h7e PTOLEMAEUS. appear to have added to his predecessor at all, in discovery at least. On this theory of epicycles, we may say a word once for all. The common notion is that it was a cumbrous and useless apparatus, thrown away by the moderns, and originating in the Ptolemaic, or rather Platonic, notion, that all celestial motions mttst either be circular and uniform motions, or compounded of them. But on the contrary, it was an elegant and most efficient mathematical instru- ment, which enabled Hipparchus and Ptolemy to represent and predict much better than their pre- decessors had done ; and it was probably at least as good a theory as their instruments and capabi- lities of observation required or deserved. And many readers will be surprised to hear that the modern astronomer to this day resolves the same motions into epicyclic ones. When the latter ex- presses a result by series of sines and cosines (especially when the angle is a mean motion or a multiple of it) he uses epicycles ; and for one which Ptolemy scribbled on the heavens, to use Milton's phrase, he scribbles twenty. The differ- ence is, that the ancient believed in the necessity of these instruments, the modem only in their convenience ; the former used those which do not sufficiently represent actual phenomena, the latter knows how to choose better ; the former taking the instruments to be the actual contrivances of nature, was obliged to make one set explain every thing, the latter will adapt one set to latitude, another to longitude, another to distance. Difference enough, no doubt ; but not the sort of difference which the common notion supposes. The fourth and fifth books are on the theory of the moon, and the sixth is on eclipses. As to the moon, Ptolemy explains the first inequality of the moon's motion, which answers to that of the sun, and by virtue of which (to use a mode of expression very common in astronomy, by which a word properly re- presentative of a phenomenon is put for its cause) the motions of the sun and moon are below the average at their greatest distances from the earth, and above it at their least. This inequality was well known, and also the motion of the lunar apogee, as it is called ; that is, the gradual change of the position of the point in the heavens at which the moon appears when her distance is greatest. Pto- lemy, probably more assisted by records of the ob- servations of Hipparchus than by his own, detected that the single inequality above mentioned was not sufficient, but that the lunar motions, as then known, could not be explained without supposition of an- other inequality, which has since been named the erection. Its effect, at the new and full moon, is to make the effect of the preceding inequality ap- pear different at different times ; and it depends not only on the position of the sun and moon, but on that of the moon's apogee. The disentangle- ment of this inequality, the magnitude of which depends upon three angles, and the adaptation of an epicyclic hypothesis to its explanation, is the greatest triumph of ancient astronomy. The seventh and eighth books are devoted to the stars. The celebrated catalogue (of which we have before spoken) gives the longitudes and lati- tudes of 1022 stars, described by their positions in the constellations. It seems not unlikely that in the main this catalogue is really that of Hip- parchus, altered to Ptolemy's own time by assum^ ing the value of the precession of the equinoxes PTOLEMAEUS. given by Hipparchus as the least which could "be ; some changes having also been made by Ptoiemy 8 own observations. This catalogue is pretty well shown by Delambre (who is mostly successful when he attacks Ptolemy as an observer) to repre- sent the heaven of Hipparchus, altered by a wrong precession, better than the heaven of the time at which the catalogue was made. And it is observed that though Ptolemy observed at Alexandria, where certain stars are visible which are not visible at Rhodes (where Hipparchus observed), none of those stars are in Ptolemy's catalogue. But it may also be noticed, on the other hand, that one original mistake (in the equinox) would have the effect of making all the longitudes wrong by the same quantity ; and this one mistake might have oc- curred, whether from observation or calculation, or both, in such a manner as to give the suspicious appearances. The remainder of the thirteen books are devoted to the planets, on which Hipparchus could do little, except observe, for want of long series of observa- tions. Whatever we may gather from scattered hints, as to something having been done by Hip- parchus himself, by Apollonius, or by any others, towards an explanation of the great features of planetary motion, there can be no doubt that the theory presented by Ptolemy is his own. These are the main points of the Almagest, so far as they are of general interest. Ptolemy ap- pears in it a splendid mathematician, and an (at least) indifferent observer. It seems to us most likely that he knew his own deficiency, and that, as has often happened in similar cases, there was on his mind a consciousness of the superiority of Hipparchus which biassed him to interpret all his own results of observation into agreement with the predecessor from whom he feared, perhaps a great deal more than he knew of, to differ. But nothing can prevent his being placed as a fourth geometer with Euclid, Apollonius, and Archimedes. De- lambre has used him, perhaps, harshly ; being, certainly in one sense, perhaps in two, an ind^'- ferent judge of the higher kinds of mathematical merit. As a literary work, the Almagest is entitled to a praise which is rarely given ; and its author has shown abundant proofs of his conscientious fairness and nice sense of honour. It is pretty clear that the writings of Hipparchus had never been public property : the astronomical works which intervene between Hipparchus and Ptolemy are so poor as to make it evident that the spirit of the former had not infused itself into such a number of men as would justify us in saying astronomy had a scien- tific school of followers. Under these circum- stances, it was open to Ptolemy, had it pleased him, most materially to underrate, if not entirely to suppress, the labours of Hipparchus ; and without the fear of detection. Instead of this, it is from the former alone that we now chiefly know the latter, who is constantly cited as the authority, and spoken of as the master. Such a spirit, shown by Ptolemy, entitles us to infer that had he really used the catalogue of Hipparchus in the manner hinted at by Delambre, he would have avowed what he had done ; still, under the circumstances of agreement noted above, we are not at liberty to reject the suspicion. We imagine, then, that Ptolemy was strongly biassed towards those me- thods both of observation and interpretation, which 1
