viii PREFACE BY TRANSLATOR INTO ENGLISH the Continental practice of stating metric values has been fol- lowed, as it obviates the use of the decimal point. The use of the metric system in work of this character is practically compulsory and practically all of the basic data are available in metric units. The results, if desired, may readily be transformed into English units, the transformation factors, in many cases, being simple and easily memorized numbers. The translator holds no brief for the metric system. Its logical and simple numerical constants supply a most potent argument for its use in all technical work. It reduces many of the problems of engineering from the tedious computations of the English system to exceedingly simple mental computations. It is unfortunate that German methods are much more widely known than the extremely simple methods used in France, as a result of German propaganda which has been spread over the world and accepted without due investigation. The Germans have claimed as their own many technical discoveries for which credit is really due to men of other nations. The purpose of this translation is to convey the ideas of the original author. In order to enhance the usefulness of the work, some additions have been made in the shape of appendices supply- ing methods not elsewhere available in English.