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fluenced by the disposition or density of the materials at 

 the surface, become of comparatively minor importance. 

 The ellipticity derived from this combination is there- 

 fore not only unaffected by the supposed error of which 

 we are treating, but is also much less liable to be 

 affected by errors of other kinds, than are the results of 

 the two following combinations in which the arcs are of 

 inferior extent. 2nd, In combining the middle latitude 

 series with one portion say, the equatorial of the 

 other series, the error of the assumption, if there be 

 one, is involved ; and though it may be a very small 

 error, its influence on the ellipticity derived from this 

 combination may be comparatively large, because the 

 arc comprehended by the stations is now reduced to 

 nearly one half of the extent it had when the polar and 

 equatorial series were taken together. 3rd, The same 

 reasoning holds when the middle latitude series is com- 

 bined with the other portion, i. e. the polar portion, of 

 the series with the invariable pendulum: but in this 

 case the ellipticity resulting from the combination will 

 have an error in the opposite sense to the deduction in 

 No. 2. 4th and lastly, When the whole of the results 

 of the two series are combined, by means of an assump- 

 tion which involves a small error in the comparability of 

 the middle latitude results with those of the polar and 

 equatorial stations, the ellipticity resulting therefrom will 

 exhibit a small difference from that derived from the 

 combination of the polar and equatorial results, for the 

 strict comparability of which no such assumption was 

 required ; but the difference will be small in comparison 

 with that in 2 and 3, partly because opposite effects 

 tend to counterbalance each other, and partly because 



