CALCULATION OF AN ECLIPSE OF THE MOON. 297 



Benares lies sbcty-four yojans eastward from this meridian ; 

 its longitude is therefore fourty-four palas. 



To determine the moon's distance, or her parallax, they 

 observe the time of the moon's rising, and compare it with 

 the computed time ; the difference is the tmie in which she 

 describes an arc of her orbit, equal in length to the earth's 

 semidiameter ; this difference of time is to her periodic 

 month as 800 yojans to the circumference 324,000. Thev 

 neglect refiraetion, of which they seem to have no know- 

 ledge, although they are not quite ignorant of optics, be- 

 cause they know that the angle of incidence is equal to the 

 angle of reflection of a ray. They also reckon the motion 

 along the sine instead of the arc. In this way they find the 

 parallax to be 53' 20", and her distance from the earth's 

 centre to be 51,.570 yojans, which answer to about 220,184 

 geographical miles. European science has determined it to 

 be about 240,000 miles, which is about a fifteenth part more 

 than the Hindoos had found it so long ago as the time of 

 Meya, the author of the Surya Siddhanta. 



The Hindoos suppose that all the planets move in their 

 orbits with the same velocity. The dimensions of the 

 moon's orbit being known, those of the other planets are 

 determined by the rule of proportion. 



To find the diameters of the sun and moon, the time that 

 elapses between the upper limb of the rising sun toucliing 

 the horizon and the lower limb reaching it is obser\-ed ; in 

 this way the sun's diameter has been found 6500 yojans, 

 and that of the moon 480 yojans. These diameters are 

 varied according as they exceed or fall short of the mean in 

 the calculation of eclipses, ^\^len the moon's anomalv is 

 three signs, her diameter is reckoned to be 32' 24", which 

 is suflSciently exact. 



The calculation of an eclipse of the moon, by the prin- 

 ciples of European astronomy, with the aid of the more 

 simple tables, — those in Ferguson's Astronomy for example, 

 — is not a tedious operation. It is, however, otherwise in 

 the Indian astronomy. The first step of the process is to 

 find the number of mean solar days from the time of the 

 creation to the time of the eclipse ; the next, to find the mean 

 longitude of the sun, moon, and the ascending node : these are 

 determined by very tedious operations in multiplication and 

 division. The astronomical calculations in Europe led to 



