160 



PROCEEDINGS OF THE AMERICAN ACADEMY 



From the residuals of Table VIII., we have the following normal equation3 

 for determining the periodic coefficients for errors of double period : — 



Green- "Wash, 

 wich. I. Oxford. Paris. 



15.707n'— .4I«'=2r'sin2a= — 19 +39 —74 —22 

 .4lTO'+16.28K'=Sr/cos2a= +15 —77 +5 +77 



Edinburgh. 

 12.64 m'— .61 k' = 2 r' sin 2a = — 86 

 ,61 m' +13.33 n' = 2 r' cos 2a = —37 



Harvard College. 

 14.75 m'+ .28n' = 2Wsin2a = +121 

 .28 m' +15.22 n' = I,r' cos 2a = — 26 



"Whence : 



St s 



Por Greenwich ?n' = —.001 n' = +.00*1 



Washington, I = +.002 = —.005 



Oxford = —.005 = +.000 



Paris = —.001 = +.005 



Melbourne = +.002 = +.001 



Edinburgh = —.007 = —.002 



Brussels = +.003 = +.001 



Washington, II = +.005 = +.001 



Harvard College = +.008 = —.002 



Subtracting the values of r', computed with the coefficients m' and n', from the 

 residuals of Table VIII., we have finally Table IX., containing the final correc- 

 tions to the assumed places. 



TABLE V. 



