148 SCIENCE PROGRESS. 



is in accord with conclusions drawn independently of it from 

 the observed inactivity of benzene derivatives. 



The relative stability of ring-compounds, no less than 

 the isomerism they present, has been attributed to the space 

 relations of the carbon valences. If a chain of tetrahedron 

 models be formed by joining them at one corner, it will be 

 seen that, without bending the connecting rods, a free corner 

 of the fifth may be made to all but touch a free corner of 

 the first ; so that to close the ring requires but a slight 

 divergence of the linking valences from the angle of the 

 regular tetrahedron, in fact the divergence is only 3 . In 

 forming a hexa-, tetra-, tri- or di-methylene ringthedivergence 

 would be ii°, 1 9 , 49 , and 109 respectively; and it has been 

 observed that the ease with which a ring is broken, corres- 

 ponds to the divergence in question. Thus penta-, hexa-, 

 and tetra-methylene rings are the most stable, whereas the 

 trimethylene ring may be broken by means of bromine, and 

 dimethylene is saturated even by iodine. Baeyer has 

 applied the same theory to account for the explosive nature 

 of acetylene and especially of polyacetylene compounds. 



Returning to the chain of singly-linked carbons, we 



see that as the groups attached to the fifth carbon are 



nearer to the first carbon than are the groups attached 



to the fourth, so these are nearer than the groups of the 



third carbon. Accordingly we find that in an open chain 



of four carbons it is the groups attached to the end carbons, 



those which appear in an ordinary formula farthest apart, 



which are the readiest to react ; e.g., the y- and S-oxy-acids, 



which contain three and four carbon atoms between OH 



and COOH, are the readiest to form lactones in accordance 



with the formula 



c 



On making a chain of models with alternate double and 

 single linkage, it will be found that the sixth carbon atom 

 almost touches the first, thus indicating the superior stability 

 of the benzene ring. Arnold Eiloart. 



