 He returns to the original sources, indicates the principle and sketches the course of the demonstrations, and states the result, often adding something of his own.During the preparation of the Report, and as a logical consequence of the researches connected therewith, Smith published several original contributions to the higher arithmetic.Some were in complete form and appeared in the "Philosophical Transactions" of the Royal Society of London; others were incomplete, giving only the results without the extended demonstrations, and appeared in the Proceedings of that Society.