330 MM. Struve and Dollen on the Correction 



figure : albeit the return to the beginning is really a step in 

 advance, inasmuch as we see ourselves led forward through it 

 to a new conception. Let us then once more conceive the 

 earth as a homogeneous sphere : in consequence of its rotation, 

 the geodetic figure of this ball becomes, as we said before, 

 that of a particular spheroid : all observed amplitudes and 

 measured geodetic distances thus come into perfect accord, 

 or rather each of them can be exactly deduced from the other 

 by calculation upon this spheroid. But now let us imagine 

 that levellings have been extended over the whole surface 

 of the earth. These would show us that only at the poles 

 and at the equator would the surface be vertical to the 

 direction of gravity. Every other point would be found to 

 lie in a plane inclined towards the equator ; towards which, 

 were there water thereon, it would flow off. To fix our ideas, 

 let us restrict our thoughts to the northern hemisphere : there 

 we should at every point recognize an excess of matter to 

 the north, and consequently should calculate for a deflection 

 of the plumb-line towards the north, that is to say, for a 

 positive correction to the observed latitudes. If we followed 

 this up logically at every point, a figure would doubtless 

 result, which would strictly represent all the data furnished 

 by observation, namely the geodetic distances and the cor- 

 rected amplitudes. Though it is unnecessary to consider at 

 present this figure more closely, so much at least is evident, 

 that it would be different from the one corresponding to the 

 uncorrected latitudes. But now, what do we learn from this ? 

 It is an open choice which of the two we will have. Certainly 

 it would be better to have both if possible ; but can further 

 argument be necessary to show the confusion that would be 

 introduced into the whole matter should one allow oneself 

 to be seduced into permitting small portions of these correc- 

 tions to be made here and there ! 



" We think to stop at this point. To try and exhaust the 

 subject would be neither suited to our powers nor demanded 

 by the occasion. We have, on the contrary, tried to resist the 

 frequently recurring temptation to closer detail or wider scope ; 

 but the object proposed we hope to have attained. Looking 

 back upon the foregoing pages, we think to have shown that 

 the view that, for the determination of the mean figure of the 

 earth, directly observed latitudes may without further justi- 

 fication be corrected for the amount of the apparent dis- 

 turbance of the plumb-line, and even that the calculation of 

 these corrections is an essential requirement of an arc measure, 

 rests either upon a confusion of ideas (that is to say, upon a 

 want of comprehension of what is really needed), or upon sup- 



