of Latitudes for Local A ttraction. 319 



geodesy the further task of expressing as nearly as possible the 

 whole surface of the earth accurately by a simple formula; that 

 is, to find a formula which shall represent all observed quantities 

 as nearly as possible; where it is scarcely necessary to add, that 

 before the actual solution of the problem is entered upon, the 

 expression here used, "as nearly as possible," must be assigned 

 its strict mathematical significance. The figure expressed by 

 this formula we will call, in opposition to the actual or local 

 figure, the mean or general figure of the earth. The attempts 

 which have been made to determine this figure permit it to be 

 regarded, as things now stand, as one of revolution, the axis 

 of which coincides with the earth's axis of rotation ; for in 

 the whole assembly of observations at our command there 

 is not the slightest indication that any amendment of this 

 assumption is demanded by them*. The problem is thus 

 essentially simplified, as it now merely consists in this, to 

 find the equation to a curve by the rotation of which this 

 mean figure of the earth shall be plainly presented. Now here, 

 indeed, the question might be raised whether for this purpose, 

 namely, the determination of the mean figure of the earth, it 

 might not be proper to correct the observed astronomical 

 amplitudes for the influence of visible inequalities of the earth's 

 surface upon the direction of gravity at the points of observa- 

 tion. The question has here at least a totally different meaning 

 from what it had above, where it had reference to the actual 

 figure of the earth. This view, which is not the one we hold, 

 is supported, as far as we can see, by the following arguments. 

 Among the possibly manifold causes of the deviation of the 

 local from the mean figure of the earth (for the future we will 

 give this deviation the shortened title of disturbance) is to be 

 included at all events the present one : we are in a position to 

 determine its effect, or, say, a part of it, with some accuracy : 



* That the contrary opinion has also been advanced from time to time 

 might have passed unnoticed here, bat that we wish to avoid any appear- 

 ance of ignoring altogether General Schubert's recent paper on this 

 subject ("Essai d'une determination de la veritable figure de la terre") 

 published by this xlcademy itself. Simply therefore for this reason, and 

 certainly not for the purpose of offering criticism, which would here be 

 out of place, we must say that the numbers given in that paper, if any 

 importance can be attached to them at all, contain a testimony for and 

 not against the statement made by us above. The whole essay seems to 

 us to be a truly striking instance of what may happen, if one attempts to 

 build upon figures derived from observation without first gaining a pre- 

 cise idea of the uncertainty which must attach to them on account of 

 their nature and the manner of their acquisition. Positive conclusions 

 are there based upon the wow-agreement of numbers which, in truth, 

 agree not only satisfactorily, but much more exactly than we could have 

 expected, 



