction perpendicular to the plane 

 of the paper the force on H, is zero. This permits the atom 

 H T to revolve freely around H 2 H 3 as an axis. 



In the c-direction the distances are such that the upward 

 repulsion of H 3 f or H 2 just balances the downward attraction 

 which Hi has for H 2 , thus making the c-force upon both H 2 

 and H 3 zero. 



A detailed discussion of the question of stability or insta- 

 bility of the various molecules shown is omitted here. It is 

 not sufficient to displace a single atom of the molecule and 

 imagine that the others remain in their former positions, 

 because a displacement of the one moves the others 

 simultaneously. In this H 3 molecule a normal oscillation 

 would be an expansion and a contraction of the whole 



