[122] Principia, Book III., proposition 10.
[123] It is important for the purposes of this discussion to notice that the vertical is not the line drawn from the centre of the earth to the place of observation.
[124] 69 miles is 364,320 feet, so that the two northern degrees were a little more and the Peruvian are a little less than 69 miles.
[125] The remaining 8,000 stars were not “reduced” by Lacaille. The whole number were first published in the “reduced” form by the British Association in 1845.
[126] A mural quadrant.
[127] The ordinary approximate theory of the collimation error, level error, and deviation error of a transit, as given in textbooks of spherical and practical astronomy, is substantially his.
[128] The title-page is dated 1767; but it is known not to have been actually published till three years later.
[129] For a more detailed discussion of the transit of Venus, see Airy’s Popular Astronomy and Newcomb’s Popular Astronomy.
[130] Some other influences are known—e.g. the sun’s heat causes various motions of our air and water, and has a certain minute effect on the earth’s rate of rotation, and presumably produces similar effects on other bodies.
[131] The arithmetical processes of working out, figure by figure, a non-terminating decimal or a square root are simple cases of successive approximation.