FORE:But the Allies had only fallen back behind the Elbe, and taken up a strong position at Bautzen, on the Spree, about twelve leagues from Dresden, whilst an army under Bülow covered Berlin. No sooner did the Allies fall back to the right bank of the Elbe than Davoust attacked Hamburg on the 9th of May with five thousand men, and vowed vengeance on the city for having admitted the Allies. To their surprise the citizens found themselves defended by a body of Danes, from Altona, who were the allies of France, but had been just then thinking of abandoning Napoleon. But the fate of the battle of Lützen changed their views, and they retired in the evening of that day, leaving Hamburg to the attacks of the French. Bernadotte, not having received the promised reinforcements, did not venture to cover Hamburg. Davoust entered the place like a devil. He shot twelve of the principal citizens, and drove twenty-five thousand of the inhabitants out of the city, pulled down their houses, compelling the most distinguished men of the town to work at this demolition and at raising the materials into fortifications. The people had long been subjected by the French to every possible kind of pillage and indignity; no women, however distinguished, had been allowed to pass the gate without being subjected to the most indecent examinations. But now the fury of the French commander passed all bounds. He levied a contribution of eighteen millions of dollars: and not satisfied with that, he robbed the great Hamburg bank, and declared all his doings to be by orders of the Emperor.While an impulse was thus given to the mathematical theory of light in the University of Cambridge, similar progress was being made in the sister University of Dublin, where three of her most eminent professorsSir William Rowan Hamilton, Dr. Lloyd, and Mr. M'Cullaghdevoted themselves energetically to its improvement and verification. Sir William Hamilton, a geometer of the first order, having undertaken a more complete discussion of the wave surface of Fresnel, to the equation of which he gave a more elegant form, ascertained the exact nature of that surface, and consequently the exact direction of refracted rays in the neighbourhood of the optic axes. The beautiful and unexpected results he obtained were verified by his friend Dr. Lloyd. The names of Sir William R. Hamilton and Dr. Lloyd will be handed down to posterity in connection with this discovery. "But," says Professor Forbes, "they have other claims to our respect. The former has generalised the most complicated cases of common geometrical optics, by a peculiar analysis developed in his essays on 'Systems of Rays.' To Dr. Lloyd we are indebted for several interesting experimental papers on optics, for an impartial review of the progress of the science, and for an excellent elementary treatise on the wave theory."