given in 

 xve 



1808.] The Adjustment of the Hindu Calendar. 183 



4> = Polar Longitude. 

 A = True Longitude. 



g^. Cot w = tan a. 

 sin a sin <f> = sin A. 

 tan A. Cot a = sin /*, the quantity to be added or subtracted from <f> 

 to give A. 



Position in its portion or hhdga, 8° 



Polar Longitude, go 



Polar Latitude, jqo 



From the above we deduce the following by formula for Acvini. 



Lat 90° UN 



I^ng 11° 59' 



This is the position of Acvini according to the Hindu Tables and 

 astronomical works. This position of the junction star refers us back to 

 the fifth century A. C. In each case, to reduce the distance w 

 Flamsted's Catalogue for the Vernal Equinox of A. C. 560, we h 

 subtracted 15° 40' from the longitude there given. 



The following, however, are the real position of a and /? Arietis by 

 European calculations. 



Longitude of /? Arietis at about 560 A. C, 13° 56' 



Latitude, go 2g' i^- 



Longitude of a Arietis, 17° 37' 



Latitude, 90 57/ ^ 



Comparing these we find that the position of Acvini coincided 

 more with that of /? Arietis than with that of a Arietis. The Hindus 

 used very rude instruments of observation, and an error of even a 

 degree is allowable in their calculations. 



The retrograde motion of the equinoxes together with an error in 

 determining the exact length of the year has brought on this difference 

 in their calendar. 



The Hindu year, like all solar sidereal years, begins at the moment 

 of the sun's entrance into Acvini, the first asterism of the constella- 

 tion Aries, and ends with the moment the luminary leaves Piscium 

 to re-enter Acvini. Such a method of determining the length of the 

 year accompanied by the following easy but ingenious distribution of 

 the fractional parts of a day has saved the Hindu year from the error 

 which was an element in the European years before .the Julian correc- 



