Hydrogen = The least dense element,
we signify that the object or group of objects denoted by one term is identical with that denoted by the other, in everything except the names. The general formula
A = B
must be taken to mean that A and B are symbols for the same object or group of objects. This identity may sometimes arise from the mere imposition of names, but it may also arise from the deepest laws of the constitution of nature; as when we say
Gravitating matter = Matter possessing inertia,
Exogenous plants = Dicotyledonous plants,
Plagihedral quartz crystals = Quartz crystals causing the plane of polarisation of light to rotate.
We shall need carefully to distinguish between relations of terms which can be modified at our own will and those which are fixed as expressing the laws of nature; but at present we are considering only the mode of expression which may be the same in either case.
Sometimes, but much less frequently, we require a symbol to indicate difference or the absence of complete sameness. For this purpose we may generalise in like manner the symbol ~, which was introduced by Wallis to signify difference between quantities. The general formula
B ~ C