Figure of the Earth from Geodetic Data. 1 9 



tance from its proper place. In fact, owing to the mere chance 

 condition of the several divisions of the arc, the most important 

 point of all (the reference-station) being left out of considera- 

 tion, the Anglo-Gallic arc may be shifted one way, the Russian 

 the other, and so of the rest ; and the problem solved will be 

 something of this kind, Given a certain number of pieces of 

 curves, to find the nearest ellipse to which they can be made 

 to belong, no restriction being imposed as to the parts of the 

 ellipse to which they are respectively applied. This, of course, 

 is not the physical problem which we have to solve; which is 

 rather this, To find the nearest ellipse to which the several pieces 

 of curves can be made to fit, the pieces all retaining their actual 

 places. 



3. The error, then, in BessePs process is, I conceive, his treat- 

 ing x as an independent variable, which amounts to the same as 

 his not taking into account the effect of local attraction in the 

 correction x of the reference-station. It was to remove this defect 

 that I published my method, which I will now describe. 



II. To explain my own method, as already published. 



4. The first thing is to introduce a correction for local attrac- 

 tion. But there are no known means of determining its amount ; 

 all that is known is that it may be zero, or it may be, for all we 

 know a priori , as much as (say) 30", more or less. Our igno- 

 rance of its amount is no excuse for leaving it out altogether ; 

 for it may have a very important effect. It must be some defi- 

 nite constant quantity at each station. Our only course is, 

 therefore, to put an algebraical symbol, such as the constant t, 

 to represent its amount. 



Suppose ABCD is the measured arc, and a b c d is the mean 

 ellipse ; and let a/3 y 8 be any other ellipse near the mean ellipse, 



and whieh I will call the variable ellipse. Let m A be the ver- 

 tical at A in which the plumbline hangs, nAa a normal through 



C2 



