A Treatise on Electricity and Magnetism, Vol. I

In this approach, we begin with the whole and arrive at the parts by analysis, while the ordinary mathematical methods were founded on the principle of beginning with the parts and building up the whole by synthesis.

I also found that several of the most fertile methods of research discovered by the mathematicians could be expressed much better in terms of ideas derived from Faraday than in their original form.

The whole theory, for instance, of the potential In physics, potential refers to the amount of energy stored in a system due to the position of its parts, such as an object in a gravitational or electric field., considered as a quantity which satisfies a certain partial differential equation A type of mathematical equation used to describe how a physical quantity, like heat or electricity, changes over space and time., belongs essentially to the method which I have called that of Faraday. According to the other method, the potential—if it is to be considered at all—must be regarded as the result of a summation The process of adding together many small parts to find a total. of the electrified particles, each divided by its distance from a given point. Hence, many of the mathematical discoveries of Laplace, Poisson, Green, and Gauss find their proper place in this treatise, and their appropriate expression in terms of conceptions mainly derived from Faraday.

Great progress has been made in electrical science, chiefly in Germany, by those who cultivate the theory of action at a distance The concept that an object can be moved, changed, or affected without being physically touched by another object, often associated with Newtonian gravity.. The valuable electrical measurements of W. Weber are interpreted by him according to this theory. Furthermore, the electromagnetic speculation which was originated by Gauss and carried on by Weber, Riemann, J. and C. Neumann, Lorenz, and others, is founded on the theory of action at a distance, but depending either directly on the relative velocity of the particles or on the gradual propagation of something.