58 
SIR B. C. BRODIE ON THE CALCULUS OE CHEMICAL OPERATIONS. 
with hypothesis a, but which are not discordant with hypothesis a 2 . In the former case 
the units of matter cannot be expressed by an integral number of prime factors, either 
on hypothesis a or on hypothesis a 2 ; in the second case the units of matter can be 
expressed by an integral number of prime factors on hypothesis a 2 , but cannot be so 
expressed on hypothesis a. The question has been (up to a certain point) discussed in 
Part I. Section VIII., where a Table is given of these exceptions [Part I. Sec- 
tion VIII. (3)]. . 
I shall not enter on the former class of exceptions, not only for the reason that the 
difficulties presented by them are not peculiar to this method, but also that these 
obstacles are rapidly being removed by a careful scrutiny of the facts, and so many such 
obstacles have actually disappeared that the removal of the rest must be regarded simply 
as a question of time and trouble. The second class of exceptions, however, stands on 
a very different footing. They go to the very root of the matter, and no rational expla- 
nation of these exceptions has (so far as I am aware) been ever suggested from the 
present point of view of chemistry. We will fix our attention on two salient examples, 
the binoxide and tetroxide of nitrogen. 
Assuming the gaseous densities of these substances as given by various observers to 
be the true densities of homogeneous gases, it must be admitted that the ponderable 
matter of two units of binoxide of nitrogen is identical with the ponderable matter of 
a unit of nitrogen and a unit of oxygen ; and also it must be admitted that the ponder- 
able matter of two units of tetroxide of nitrogen is identical with the ponderable matter 
of a unit of nitrogen and two units of oxygen. The facts here stated are incompatible 
with the expression of the symbols of the units of the binoxide of nitrogen and of the 
tetroxide of nitrogen respectively by an integral number of prime factors, on the hypo- 
thesis that the symbol of hydrogen is expressed as a [Part I. Section VIII. (2)] ; for we 
cannot find, on that hypothesis, any positive and integral solutions of the indeterminate 
equations connecting the integers, which are the indices of the prime factors by which 
these symbols are expressed. 
Now if this be regarded as a true statement of the facts, it must be allowed that the 
binoxide and tetroxide of nitrogen are not only (what indeed, perhaps without excep- 
tion, they are) the most curious of all chemical substances *, but are absolutely unique 
objects not made in the same way as other things, or turned out of the same workshop 
with them ; in short (as I before said) they must be “ chemical monstrosities,” “lusus 
* Laurent endeavours to get out of the difficulty by drawing a distinction between the molecule and (what 
I have termed) the unit. The unit, he says, is indeed NO, but the molecule is N 2 0 2 . As, however, a mole- 
cule can only be defined by referring it to the unit and saying that in all cases two units of matter are consti- 
tuted of an equal number of molecules, this explanation is not very satisfactory, although it is a path in which 
Laurent has been contentedly followed by the greater number of chemists. Laurent w;as fully alive to the 
difficulties of the case, as appears from the following sentence : — “ Unfortunately nitric oxide and peroxide of 
nitrogen are such singular bodies that it appears somewhat difficult to discover their analogues,” taken together 
with the note attached (‘ Chemical Method,’ translation, Cavendish Society, 1855, p. 82). 
