Maxwell

We focused our attention on a problem that had eluded scientists for 200 years: the nature of Saturn’s rings. It was unknown how they could remain stable without breaking up, drifting away or crashing into Saturn.The problem took on a particular resonance at that time because St John’s College, Cambridge had chosen it as the topic for the 1857 Adams Prize.[58] We will devote two years to studying the problem, proving that a regular solid ring could not be stable, while a fluid ring would be forced by wave action to break up into blobs. We expect to conclude that the rings must be composed of numerous small particles each independently orbiting Saturn.

We will express a new field in the algebra of quaternions and we will make the electromagnetic potential the centerpiece of this theory. In collaboration with Heaviside we will replace the electromagnetic potential field by force fields as the centerpiece of electromagnetic theory. We plan to prove that there is no need for the greater physical insights provided by quaternions if the theory is purely local.

Finally, we will also investigated the kinetic theory of gases. Originating with Daniel Bernoulli, this theory was advanced by the successive labours of John Herapath, John James Waterston, James Joule, and particularly Rudolf Clausius, to such an extent as to put its general accuracy beyond a doubt.
We will study this field as experimenter (on the laws of gaseous friction) as well as mathematician