254 
TRIGONOMETRY 
The work of Hipparchus. 
Discovery of ‘precession. 
1. The greatest is perhaps his discovery of the precession 
of the equinoxes. Hipparchus found that the bright star 
Spica was, at the time of his “observation of it, 6° distant 
from the autumnal equinoctial point, whereas he deduced from 
observations recorded by Timocharis that Timocharis had 
made the distance 8°. Consequently the motion had amounted 
to 2° in the period between Tirnocharis’s observations, made in 
283 or 295 B.C., and 129/8 B.C., a period, that is, of 154 or 
166 years; this gives about 46-8" or 43-4" a year, as compared 
with the true value of 50-3757". 
Calculation of mean lunar month. 
2. The same discovery is presupposed in his work On the 
length of the Year, in which, by comparing an observation 
of the summer solstice by Aristarchus in 281/0 b.c. with his 
own in 136/5 B.C., he found that after 145 years (the interval 
between the two dates) the summer solstice occurred half 
a day-and-night earlier than it should on the assumption of 
exactly 365^ days to the year; hence he concluded that the 
tropical year contained about -g^oth °f a day-and-night less 
than 365^ days. This agrees very nearly with Censorinus’s 
statement that Hipparchus’s cycle was 304 years, four times 
the 76 years of Callippus, but with 111,035 days in it 
instead of 111,036 ( = 27,759 x 4). Counting in the 304 years 
12 x 304 + 112 (intercalary) months, or 3,760 months in all, 
Hipparchus made the mean lunar month 29 days 12 hrs. 
44 min. 2\ sec., which is less than a second out in comparison 
with the present accepted figure of 29-53059 days! 
3. Hipparchus attempted a new determination of the sun’s 
motion by means of exact equinoctial and solstitial obser 
vations; he reckoned the eccentricity of the sun’s course 
and fixed the apogee at the point 5° 30' of Gemini. More 
remarkable still was his investigation of the moon’s 
course. He determined the eccentricity and the inclination 
of the orbit to the ecliptic, and by means of records of 
observations of eclipses determined the moon’s period with 
extraordinary accuracy (as remarked above). We now learn