Some of Hume's notes, of matters which have occurred to him in the course of his reading as worthy of observation, or of remarkable thoughts passing through his mind, have been preserved.[125:1] They appear to be merely a few stray leaves, which have accidentally survived the loss of many others, as the number of subjects to which they refer is limited in comparison with the wide compass of knowledge embraced in Hume's various works. The specimens so preserved, appear generally to have been written at this period of his life, with the exception, perhaps, of those which are printed above, and which have reference to physical science.[125:2] They are set down with clearness and precision, as if by one who knew both the step in a series of reasoning to which each of them belongs, and the form in which it should be expressed. They are written on long sheets of paper; and unless the few that appear under the head "Natural Philosophy," and some which have the general heading "Philosophy," they appear to have been subjected to no system of pre-arrangement, such as that which Locke suggested, but to have been set down according as the fruits of the annotator's reading or thought presented themselves to him. A few specimens are here given: they will be found to have been chiefly made use of in the "Natural History of Religion," and in the "Essay on the Populousness of Ancient Nations," while a few of them--as for instance that relating to Gustavus Vasa--make their appearance in the little volume of "Essays, Moral and Political," published in 1741.[125:3] A considerable proportion of them have not been made use of in Hume's printed works, and some of them contain information which is embodied in Smith's "Wealth of Nations." It is an occurrence quite characteristic of the friendship of these two great men, that either of them should have supplied the other with facts or ideas applicable to the subjects on which he might be engaged. EXTRACTS FROM A COLLECTION OF MEMORANDUMS. Perhaps the custom of allowing parents to murder their infant children, though barbarous, tends to render a state more populous, as in China. Many marry by that inducement; and such is the force of natural affection, that none make use of that privilege but in extreme necessity. A pound of steel, when manufactured, may become of £10,000 value. No hospitals in Holland have any land or settled revenue, and yet the poor better provided for than any where else in the world. The Romans had two ways chiefly of levying their taxes,--by public lands, which were all dissipated by popular tribunes about the end of the republic; or by customs upon importation, which were different in different places; in some the fortieth part of the value; in Sicily the twentieth. They had also a kind of excise, which began with the emperors, and was the two-hundredth or one-hundredth part of the value of all goods sold, the fiftieth of slaves.