Prof. Sylvester on Periodical Changes of Orbit, fyc. 28i 



Although the Gerhardt type theory is a most palpable perver- 

 sion of fact, for organic compounds fall quite as naturally under 

 three dozen general types as under these favoured three, and 

 although it has been abandoned with surprising rapidity, and 

 although, like the simple compound-radical theory of Berzelius 

 and Liebig, it simply accepts a multitude of radicals without 

 offering any explanation of their structure, yet it has completely 

 changed the aspect of the science. It was put forward in a 

 most splendid manner, and brought into prominence many of 

 the most fundamental doctrines, — e. g., that the elements are not 

 composed of isolated atoms, but of groups of similar atoms ; that 

 chemical change consists in the vast majority of cases in double 

 decomposition ; that the occupation of equal volumes in the state 

 of vapour is an excellent sign of the relative magnitudes of che- 

 mical groups; and much besides which I have no time to point 

 out. 



The other attempt was that of Kolbe and Frankland, who 

 more than ten years ago had made the practical discovery of the 

 real saturating capacity of carbon, and who recognized that by 

 simple double decomposition the homologous series of alcohols 

 and acids might be built up. It is a remarkable fact, that 

 although Kolbe and Frankland were actually employing methods 

 the validity of which depended upon the fact that the saturating 

 power of the atom of carbon is equal to four of hydrogen, it 

 should have been reserved for Kekule to make the announce- 

 ment that if we assign to carbon a fundamental saturating power 

 equal that of four atoms of hydrogen, we are able to exhibit 

 organic compounds with the form of their structure deducible 

 from the fundamental saturating power of the carbon which they 

 contain. 



XLIV. Note on the Periodical Changes of Orbit, under certain 

 circumstances, of a particle acted on by a central force, andonVec- 

 torial Coordinates, fyc, together with a new Theory of the Ana- 

 logues to the Cartesian Ovals in Space, being a Sequel to "As- 

 tronomical Prolusions ■" By Prof. J. J. Sylvester, F.R.S* 



AVERY singular and previously unnoticed species of die- 

 continuity arises when, according to the equations of 

 motion interpreted in the ordinary manner, a particle solicited 

 by a continuous central force would seem as if it ought to describe 

 an orbit external to the force-centre. An instance of this kind, 

 probably for the first time, presented itself in a question inci- 

 dentally brought forward by myself in the paper inserted in the 



* Communicated by the Author. 



