387 



Article XII. 



Determination of the Axes of the Elliptic SpJieroid of Revolu- 

 tion rvhich most nearly corresponds with the existinr/ Measure- 

 ments of Arcs of the Meridian. By F. W. Bess el. 



[From the Astronomische Nachrichttn, No. 333.] 



1 HE observed latitudes of points on the earth's surface, and 

 the distances between the parallels on which those points are 

 situated, have a relation which M"ould be given by a knowledge 

 of the figure of the earth. If the equation of the earth's surface 

 were known, we should be enabled to determine the constants, 

 whereby the measured distances between the parallels and the 

 observed latitudes of the parallels would be brought into accord 

 within the limits of the eiTors of observation. But the figure of 

 the earth is not know n, — or, rather, we know that it is irregular. 

 There is, however, an elliptical spheroid of revolution, the sur- 

 face of which is not far removed from the surface of the earth 

 at any point ; but whether at all points of the resjoective sur- 

 faces this distance may be regarded as a small quantity, com- 

 pared with the elhpticity of the spheroid, is a question yet to be 

 decided by the combination of sevei'al measurements of arcs. In 

 the mean time we may make progress in the inquiry by deter- 

 mining the axes of the spheroid which would most nearly repre- 

 sent the existing measurements. If we regard the deviations 

 of the surface of the earth from the surface of the spheroid as 

 following no definite law, their influence on the latitudes is com- 

 bined with that of the errors of observation of the latitudes, and 

 we must consider that spheroid to be the one sought for, which 

 brings the measured distances between the parallels in corre- 

 spondence with the latitudes, by correcting the observed lati- 

 tudes in accordance with the conditions of the method of least 

 squares. 



Walbeck first commenced the investigation upon this correct 

 view, but took into account only the most southern and the 

 most northern points of each measured arc, omitting in his 

 calculation the intervening astronomically determined points. 

 Schmidt improved on the earUer calculation, not only by giving 

 proper weight to all the observed latitudes, but also by taking 



