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180 direction of the writer, by his friends and assistants, six machines having been at various times especially fitted up for this purpose. The exact determination of these laws and their reduction to formulæ have proved a slow but most interesting problem; but by far the most difficult undertaking has been the development of the methods and finally the appliances (i.e., slide rules) for making practical use of these laws after they were discovered.

In 1884 the writer succeeded in making a slow solution of this problem with the help of his friend, Mr. Geo. M. Sinclair, by indicating the values of these variables through curves and laying down one set of curves over another. Later my friend, Mr. H. L. Gantt, after devoting about 1 years exclusively to this work, obtained a much more rapid and simple solution. It was not, however, until 1900, in the works of the Bethlehem Steel Company, that Mr. Carl G. Barth, with the assistance of Mr. Gantt and a small amount of help from the writer, succeeded in developing a slide rule by means of which the entire problem can be accurately and quickly solved by any mechanic.

The difficulty from a mathematical standpoint of obtaining a rapid and accurate solution of this problem will be appreciated when it is remembered that twelve independent variables enter into each problem, and that a change in any of these will affect the answer.

The instruction card can be put to wide and varied use. It is to the art of management what the drawing is to engineering, and, like the latter, should