Albert C. Lewis

The Influence of Grassmann’s Theory of Tides on the Ausdehnungslehre

Michael Crowe has shown in his History of Vector Analysis (Crowe 1985) that Grassmann’s earliest mathematical work, the Theory of Tides, contains almost all of the key vectorial notions that appeared four years later in the Ausdehnungslehre. On the other hand, Grassmann never published the Theory of Tides—it first appeared in 1911 in Grassmann’s collected works (Grassmann 1840). Many of the physical applications, however, did appear in 1877, the last year of Grassmann’s life, as “Die Mechanik nach den Prinzipien der Ausdehnungslehre” in the Mathematische Annalen. The only essential difference between this later version and the 1840 appearance appears to me to be ostensibly minor changes of notation. I believe, however, that it is just this difference that points to the contribution that the Theory of Tides can make to our understanding of how the Ausdehnungslehre came to be.