Hagen.] ^-^-^ [Feb. 3, 



the true zenith distance ^ cannot be separated from the constant «, or, to 

 speak more exactly, from the constant q, they giving always the value of 

 ^ — q. Nor will it be possible to separate zenith distances from this incli- 

 nation by sextants or reflecting circles. The inclination 5 perpendicular to 

 the plane of the sextant or i-eflecting circle has indeed no influence on 

 finding altitudes, yet this is the case with the inclination a in the plane of 

 tlie instrument, all the readings of altitudes being too great by the angle «, 

 if an artificial horizon is used, while in case of a sea horizon the dip will be 

 aTIected by this inclination. Neither ot these errors can be eliminated by 

 these instruments. Thus by altitude observations the inclination of the 

 artificial horizon may be found as far as it depends on the attraction of the 

 instrument and its piers, but not as far as it depends on local irregularities 

 of the earth. 



Now to come to a conclusion, the question turns up to the astronomer, 

 by what means he will find the latitude and the time of his place. Since 

 in case that his apparent meridian line is not parallel to the true horizon, 

 all observations of stars will give him the latitude not of his place, but of 

 such places, whose true horizon is parallel to his apparent meridian line. 

 And in lilie manner if the plane of his apparent meridian does not go 

 through the centre of the earth, all observations of stars will furnish him 

 with the time not of his place, but of such places as are lying in a plane 

 parallel to his apparent meridian and touching the centre of the earth. 

 Consequently, all the methods of finding the longitude by immediate 

 transportation of time or by observation of signals visible at the same in- 

 stant will give him the longitude not of his place, but of the places just 

 defined. 



He must therefore look out for other means to find the errors in the dc- 

 lermination of the latitude and the longitude of his place, and consequently 

 also the constants of correction for his instruments, and such means seem 

 to be geodetic mensurations and the observation of parallactic phenomena. 

 If as many places of the earth as possible are combined by such observa- 

 tions and mensurations and the condition is made, that the sum of the 

 squares of diff"erences between the calculated and observed longitudes and 

 latitudes becomes a minimum, the probable errors in determining the posi- 

 tion of these places may be found. The first method has been partially 

 employed by Prof Schmidt in Gottingen and later also by the U. S. Coast 

 Survey.* On the instigation of the celebrated Gauss Prof Schmidt made 

 use of the different meridian mensurations to calculate the dimensions of 

 the terrestrial ellipsoid, so that the sum of the squares of difi^erences be- 

 tween the computed and observed latitudes was a minimum. He found 

 for the mean error of latitudes 3" .193. But it may be interesting to have 

 the complete result of his computation here reprinted from his " Lt'hrbuch 

 tier mathem. u. phys. Geography, Gottingen, 18.29, i. p. 199." 



* Report for 1853. 



