It may be convenient here to deal with the theory of the Quinary System, which was promulgated with great zeal by its upholders during the end of the first and early part of the second quarter of the 19th century, and for some years seemed likely to carry all before it.
But, confining ourselves to what is here our special business, it is to be remarked that perhaps the heaviest blow dealt at these strange doctrines was that delivered by Rennie, who, in an edition of Montagu's Ornithological Dictionary (pp. xxxiii.-1v.), published in 1831 and again issued in 1833, attacked the Quinary System, and especially its application to ornithology by Vigors and Swainson, in a way that might perhaps have demolished it, had not the author mingled with his undoubtedly sound reason much that is foreign to any question with which a naturalist, as such, ought to deal - though that herein he was only following the example of one of his opponents, who had constantly treated the subject in like manner, is to be allowed.
Though attempts were now and then made by its adherents to revive it; and, even ten years or more later, Kaup, one of the few foreign ornithologists who had embraced Quinary principles, was by mistaken kindness allowed to publish Monographs of the Birds-of-Prey (Jardine's Contributions to Ornithology, 18 49, pp. 68 -75, 96-121; 1850, pp. 51-80; 1851, pp. 119-130; 1852, pp. 103-122; and Trans.
The mischief caused by this theory of a Quinary System was very great, but was chiefly confined to Britain, for (as has been will be necessary to limit this survey, as before indicated, to those countries alone which form the homes of English people, or are commonly visited by them in ordinary travel.
Or, on the quinary-binary system, we need only give independent definitions to the numbers up to five; the numbers six, seven,..
The introduction of these other symbols produces a compound scale, which may be called a quinarybinary, or, less correctly, a quinary-denary scale.
Thus 1878 in the quinary-binary scale would be 1131213, and 1828 would be 1130213; the meaning of these is seen at once by comparison with MDCCCLXXVIII and MDCCCXXVIII.
Examples of this are given in § 20; it is worthy of notice that the vigesimal (or, rather, quinary-quaternary) system was used by the Mayas of Yucatan, and also, in a more perfect form, by the Nahuatl (Aztecs) of Mexico.
If a quinary-binary system (such as would naturally fit in with counting on the fingers) is not adopted, teachers unconsciously resort to a binary-quinary system.
(ii) Beyond ten, and in many cases beyond five, the names have reference to the use of the fingers, and sometimes of the toes, for counting; and the scale may be quinary, denary or vigesimal, according as one hand, the pair of hands, or the hands and feet, are taken as the new unit.