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 Trans. 1686, No. 185) refuted M. Mallemont de Messange, who published at Paris in 1686. He does it in a very serious style, and shows himself a mathematician. And yet in the year in which, in the Phil. Trans. he was a geometer, and one who rebukes his squarer for quoting Matthew xi. 25, in that very year he was the visionary who, in the Leipzig Acts, professed to build a world resembling the divine mind by multiplying together 1, 2, 3, 4, &c. up to infinity.

There is a very pretty opening for a paradox which has never found its paradoxer in print. The philosophers teach that the rainbow is not material: it comes from rain-drops, but those rain-drops do not take colour. They only give it, as lenses and mirrors; and each one drop gives all the colours, but throws them in different directions. Accordingly, the same drop which furnishes red light to one spectator will furnish violet to another, properly placed. Enter the paradoxer whom I have to invent. The philosopher has gulled you nicely. Look into the water, and you will see the reflected rainbow: take a looking-glass held sideways, and you see another reflexion. How could this be, if there were nothing coloured to reflect? The paradoxer's facts are true: and what are called the reflected rainbows are other rainbows, caused by those other drops which are placed so as to give the colours to the eye after reflexion, at the water or the looking-glass. A few years ago an artist exhibited a picture with a rainbow and its apparent reflexion: he simply copied what he had seen. When his picture was examined, some started the idea that there could be no reflexion of a rainbow; they were right: they inferred that the artist had made a mistake; they were wrong. When it was explained, some agreed and some dissented. Wanted, immediately, an able paradoxer: testimonials to be forwarded to either end of the rainbow, No. 1. No circle-squarer need apply, His Variegatedness having been pleased to adopt 3.14159… from Noah downwards.

The system of Tycho Brahé, with some alteration and addition, has been revived and contended for in our own day by a Dane, W. Zytphen, who has published 'The Motion of the Sun in the Universe,' (second edition) Copenhagen, 1865, 8vo., and 'Le Mouvement Sidéral,' 1865, 8vo. I make an extract.—

How can one explain Copernically that the velocity of the Moon must be added to the velocity of the Earth on the one place in the Earth's orbit, to learn how far the Moon has advanced from one fixed star to another but in another place in the orbit these velocities must be subtracted (the movements taking place in opposite directions) to