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Not content with translating Faraday’s ideas into mathematical form. Maxwell went on to develop the mathematical consequences of the theory and to extend its realm. Soon he came to a contradiction. Evidently all was not well with the theory, but what the remedy might be was not easy to determine. Various scientists sought for a cure, among them Maxwell himself. So refined and mathematical had the theory of electricity and magnetism become by now that when Max well arrived at a cure by sheer intuition based upon most unreliable analogies, he produced a group of equations differing but slightly in external form from the old equations. But not only did the new equations remove the contradiction, they also carried a significant new implication. They required that there should exist such, things as electromagnetic waves, that these waves should move with the speed of light, and that they should have all the other major known physical properties of light.

What was that contradiction?