17. Here _passeth any-thing the south westward_ means, passes somewhat to the westward of the South line. The problem is, to find the degree of the zodiac which is on the meridian with the star. To do this, find the altitude of the star _before_ it souths, and by help of problem 3, find out the ascending degree of the zodiac; secondly, find the ascending degree at an equal time _after_ it souths, when the star has the same altitude as before, and the mean between these will be the degree that ascends when the star is on the meridian. Set this degree upon the Eastern part of the _horizon obliquus_, and then the degree which is upon the meridional line souths together with the star. Such is the solution given, but it is but a very rough approximation, and by no means always near to the truth. An example will shew why. Let Arcturus have the same altitude at 10 P.M. as at 2 A.M. In the first case the 4th of Sagittarius is ascending, in the second (with sufficient accuracy for our purpose) the 2nd of Aquarius; and the mean between these is the 3rd of Capricorn. Set this on the Eastern horizon upon a globe, and it will be seen that it is 20 min. past midnight, that 10° of Scorpio is on the meridian, and that Arcturus has past the meridian by 5°. At true midnight, the ascendent is the 29° of Sagittarius. The reason of the error is that right ascension and longitude are here not sufficiently distinguished. By observing the degrees of the _equinoctial_, instead of the _ecliptic_, upon the Eastern horizon, we have at the first observation 272°, at the second 332°, and the mean of these is 302°; from this subtract 90°, and the result, 212°, gives the right ascension of Arcturus very nearly, corresponding to which is the beginning of the 5° of Scorpio, which souths along with it. This latter method is correct, because it assumes the motion to take place round the axis of the equator. The error of Chaucer's method is that it identifies the motion of the equator with that of the ecliptic. The amount of the error varies considerably, and may be rather large. But it can easily be diminished, (and no doubt was so in practice), by taking the observations _as near the south line as possible_. Curiously enough, the rest of the section explains the difference between the two methods of reckoning. The modern method is to call the co-ordinates _right ascension_ and _declination_, if reckoned from the equator, and _longitude_ and _latitude_, if from the ecliptic. Motion in _longitude_ is not the same thing as motion in _right ascension_.