94 ON NEW TABLES OF THE MOON'S PARALLAX. [17 



For the sake of comparison I will here give the formula on which 

 Burckhardt's own Tables are constructed, which is as follows : 



0-4- 0'4 cos (Arg. 1) 



0'8+ 0'8 cos (Arg. 2) 



0'3+ 0'3 cos (Arg. 4) 



0'8+ 0'8 cos (Arg. 5) 



1-1+ 0'8 cos (Arg. 6) 



0-6- 0-6 cos (Arg. 8) 



1-8+ 1-8 cos 2 (Arg. 9) 



07+ 07 cos (Arg. 12) 



1-0+ I'O cos (Arg. 13) 



43-0+ 37 "4 008^ + 0"-4cos2J? 

 30-0 - 1 -0 cos V+ 26" -3 cos 2 V+ 0"'3 cos 3 V 

 55' 40-0 + 187-0 cos A + 10"'2 cos 2A + 0"'3 cos 3A 



The sum of the constants in this formula is 3420"'5. 



The errors of the coefficients of Equations 2 and 12 arise from the 

 mistake respecting the formation of the Argument of Variation before ex- 

 plained, and those of the coefficients of Equations 4 and 13 from the similar 

 mistake respecting the Argument of Evection. 



Equation 6 is taken with a wrong sign, and in the Variation Equation 

 3 V appears to be wrongly substituted for 4 V, though I find that the 

 corresponding term, when reduced to Burckhardt's form, has a smaller co- 

 efficient. 



In consequence of the way in which most of these errors originate, 

 their amount will be generally greatest in March and September, and least 

 about the beginning of January and July, when the Sun's mean and true 

 places coincide. 



The total error of Burckhardt's Tables may amount to nearly 6", in- 

 dependently of the change in the value of the constant. 



Looking at the accuracy of modern observations, it is easy to imagine 

 to what an extent the value of comparisons between observed and tabular 

 places may be diminished by their being liable to an error of this kind. 



In determining differences of longitude by means of occultations, it is 



