Figure of the Earth from Geodetic Data. 21 



which omits altogether the effect of local attraction at the refer- 

 ence-station. But I have now one step more to take. 



III. To suggest an Improvement of my Method. 



5. I intend now to propose an improvement of my method 

 which I think will correct, not only the larger defect of BessePs, 

 but also the smaller error which I have hitherto left uncorrected 

 in my own. I will retain the correction z. It is necessary to 

 frame an hypothesis regarding it in order to apply the principle 

 of least squares. The hypothesis that z is an independent vari- 

 able breaks down, as I have shown, and leads us into error. The 

 hypothesis that z should have that particular form assigned to it 

 which the principle of least squares suggests, viz. the average 

 value, with its sign changed, of all the corrections of the several 

 stations of the arc relatively to the reference- station and mea- 

 sured along the variable ellipse, also breaks down for the same 

 cause ; t is swept away from the equations when reduced ; the 

 measured arc, in fact, is allowed to shift away, as before, to a 

 part of the ellipse to which it may not belong. It is necessary, 

 therefore, to make some other hypothesis. I will give to z that 

 particular value of the form above referred to which appertains 

 to the mean ellipse; in short, z shall equal 



(m) + (a)V + (13)\ ^ 

 i 



a constant quantity. This hypothesis is free from the objec- 

 tions to the other two, and suits the problem. 



This leaves the elaborate calculation in my paper in the Pro- 

 ceedings of the Royal Society, No. 64, untouched, except that 

 z + t y a constant quantity, must be substituted for t in the for- 

 mulae. 



6. In the case of the three arcs, the Anglo-Gallic, the Rus- 

 sian, and the Indian, I gather from Tables II. and I., p. 262 

 of that paper, and p. 270, that 



„_ K) + ( ai )U+(/3,)V 



66-760-30-7150 x 0-3581-12-3936 x 0-8819 

 34 



69 531 - 54-4933 x Q-3581 - 15-9852 x 0-8819 

 13 



1-764+ 1-5836 x 0-3581-2-6109 x 0-8819 _ 

 8 ~~" 



= -2"-76, 

 -0"003. 



