4 CLARKE 



products of combustion gaseous, gives 191 084 calories. In 

 this way I have adjusted Thomsen's data ; and in their new 

 form they become the basis of my own calculations. 



With values thus reduced, we may now write equations which 

 shall represent, in thermochemical terms, the process of com- 

 bustion of any organic substance which, upon burning, under- 

 goes complete dissociation. Any hydrocarbon, for example, 

 when burnt to form carbon dioxide and water, must have its 

 atoms completely torn apart before they can combine with sim- 

 ilarly dissociated atoms of oxygen. Now let x represent the 

 absolute molecular heat of formation of CO2 ; y the absolute 

 heat of formation of water ; z the heat lost by the dissociation 

 of one oxygen molecule, and r the heat lost by the decomposi- 

 tion of the substance burned ; then for CH^ the equation be- 

 comes 



X ■\- ^y — iz — r = 191 084. 



This is a simple case, in other instances the equations must be 

 doubled, or in the study of some organic halides and nitrogen 

 compounds, quadrupled, in order to avoid fractional molecules 

 of oxygen, of nitrogen, or of a halogen element. For the sake 

 of uniformity, then, I prefer to write quadrupled equations 

 throughout ; and the formula for the combustion of methane 



becomes 



a^x -\- %y — %z — ^r = 764336. 



Unfortunately, equations of this kind are indeterminate, for 

 every new formula introduces a new quantity, and so the un- 

 knowns are always in excess. A direct algebraic solution is 

 therefore impossible, and at first sight it would seem as if the 

 entire system of equations was valueless. That this impression 

 is incorrect I shall endeavor to show. On careful examination 

 the equations exhibit regularities which suggest various hypoth- 

 eses ; upon the latter, trials can be based, and in that way 

 common factors are discoverable which satisfy the formulas in 

 a fairly definite manner. By long study and various trials of 

 this kind I have obtained a general formula of curious signifi- 

 cance, at least with respect to the aliphatic hydrocarbons and 

 their non-oxygenated derivatives. It is constructed as follows : 



