Dimensional Analysis

Excerpt from Dimensional AnalysisThe substance of the following pages was given as a series of five lectnres to the Graduate Conference in Physics of Harvard University in the spring of 1920.The growing use of the methods of dimensional analysis in technical physics, as well as the importance of the method in theoretical investigations, makes it desirable that every physicist should have this method of analysis at his command. There is, however, nowhere a systematic exposition of the principles of the method. Perhaps the reason for this lack is the feeling that the subject is so simple that any formal presentation is superfluous. There do, nevertheless, exist important misconceptions as to the fundamental character of the method and the details of its use. These misconceptions are so widespread, and have so profoundly influenced the character of many speculations, as I shall try to show by many illustrative examples, that I have thought an attempt to remove the misconceptions well worth the effort.I have, therefore, attempted a systematic exposition of the principles underlying the method of dimensional analysis, and have illustrated the applications with many examples especially chosen to emphasize the points concerning which there is the most common misunderstanding, such as the nature of a dimensional formula, the proper number of fundamental units, and the nature of dimensional constants. In addition to the examples in the text, I have included at the end a number of practise problems, which I hope will be found instructive.The introductory chapter is addressed to those who already have some acquaintance with the general method. Probably most readers will be of this class. I have tried to show in this chapter by actual examples what are the most important questions in need of discussion. The reader to whom the subject is entirely new may omit this chapter without trouble.I am under especial obligation to the papers of D…