But the paramount influence proceeds from the names of the numerals.  Our nomenclature is perfectly barbarous, and that of other civilised nations is not better than ours, and frequently worse, as the French “quatre-vingt dix-huit,” or “four score, ten and eight,” instead of ninety-eight.  We speak of ten, eleven, twelve, thirteen, etc., in defiance of the beautiful system of decimal notation in which we write those numbers.  What we see is one-naught, one-one, one-two, etc., and we should pronounce on that principle, with this proviso, that the word for the “one” having to show both the place and the value, should have a sound suggestive of “one” but not identical with it.  Let us suppose it to be the letter o pronounced short as in “on,” then instead of ten, eleven, twelve, thirteen, etc., we might say on-naught, on-one, on-two, on-three, etc.

The conflict between the two systems creates a perplexity, to which conclusive testimony is borne by these numerical forms.  In most of them there is a marked hitch at the 12, and this repeats itself at the 120.  The run of the lines between 1 and 20 is rarely analogous to that between 20 and 100, where it usually first becomes regular.  The ’teens frequently occupy a larger space than their due.  It is not easy to define in words the variety of traces of the difficulty and annoyance caused by our unscientific nomenclature, that are portrayed vividly, and, so to speak, painfully in these pictures.  They are indelible scars that testify to the effort and ingenuity with which a sort of compromise was struggled for and has finally been effected between the verbal and decimal systems.  I am sure that this difficulty is more serious and abiding than has been suspected, not only from the persistency of these twists, which would have long since been smoothed away if they did not continue to subserve some useful purpose, but also from experiments on my own mind.  I find I can deal mentally with simple sums with much less strain if I audibly conceive the figures as on-naught, on-one, etc., and I can both dictate and write from dictation with much less trouble when that system or some similar one is adopted.  I have little doubt that our nomenclature is a serious though unsuspected hindrance to the ready adoption by the public of a decimal system of weights and measures.  Three quarters of the Forms bear a duodecimal impress.

I will now give brief explanations of the Number-Forms drawn in Plates I., II., and III., and in the two front figures in Plate IV.

DESCRIPTION OF PLATE I.

Fig. 1 is by Mr. Walter Larden, science-master of Cheltenham College, who sent me a very interesting and elaborate account of his own case, which by itself would make a memoir; and he has collected other information for me.  The Number-Forms of one of his colleagues and of that gentleman’s sister are given in Figs. 53, 54, Plate III.  I extract the following from Mr. Larden’s letter—­it is all for which I can find space:—­