280 
NOTES AND QUERIES. 
[No. 18. 
the subject, that, without this principle, no im- 
provement in mere notation would have been of 
material use in arithmetic ; and on the other hand 
that the main difference between the arithmetic 
of the abacus and the arithmetic of the slate, con- 
sists in the inevitable consequences of the deno- 
tation of the single digits by single symbols. 
The abacus, however, in its ordinary form, is 
essentially a decimal instrument: but its form 
was also varied for commercial purposes, perhaps 
in different ways. I never heard of the existence 
of one in any collection: but there is preserved in 
the British Museum a picture of one. This was 
printed by Mr. Halliwell in his Rara Mathematica 
—not a fac-simile, but a rule and type repre- 
sentation of it, ciphers being used by him for the 
circles in the original. Mr. Halliwell gives it 
without note or remark; and evidently had not 
divined its meaning. This was done, however, 
soon after in a review of Mr. Halliwell’s book in 
the Philosophical Magazine. I am not able at this 
moment to refer to either, so as to give exact 
dates: but it was somewhere from 1838 to 1840. 
Perhaps, however, I am giving “E. V.” infor- 
mation that may be irrelevant to his purpose; 
though it may be of some use to another class of 
inquirers. I proceed, therefore, to one or two 
notices that seem to have a more direct bearing 
on his object : — 
1. Chasles’ Apergu Historique sur T Origine et le 
Développement de Méthodes en Géométrie ; passim, 
but especially in note xii.: 4to., Bruxelles, 1837. 
2. Chasles’ several notices in Comptes Rendus 
des Séances de l’ Acad. des Sciences. All subse- 
quent to the “ Apergu.” 
His Catalogue des Manuscrits de la Bibliotheque 
de Ville de Chartres should be also consulted, if 
accessible to “E. V.” Copies of it, however, are 
very rare in this country, as it was privately 
printed, and never published. If, however, your 
correspondent have any serious inquiry in view 
which should render his consultation of it desi- 
rable, 1 can put it in his power to do so personally 
through you. 
8. Libri, several notices in the same series of 
papers. 
4. Libri, Histoire des Sciences Mathématiques 
en Italie. Several places. Bactulica. Paris, 1838 
— 1841. 4tomes. 8vo. 
5. Peacock (Dean of Ely), “ Arithmetic,” in the 
Encyclopedia Metropolitana. This is now, 1 be- 
lieve, to be had either separately, or in the volume 
devoted to pure “ Mathematics.” 
6. De Morgan, Penny Cyclopedia in loc., and 
occasionally elsewhere in the work. 
7. Leslie’s Philosophy of Arithmetic. 
8. Humboldt, in a paper which is translated in 
the Journal of the Royal Institution, vol. xxix. 
I believe a good many other references might 
be made, with little trouble, to foreign Mémoires ; 
| 
and (perhaps still more to your correspondent’s 
apparent purpose) to some amongst the Mémoires 
that relate to inscriptions and topography, rather 
than amongst those relating directly to science or 
literature. However, the two parts of the subject 
cannot be effectively studied separately from each 
other; and I am not without a hope that these 
straggling notes may be of some use to “ E. V.” 
Under the view of inscriptions, it occurs to my 
memory that in two or three places on the church 
of St. Brelade in Jersey, there are marked four 
vertical straight lines, which are interpreted by 
the natives to signify the Arabic numerals 1111; 
as the date mcxi. of the building of the church. 
The church is evidently a very ancient one, and it 
is agreed to be the oldest in the island, and the 
island historians assign it to the early part of the 
12th century. For these symbols being coeval 
with the building I do not vouch: as (though it 
is difficult to say what may constitute antiquity 
in the look of four parallel lines) I confess that 
to my eye they had “as modern a look” as four 
such lines could well have. The sudden illness 
of one of my party during our visit (1847), how- 
ever, precluded my examining that beautiful spot 
and its interesting little church with the care I 
should have wished. 
I may be allowed to suggest the necessity of 
some degree of caution in discussing this question: 
especially not to assume that any Arabic numerals 
which appear in ecclesiastical inscriptions are co- 
eval with the dates they express; but rather 
inquire whether, from the condition of the stone 
bearing the inscription, these numbers may not 
have been put there at a later period, during 
repairs and alterations of the building itself. It 
is for many reasons improbable, rather than other- 
wise, that the Arabic numerals should have been 
freely used (if used at all) on ecclesiastical struc- 
tures till long after the Reformation: indeed they 
are not so even yet. 
But more. Even where there is authentic 
evidence of such symbols being used in eccle- 
siastical inscriptions, the forms of them will tell 
nothing. For generally in such cases an antique 
form of symbol would be assumed, if it were the 
alteration of a “learned clerk ;” or the arabesque 
taste of the carver of the inscription would be 
displayed in grotesque forms. We should rather 
look for genuine than coeval symbols of this kind 
upon tombs and monuments, and the altar, than 
upon the building itself; and these will furnish 
collateral proofs of the genuineness of the entire 
inscription rather than any other class of archi- 
tectural remains. The evidence of the inscrip- 
tions on “Balks and beams” in old manorial 
dwellings are especially to be suspected. T.S.D. 
Shooter’s Hill, Feb. 11. 1850. 
a 
ee 
Arabic Numerals. —If you think the following | 
