Notes: 1. An Enquiry into the Nature and Causes of the Wealth of Nations, by Adam Smith. 2. Note sur la publication, proposee par le gouvernement Anglais des grandes tables logarithmiques et trigonometriques de M de Prony De l'imprimerie de F. Didot, December 1, 1829, p. 7 3. Since the publication of the second edition of this work, one portion of the engine which I have been constructing for some years past has been put together. It calculates, in three columns, a table with its first and second differences. Each column can be expressed as far as five figures, so that these fifteen figures constitute about one ninth part of the larger engine. The ease and precision with which it works leave no room to doubt its success in the more extended form. Besides tables of squares, cubes, and portions of logarithmic tables, it possesses the power of calculating certain series whose differences are not constant; and it has already tabulated parts of series formed from the following equations: The third differential of ux = units figur of delta ux The third differential of ux = nearest whole no. to (1/10,000 delta ux) The subjoined is one amongst the series which it has calculated: 0 3,486 42,972 0 4,991 50,532 1 6,907 58,813 14 9,295 67,826 70 12,236 77,602 230 15,741 88,202 495 19,861 99,627 916 24,597 111,928 1,504 30,010 125,116 2,340 36,131 139,272 The general term of this is, ux = (x(x-1)(x-2))/(1 X 2 X 3) + the whole number in x/10 + 10 Sigma^3 (units figure of (x(x-1)/2) Chapter 21 On the Cost of Each Separate Process in a Manufacture 253. The great competition introduced by machinery, and the application of the principle of the subdivision of labour, render it necessary for each producer to be continually on the watch, to discover improved methods by which the cost of the article he manufactures may be reduced; and, with this view, it is of great importance to know the precise expense of every process, as well as of the wear and tear of machinery which is due to it. The same information is desirable for those by whom the manufactured goods are distributed and sold; because it enables them to give reasonable answers or explanations to the objections of enquirers, and also affords them a better chance of suggesting to the manufacturer changes in the fashion of his goods, which may be suitable either to the tastes or to the finances of his customers. To the statesman such knowledge is still more important; for without it he must trust entirely to others, and can form no judgement worthy of confidence, of the effect any tax may produce, or of the injury the manufacturer or the country may suffer by its imposition.