In describing the phenomena, I shall select those which most clearly illustrate the fundamental ideas of the theory, omitting others, or reserving them till the reader is more advanced. The most important aspect of any phenomenon from a mathematical point of view is that of a measurable quantity. I shall therefore consider electrical pheno mena chie?y with a view to their measurement, de scribing the methods of measurement, and defining the standards on which they depend. In the application of mathematics to the calculation of electrical quantities, I shall endeavour in the first place to deduce the most general conclusions from the data at our disposal, and in the next place to apply the results to the simplest cases that can be chosen. I shall avoid, as much as I can, those questions which, though they have elicited the skill of mathematicians, have not enlarged our knowledge of science.