168 Journal of the Asiatic Society of Bengal. [N.S., XV, 
lutions (#) given were obtained. They first appear in the 
texts in a fairly accurate form and their appearance coincides 
with the introduction of the larger cycles—which, indeed, were 
introduced in order to express the planetary revolutions in 
integral quantities. 
12. Synodic revolutions.—The synodic A adateare are 
not usually given in the texts, but they occur in a somewhat 
disguised form in the Pafichasiddhantika (Ch. xviii). if re is 
the synodic period of a planet and P, is its sidereal period and 
E is the sidereal year we have 
where the upper sign is to be taken for a superior and the 
lower for an inferior planet; and since P, = YE/R we have 
P,= YE/+(Y-—R) which is the ae ‘implied by Varaha 
Mihira. His synodic revolutions are given in saura days as 
ows :— 
Mars. Mercury. Jupiter. Venus. Saturn. 
768% 114.8, 393} 5752 3722 saura days. 
and since 360 saura days = 365°256 mean solar days approxi- 
mately these values becom 
Mars. Merc Jupiter. Venus. Saturn. 
780 1159 3988  583°9 378 days. 
13. Epicycles.—The calculated mean positions of the 
planets were corrected for the so-called ‘ first inequality ’ (that 
one, namely, which depends on the planet’s position relative 
to the sun), in the Greek fashion, by assuming certain epicyclic 
motions. The Greek astronomers taught that, while the 
planet’s mean motion could be represented as a movement on 
the circumference of one circle, called the deferent, its actual 
motion was on the circumference of another circle, called the 
epicycle, whose centre was the mean position on the circum- 
ee & the deferent. This is the scheme in broad outline 
only: it was apparently based on the principle that the motions 
of a Fania nly body must be made up of pure circular motions 
—a principle that does not appear to have influenced the 
Hindus 
In figure 10 the epicyclic motion of an outer planet of 
the type of Mars is roughly represented. The point E repre- 
sents the position of the earth, the circle A, A, Ag, etc., is the 
position of the planet is at A,. The e epicycle is not drawn for 
other mean positions, but its radius is marked (A, B,, A; Bz, 
etc.). The points A,, A), A,, etc. mek the mean position on 
