Focal Length Quotes (2 quotes)
Think of the image of the world in a convex mirror. ... A well-made convex mirror of moderate aperture represents the objects in front of it as apparently solid and in fixed positions behind its surface. But the images of the distant horizon and of the sun in the sky lie behind the mirror at a limited distance, equal to its focal length. Between these and the surface of the mirror are found the images of all the other objects before it, but the images are diminished and flattened in proportion to the distance of their objects from the mirror. ... Yet every straight line or plane in the outer world is represented by a straight line or plane in the image. The image of a man measuring with a rule a straight line from the mirror, would contract more and more the farther he went, but with his shrunken rule the man in the image would count out exactly the same results as in the outer world, all lines of sight in the mirror would be represented by straight lines of sight in the mirror. In short, I do not see how men in the mirror are to discover that their bodies are not rigid solids and their experiences good examples of the correctness of Euclidean axioms. But if they could look out upon our world as we look into theirs without overstepping the boundary, they must declare it to be a picture in a spherical mirror, and would speak of us just as we speak of them; and if two inhabitants of the different worlds could communicate with one another, neither, as far as I can see, would be able to convince the other that he had the true, the other the distorted, relation. Indeed I cannot see that such a question would have any meaning at all, so long as mechanical considerations are not mixed up with it.
In 'On the Origin and Significance of Geometrical Axioms,' Popular Scientific Lectures< Second Series (1881), 57-59. In Robert Édouard Moritz, Memorabilia Mathematica (1914), 357-358.
What caused me to undertake the catalog was the nebula I discovered above the southern horn of Taurus on September 12, 1758, while observing the comet of that year. ... This nebula had such a resemblance to a comet in its form and brightness that I endeavored to find others, so that astronomers would not confuse these same nebulae with comets just beginning to shine. I observed further with suitable refractors for the discovery of comets, and this is the purpose I had in mind in compiling the catalog.
After me, the celebrated Herschel published a catalog of 2000 which he has observed. This unveiling the sky, made with instruments of great aperture, does not help in the perusal of the sky for faint comets. Thus my object is different from his, and I need only nebulae visible in a telescope of two feet [focal length].
After me, the celebrated Herschel published a catalog of 2000 which he has observed. This unveiling the sky, made with instruments of great aperture, does not help in the perusal of the sky for faint comets. Thus my object is different from his, and I need only nebulae visible in a telescope of two feet [focal length].
Connaissance des Temps for 1800/1801. In Charles Coulston Gillespie (ed.), Dictionary of Scientific Biography (1974), Vol. 9, 330.
In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion.
(1987) -- 
