“While all previous contrivances,” says Sir David, {28a} “performed only particular arithmetical operations, under a sort of copartnery between the man and the machine, the extraordinary invention of Mr Babbage actually substitutes mechanism in the place of man. A problem is given to the machine, and it solves it by computing a long series of numbers following some given law. In this manner it calculates astronomical, logarithmic, and navigation tables, as well as tables of the powers and products of numbers. It can integrate, too, innumerable equations of finite differences; and, in addition to these functions, it does its work cheaply and quickly; _it corrects whatever errors are accidentally committed_, _and it prints all its calculations_.” Notwithstanding this brilliant picture, the great expense and the complications involved in the construction of such an instrument have seriously interfered with its success. It is said that Mr Babbage’s machine, much more his marvellous analytic engine, have never yet been properly constructed. {28b} Pascal fortunately turned his thoughts into a new and more fruitful channel. We have now to contemplate him as one of an illustrious band associated in a great discovery in physical science. Before his time considerable progress had been made towards a knowledge of atmospheric pressure. Galileo and his pupil Torricelli had both been busy with the subject. To Pascal, however, remains the glory of carrying successfully to a conclusion the suggestion of Torricelli, and of verifying the results which he had indicated. Here, as in almost all such discoveries, it is found that different minds have been actively pursuing the same or similar lines of thought and observation, and controversy has arisen as to the exact merits of each; but Pascal has himself so candidly explained {29a} how far he was indebted to his great Italian predecessors, and how far he made original experiments of his own, that both his relation to them and his own work stand clearly apparent.