( r>2 ) 



circle) reduced to about one half. If the motion of the pole of inertia 

 is not simply elliptic, but, more generalh, expressible bv a series of 

 periodic terms, these are transmitted more and more reduced to the 

 pole of rotation the higher the terms we reach. So in general to 

 irregularities in the motion of the former will correspond much 

 smaller ones in that of the latter, 



All this remains not only true in principle, when we take the 

 period proper ol' the axis of the earth to amount to 431 days, but 

 also the numerical values remain about the same '). So it is pos- 

 sible and important to consider which motion of the pole of inertia 

 must be assumed to explain the yearly motion found for the pole 

 of rotation. Substituting my final results for 1890—96 in the gene- 

 ral formulae, we find as co-ordinates for the pole of inertia with 

 respect to the axes finally adopted : 



X = 4- 0".055 cos 2 n 



y—-}- 0".084 si7i 2 n 



«—Sept. 28 

 365 



<— Sept. 28 

 365 



that is, the motion must be retrograde^ the principal axes have 

 the same direction as those of the pole of rotation, but the major 

 and minor axes have changed places, and the motion of the pole of 

 inertia is but slightly smaller than that of the pole of rotation. "We 

 would have found a more considerable proportion had the ellipse of 

 the latter been assumed less excentric. 



So after all little has been gained for the explanation of the 

 phenomenon. Only it is perhaps more intelligible that the yearly 

 motion of the pole of rotation may be pretty regular, {\\Q\xg\i a priori 

 the reverse be probable for the pole of inertia. 



5. Comparison of the observed motion with the -sum of the two 

 adopted terms. 



In the first place the x and y of Albrecht have been compared 

 with the computed values. I adopted for the motion of 431 days 

 the same elements which have served for the derivation of the yearly 

 motion, and for the yearly motion my final results for the whole 

 period. So I found the following diflFerences between observation 

 and computation expressed in hundredths of seconds. 



1) See also Newcomb Moiithl. Not. 1892, March. 



