52 
SIE B. C. BEODIE ON THE CALCULUS OF CHEMICAL OPEEATIONS. 
system of combinations constructed upon hypothesis a does not include those pretended 
compounds of carbon, hydrogen, oxygen, chlorine (recognized as possible compounds of 
these elements in the other system) in the case of which the sum of the units of 
hydrogen, chlorine . . . (and generally the sum of the units of the dyad elements) formed 
by the decomposition of two units of the compound is other than an even number. 
Hypothesis a affords no means of manufacturing these compounds ; so that we are led 
to the conclusion that such things are to be regarded as mere “ non-entities ” or “ mon- 
strosities,” combinations of incompatible ingredients, which cannot be made up, by any 
known chemical operations, of the matter of those actual chemical elements out of 
which all known chemical existences are constructed*. It is hardly necessary to 
observe that such things cannot, as a matter of fact, be made — the limitation intro- 
duced by hypothesis a being the celebrated law of Even Numbers, discovered as an 
empirical truth by Laurent and Gerhardt, which is here referred to its origin, and 
deductively established, as a consequence of this hypothesis. 
Were we to proceed to enumerate the combinations of hydrogen, chlorine, nitrogen, 
and the other dyad elements, as indicated by the two hypotheses respectively, and com- 
pare the systems thus indicated with the systems actually existing, we should find that 
the combinations indicated in the case of hypothesis a 2 were twice as numerous as in the 
case of hypothesis a ; and we should, in fact, on this hypothesis (a 2 ) make a blunder in 
every alternate statement, knowing neithe! more nor less about the result than we do in 
tossing a halfpenny whether it will fall head or tail — a position very different to that of 
one who, having obtained information that the coin is weighted, never makes any such 
mistakes at all, which is our position on hypothesis a. That the conclusions to which 
we are thus brought as to the nature and relations of these dyad elements are truly of 
a remarkable character is not to be denied ; but it is a sufficient reply to those persons 
who make difficulties on this score, that they may just as reasonably object to the facts 
on which these conclusions are based, which are equally remarkable with the conclu- 
sions ; and, moreover, that the value of an hypothesis is to be tested, not by the coin- 
cidence of its conclusions with our previous expectations, but by their agreement with 
the facts which we wish to explain. 
Now it may be contended, admitting it to be true that hypothesis a puts a correct 
limitation upon these combinations, yet this advantage is gained at too great a cost. It 
rejects indeed (it may be said), and rightly, the combinations rejected by the empirical 
law of Even Numbers, but, in so doing, opens the door of the system to a large number 
of compounds totally unknown to us. Thus while we eradicate one set of impossible 
existences, we introduce another. Where, it is asked, are the elements %, a, v . . ., or 
* “ Desinit in piscem mulier formosa superne.” The construction of the unit of a chemical substance to be 
resolved into two units of hydrogen and three units of chlorine presents the same order of difficulties as the 
combination of the head of a woman with the tail of a fish. We cannot imagine how such a thing could be 
produced t 
