1S8?.] ^^^ [FFagen. 



to more than one thousand meters, and tinally proposes the following 

 problem to be solved : 



To find such an Ellipsoid of Revolution, 1, as has the volume of the 

 Earth; 2, that the sum of the Earth's elevations and depressions with regard 

 to this Ellipsoid become a minimum. 



This problem, however, as given by the author, seems to be indeter- 

 mined, unless a third condition is added, viz. : that the rotation axis of the 

 Ellipsoid is parallel to that of the Earth and their centres coincide. 



Mr. Hann is of the opinion that the solution of this problem would afiord 

 the solution of another problem, open already a century ago, viz. : the 

 answer to the question, why the meridian mensurations and the observa- 

 tions of the second's pendulum, made on different points of the surface of 

 the Earth, afford such different values for the compression of the Earth ? 

 These observations, he says, ought to be reduced not to the actual level of 

 the sea, but to the level of that regular ellipsoid to be found by the above 

 problem, whose compression could then be found from these observations 

 with greater accordance. 



The treatise here published is intended not to solve Hann's problem, but 

 to take one step farther towards its solution. This solution seems to be an 

 impossibility as long as the inclination of the apparent towards the true 

 horizon is not known, for as many places as possible, both as to magnitude 

 and direction. On the following pages, therefore, the formulas shall be 

 developed by which both the influence of this inclination on astronomical 

 observations will be shown and the way suggested, how to determine its 

 magnitude and direction. Astronomers are well aware of the influence 

 that the deviation of the plumb-line exerts on finding the longitude and 

 latitude of a place and have begun to distinguish between the geodetic 

 and the astronomical position of a place. By the latter expression they 

 mean the longitude and latitude of the apparent horizon ; in other words, 

 the apparmHongitude and latitude of a place.* It is, however, evident, 

 that for parallactic observations and especially for the transits of Venus 

 and Mercury, not the apparent but the true longitude and latitude are 

 needed. Consequently the following pages, though not giving direct 

 means for finding the true position of an observatory, might be of some 

 interest, as they at least call attention to the errors caused' by the inclina- 

 tion of the horizon on astronomical observations. 



Let the pole of the true or mathematical horizon be denoted by Z, and 

 that of the apparent, or as we may call it, physical horizon by Z', then the 

 arc Z Z' represents the inclination of the latter towards the former as to 

 magnitude and direction. We resolve it into two rectangular components, 

 one of Avhich a may lie in the vertical plane of the instrument used, its 

 positive direction being towards the "sight-line" of the observer, while 

 the other component, /?, may be positive right-hand of the observer. In 

 case of an artificial horizon part of the inclination « may be caused by the 



* Note.— About this distinction see Chauvenet's Manual of Spherical and Prac- 

 tical Astronomy, Vol. i, Art. 86, 160, 213. 



