( 44 ) 



tions the mean latitude for each place and to join all the results 

 to a connected system of co-ordinates, by which the instantaneous 

 positions of the pole in respect to a mean one are represented. 

 Albrecht chose as co-ordinate axes the meridian of Greenwich and 

 one 90° westward, passing centrally over America, and finally he gives, 

 besides a curve for the motion of the pole, the said co-ordinates x 

 and y for every tenth of a year from 1890.0 till 1897.5. 



The curve of Albrecht is rather intricate and so we may take 

 for granted that his adjustment, performed undoubtedly with great 

 care, has strained the observations but slightly. Therefore I thought 

 myself justified in avoiding for my further computations the prolix 

 work of falling back upon the original observations, and in making 

 use of Albrecht's x and y co-ordinates. Finally however I have 

 also compared my results with the original observations. 



It being tolerably certain that the motion of the pole consists at 

 least in the main of a 14-monthly and a yearly motion, I have 

 examined. 



1". the 14-raontlily motion; 



2°. the yearly motion; 



30. in how far the observations may be represented by the com- 

 bination of a constant 14-nionthly and yearly motion. 



3. The \^-monthlij motion. 



Leaving the results 1897.0 — 1897.5 out of consideration for my 

 computation, I had 70 a- and 70 y- co-ordinates at my disposal. 

 Assuming for the present 432 days for the length of the period we 

 find 6 periods = 7 years and 35 days. So the data allow of a good 

 separation of the two motions, but the mutual commensurability is 

 not so approximate that an easy determination of the elements 

 of both at the same time can be founded thereon. So I began by 

 deriving in P' approximation the yearly motion and proceeded to 

 to use corrected x- and y- coordinates to determine the 14-monthly 

 motion. 



The computation of the x and y was made quite independent of 

 each other and, assuming 432 days for the length of the period, I 

 united in both cases the 70 values to 8 means, which then formed 

 the basis for the computation of periodic formulae. 



So I obtained: 



„ , „ f-2412439 



.«= + 0".151 COS 2 71 



432 



