Sanscrit Writing and Language. 127 



false hypothesis, must exhibit the mean motions too great for the planets which 

 had really passed the line of conjunction at the assumed epoch ; and too little, for 

 those which then had not as yet arrived at it. The remoter, indeed, that epoch 

 is, the less will come out the error in the mean motion of each planet, as being a 

 given quantity (and that, at all events, not more than a semicircle) distributed 

 among a greater number of revolutions ; which explains the cause of the Hindoo 

 cycles being made so enormously great, and of their magnitude being increased in 

 each succeeding system. By such means the errors in mean motion may be so 

 much reduced, that the mean longitude of each of the heavenly bodies, — which 

 can be determined by the system, at a certain period not very far from the time of 

 its being constructed, just as accurately as by European tables, — shall come out 

 nearly accurate for some length of time reckoned backward and forward from 

 that period ; the interval during which the system thus answers being greater, in 

 the same proportion, as the errors in the mean motions it exhibits, are less. But 

 after some years the accumulation of errors, be they ever so small, must at last 

 become sensible ; and the farther the time for which the mean longitudes are 

 sought, recedes from the era of the construction of any set of Hindoo tables, the 

 greater must be the errors of the several computations in which those tables 

 are employed ; a circumstance which has given occasion to successive formations 

 of different systems, or rather to reconstructions of the one system, the main 

 principle on which they all are founded being the same. 



If a set of tables were framed ever so correctly upon the plan I have just 

 sketched out, they still could give the mean place of each heavenly body with 

 exactness only at one instant ; but they would so give it for every planet, apsis, 

 and node, at the same point of time, namely, at the time of their being con- 

 structed. As however the case is, no Indian tables are so correct; in all of them 

 the moment of exactness is different for different celestial objects ; but for each 

 object this moment can be ascertained in any set by a simple proportion. For 

 the error in the present mean longitude of a celestial object as given by a Hindoo 

 system, is the accumulation of error in mean motion since the instant for which 

 we are searching ; but the quantity of the former error is got by calculating the 

 present mean place of that object according to the Hindoo tables, and also 

 according to correct European ones, and then taking the difference ; and in like 

 manner the quantity of the latter error is had by calculating in each set of tables 



