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 representation 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 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' _Aperçu Historique sur l'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 subsequent to the "Aperçu." His _Catalogue des Manuscrits de la Bibliothèque 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 Mathématiques en Italie_. Several places. Bactulica. Paris, 1838-1841. 4 tomes. 8vo. 5. Peacock (Dean of Ely), "Arithmetic," in the _Encyclopædia Metropolitana_. This is now, I believe to be had either separately, or in the volume devoted to pure "Mathematics." 6. De Morgan, _Penny Cyclopædia_ 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 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."