NO. 7.] 



INCLINATION. 



133 



The difference between this and the inclination /' observed with the appa- 

 ratus, will then be the index-error of B. The result of the calculations is 

 given in the following table. 



The mean value of the index-error found in this manner at an inclination 

 of about 85, differs so considerably from that found in Hamburg and 

 Wilhelmshaven at an inclination of about 67, that 4 can hardly be regarded 

 as constant. Now if we had also had a determination of // at a place where 

 the inclination is about 75, we should, as already mentioned, have been 

 able to determine all three constants, c, p, and a, in equation (1). As this 

 is not the case, our only alternative is to put c = , if any regard at all is 

 to be paid to the variableness of the index-error with inclination and total 

 intensity. An assumption such as that the angle between the magnetic and 

 the geometrical axes of the needle is infinitesimally small in proportion to 

 the error in the inclination-determinations caused by the eccentricity of the 

 centre of gravity, will also usually be perfectly justifiable, and upon this 

 hypothesis equation (1) becomes 



^ = 4cos l/' + o). 



(4) 



We then have the following corresponding data for the determination 

 of the constants p and a: 



4 W I' 



Hamburg 1893 + Wilhelmshaven 1897 



Fram Expedition 189394 .... 49-4' 0'5352 8550'2' 

 If we substitute these values in formula (4), to which is given the form 



WJ = x cos I' y sin 1', 



where x = p cos a, and y = p sin , 



