230 NOTE ON THE CONSTANT OF LUNAR PARALLAX. [28 



coefficients of parallax and those obtained by a transformation of the results 

 of Hansen's preliminary theory was that which has the argument denoted 

 by t + z in Damoiseau's notation. 



The corresponding term in w is in Hansen's preliminary theory 



I0"-92cos(t + z), 



whereas in the Introduction to the Lunar Tables this term is 



8"73 cos (+); 



the correction to the coefficient is 2"' 19, and multiplying this as before 

 by sin 1" and by 3422" we find the correction to the corresponding term 

 of the sine of the parallax to be 



-0"'036cos(<4-z), 



and if this be applied to the value of this term in the preliminary theory, 

 viz. 0"'181 cos (t + z), 



the result is 0"'145 cos (t + z), 



which agrees perfectly with my own. 



It should be remarked that, in the Introduction to his Lunar Tables, 

 Hansen still continues to use the same fundamental data as he had done 

 in his earlier paper, so that the value of the constant term in the sine 

 of the parallax according to the data adopted in the Tables is 3422"'08. 



Note added June 17, 1880. 



In Professor Newcomb's valuable transformation of Hansen's Lunar Theory, 

 which I have just received, it is wrongly assumed that I employed the 

 same data as Hansen for the figure and dimensions of the Earth, and 

 that my value of P, viz. 3 '25 698 9 feet, relates, like Hansen's, to a point 



the sine of whose geocentric latitude is -r , whereas it should be the geo- 



v 



graphical latitude, as that is the latitude which enters into Baily's formula 

 from which my value of P is deduced. 



In consequence of this, Professor Newcomb finds a discrepancy of 0"'03 

 between Hansen's value of the constant of parallax and mine when both 

 are derived ffom the same system of fundamental data; but it has been 

 shewn above that no such discrepancy exists. 



By a typographical error, the value of P which Professor Newcomb 

 quotes from me is printed as 3'256 89 feet, instead of 3'256989 feet. 



