the matter he is seeking if he
knows the name that has been applied to it. If the pigeonholes are
arranged in alphabetical order, for example, he may find all related
material, _provided he knows the name of every related group of
material_, even though very similar things may bear names as far apart
as A and Z. But if all things were so placed that, adjacent and in
certain fixed relation to each pigeonhole, other related matter could be
found, the resemblances lessening in proportion to the separation, and
if the entire area of pigeonholes were divided, and certain areas
assigned to certain kinds of things defined in general terms, guessing
the location of and desultory search for things that may have different
names, but yet be very much alike, would be lessened and all cognate
material be bunched. A second vital factor of a system of
classification, therefore, is the arrangement of the groups.

_Infinitude of possible combinations._--There are now over 1,125,000
United States patents, each presumptively covering a creation of the
useful arts that is different from every other. Most of these patents
also disclose a plurality of elements or acts. Each of these patented
means is potentially an element of a more complex combination that may
be patented. When one considers merely the number of forms of energy,
the number of known substances and known mechanical elements, and
attempts to figure possible combinations and permutations, it becomes
apparent that the size of the numbers resulting is incomprehensible.
Consider the possibilities of combination also of the enormously varied
disclosures of patents. Calculations of the possible combinations and
permutations of a small number of objects are familiar. Different
combinations of the letters of the alphabet are sufficient to record the
sum of human knowledge in many languages. With substantially two octaves
of the diatonic scale the world's melodies have been sounded, nor do any
doubt that our successors will thrill to airs that we have never heard.
"Thirty metals may be combined into 435 binary alloys, 4,060 ternary
alloys, 27,405 quaternary alloys" (Jevons). This does not take into
consideration differences in proportion that figure so largely in
results in the arts of substance-making. The total number of possible
alloys of the known metals is incomprehensible. A moment's thought
respecting the numbers of the means of the useful arts will alleviate
any fears that the