A Dictionary of Greek and Roman biography and mythology. By various writers. Ed. by William Smith. Illustrated by numerous engravings on wood.

17 6 PTOLEMAEUS. PTOLEMAELUS.
appear to ]lave added to his predecessor at all, in given by Ilipparchus as the least which could be
discovery at least. some changes having also been made by Ptolemy's
On this theory of epicycles, we may say a word own observations. This catalogue is pretty well
once for all. The common notion is that it was a shown by Delambre (who is mostly successful
cumbrous and useless apparatus, thrown away by when he attacks Ptolemy as an observer) to reprethe moderns, and originating in the Ptolemaic, or sent the heaven of Hipparchus, altered by a wrong
rather Platonic, notion, that all celestial motions precession, better than the heaven of the time at
most either be circular and uniform motions, or which the catalogue was made. And it is observed
compounded of them. But on the contrary, it was that though Ptolemy observed at Alexandria,
an elegant and most efficient mathematical instru- where certain stars are visible which are not visible
ment, which enabled Hipparchus and Ptolemy to at Rhodes (where Hipparchus observed), none of
represent and predict much better than their pre- those stars are in Ptolemy's catalogue. But it may
decessors had done; and it was probably at least also be noticed, on the other hand, that one original
as good a theory as their instruments and capabi. mistake (in the equinox) would have the effect of
lities of observation required or deserved. And making all the longitudes wrong by the same
many readers will be surprised to hear that the quantity; and this one mistake might have ocmodern astronomer to this day resolves the same curred, whether from observation or calculation, or
motions into epicyclic ones. When the latter ex- both, in such a manner as to give the suspicious
presses a result by series of sines and cosines appearances.
(especially when the angle is a mean motion or a The remainder of the thirteen books are devoted
multiple of it) he uses epicycles; and for one to the planets, on which Hipparchus could do little,
which Ptolemy scribbled on the heavens, to use except observe, for want of long series of observaMilton's phrase, he scribbles twenty. The differ- tions. Whatever we may gather from scattered
ence is, that the ancient believed in the necessity hints, as to something having been done by Hipof these instruments, the modern only in their parchus himself, by Apollonius, or by any others,
convenience; the former used those which do not towards an explanation of the great features of
sufficiently represent actual phenomena, the latter planetary motion, there can be no doubt that the
knows how to choose better; the former taking the theory presented by Ptolemy is his own.
instruments to be the actual contrivances of nature, These are the main points of the Almagest, so
was obliged to make one set explain every thing, far as they are of general interest. Ptolemy apthe latter will adapt one set to latitude, another to pears in it a splendid mathematician, and an (at
longitude, another to distance. Difference enough, least) indifferent observer. It seems to us most
no doubt; but not the sort of difference which the likely that he knew his own deficiency, and that,
common notion supposes. as has often happened in similar cases, there was
The fourth and fifth books are on the theory of on his mind a consciousness of the superiority of
the moon, and the sixth is on eclipses. As to the Hipparchus which biassed him to interpret all his
moon, Ptolemly explains the first inequality of the own results of observation into agreement with the
moon's motion, which answers to that of the sun, and predecessor from whom he feared, perhaps a great
by virtue of which (to use a mode of expression very deal more than he knew of, to differ. But nothing
common in astronomy, by which a word properly re- can prevent his being placed as a fourth geometer
presentative of a phenomenon is put for its cause) the with Euclid, Apollonius, and Archimedes. Demotions of the sun and moon are below the average lambre has used him, perhaps, harshly; being,
at their greatest distances from the earth, and certainly in one sense, perhaps in two, an indifabove it at their least. This inequality was well ferent judge of the higher kinds of mathematical
known, and also the motion of the lunar apogee, as merit.
it is called; that is, the gradual change of the As a literary work, the Almagest is entitled to
position of the point in the heavens at which the a praise which is rarely given; and its author has
moon appears when her distance is greatest. Pto- shown abundant proofs of his conscientious fairness
lemy, probably more assisted by records of the obh and nice sense of honour. It is pretty clear that
servations of Hipparchus than by his own, detected the writings of Hipparchus had never been public
that the single inequality above mentioned was not property: the astronomical works which intervene
sufficient,but that the lunar motions,as then known, between Hipparchus and Ptolemy are so poor as to
could not be explained without supposition of an- make it evident that the spirit of the former had
other inequality, which has since been named the not infused itself into such a number of men as
evection. Its effect, at the new and full moon, is would justify us in saying astronomy had a sciento make the effect of the preceding inequality ap- tific school of followers. Under these circumpear different at different times; and it depends stances, it was open to Ptolemy, had it pleased
not only on the position of the sun and moon, but him, most materially to underrate, if hot entirely to
on that of the moon's apogee. The disentangle- suppress, the labours of Hipparchus; and without
ment of this inequality, the magnitude of which the fear of detection. Instead of this, it is from
depends upon three angles, and the adaptation of the former alone that we now chiefly know the
an epicyclic hypothesis to its explanation, is the latter, who is constantly cited as the authority,
greatest triumph of ancient astronomy. and spoken of as the master. Such a spirit, shown
The seventh and eighth books are devoted to by Ptolemy, entitles us to infer that had he really
the stars. The celebrated catalogue (of which we used the catalogue of Hipparchus in the manner
have before spoken) gives the longitudes and lati- hinted at by Delambre, he would have avowed
tudes of 1022 stars, described by their positions wvhat he had done; still, under the circumstances
in the constellations. It seems not unlikely that of agreement noted above, we are not at liberty to
in the main this catalogue is really that of Hip- reject the suspicion. We imagine, then, that
parchus, altered to Ptolemy's own time by assum- Ptolemy was strongly biassed towards those meing the value of the precession of the equinoxes thods both of observation and interpretation, which