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 is was somewhere from 1838 to 1840.
Perhaps, however, I am giving "E.V." information that may be irrelevant to his purpose; though it may 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' _Aper?u Historique sur l'Origine et le D��veloppement de M��thodes en G��om��trie_; passim, but especially in note xii.: 4to., Bruxelles, 1837.
2. Chasles' several notices in _Comptes Rendus des S��ances de l'Acad. des Sciences._ All subsequent to the "Aper?u."
His _Catalogue des Manuscrits de la Biblioth��que de Ville de Chartres_ should also be consulted, if accessible to "E.V." Copies of it, however, are very rare in the 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 desirable, I can put it in his power to do so personally through you.
3. Libri, several notices in the same series of papers.
4. Libri, _Histoire des Sciences Math��matiques en Italie_. Several places. Bactulica. Paris, 1838-1841. 4 tomes. 8vo.
5. Peacock (Dean of Ely), "Arithmetic," in the _Encyclop?dia Metropolitana_. This is now, I believe to be had either separately, or in the volume devoted to pure "Mathematics."
6. De Morgan, _Penny Cyclop?dia_ 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 M��moires; and (perhaps still more to your correspondent's apparent purpose) to some amongst the M��moires that relate to inscriptions and topography, rather that 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), however, 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 coeval 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 otherwise, that the Arabic numerals should have been freely used (if used at all) on ecclesiastical structures 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 ecclesiastical 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 would 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 inscriptions rather than any other class of architectural remains. The evidence of the inscriptions on "Balks and beams" in old manorial dwellings is especially to be suspected.
T.S.D.
Shooter's Hill, Feb 11, 1850.
[Footnote 1: In vol. iii. of the same work is another paper by the same author, entitled, "Conjectures respecting the Origin of Alphabetic writing," pp. 365-384. Reference to these
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