It is obvious also from their buildings and works of engineering, even without explicit statement, that they well understood the distribution of weight and the laws of stability.  The laws of acoustics were understood with sufficient clearness to make them applicable with success to theatres.  In practical mensuration—­a daily necessity for men who were perpetually allotting lands or marking out camps—­the Romans were experts.  In pure arithmetic the contemporary world had made some considerable advance, such as in the extraction of square-roots and cube-roots; but, as has been already said, the Roman interest was virtually confined to such arithmetic or mathematics as appeared to possess some bearing on actual use.

Of chemistry, in the modern scientific sense, the ancients knew almost nothing.  Empirically they were aware of certain properties exhibited by substances, and could perform certain manipulations; but, like moderns down to a very recent time, they had no real understanding of the quantitative or qualitative relations of elements.  Long ago Greek philosophy, followed by the Epicurean school, had set forth an “atomic theory,” which on the surface is surprisingly like the modern chemical hypothesis; but this contained strange and illogical features and had no connection with actual practice.  In this department the chief proficiency of the world of this date lay in metallurgy, in which the processes empirically discovered, chiefly by Egyptians and Phoenicians, were closely similar to those now employed.  They thoroughly understood the smelting of ores, but could render no scientific account of the processes.  Botany was in a very crude condition, scarcely extending beyond such knowledge as was required on the one hand for farming and horticulture, and on the other for the vegetable medicines used by contemporary physicians.

The doctoring of the time was also, of course, largely empirical, but assuredly hardly more so than it was a century or so ago, and distinctly more rational than it became in the Middle Ages.  We cannot conceive of a reputable doctor at Rome prescribing the nauseous mediaeval absurdities.  Practical surgery must have been surprisingly advanced, and there is scarcely a modern surgeon who does not exclaim in admiration of the instruments discovered at Pompeii and now preserved in the Naples Museum (see FIG. 69).  In physic it is, of course, tolerably certain that many of the remedies or methods of treatment were of the sound and simple kind discovered by the long experience of mankind and often put in use by our grandmothers.  The defect contemporary medicine was that it was almost wholly empirical.  The ancient surgeon could doubtless perform ordinary operations—­amputations and excisions—­with neatness, and the ancient physician knew perfectly well what to do with the ordinary complaints—­the fevers and agues, the bilious attacks, the gout, or the dropsy—­but he was baffled by any new conditions.  Moreover, if