146 



by the results of Lieutenant ARMITAGE'S observations during his western journey, also by consideration of 

 the values given on SABINE'S charts. 



Assuming the Total Force to be -6876, as determined from Mr. BERNACCHI'S observations at the Ice 

 Station, McMurdo Sound, values of Horizontal Force were calculated for each degree of Inclination between 

 82 and 87" S. 



The same assumption, viz., that the Total Force did not vary, was also employed in determining the 

 correction to Inclination observations due to the vertical force of the ship. 



This correction at the position of swinging, January 23, 1902, was ascertained by comparison of the 

 Inclination value estimated from the preliminary chart with the value of N taken as the mean of the 

 results of the four observations near N., E., S., and W., the true vertical component and the vertical 

 component on board being also calculated. 

 Now if be the absolute Inclination, 



O n Inclination on board as indicated by N, 



H absolute Horizontal Force, 



HI ,, mean Horizontal Component on board, 



V absolute Vertical Force, 



Vi mean Vertical Component on board, 



V Vi 



tan = == and tan 6 n = = , 



HI 



then 



from which 



tan 6 = tan O n x ^} 

 VjJbl 



but 



HI = XH, therefore tan 6 = tan O n x =r- . 



Over the area under consideration the ratio V/Vj will not vary to any appreciable extent and may be 

 considered constant. 



X is constant, therefore XV/Vi is constant. 



Its value as determined from observations of January 23 is 



0-9393 = log- 1 1-9728, 



which has been applied as a constant to the values of N as determined from each observation. 



The corrections for instrumental differences were determined from observations made at the Ice Station, 



McMurdo Sound, with Circle No. 27, and the two instruments used for the observations considered in this 



section, viz., 



Fox Circle No. 29, used by Mr. BERNACCHI ; and 

 Lloyd-Creak Circle No. 143, used by Lieutenant ARMITAGE. 



The results showed that the readings by these instruments were in excess of the standardised value 

 derived from observations with Circle No. 27 by the following amounts : 



Excess over Standard. 



Fox Circle No. 29 2'-7 



Needle No. 1. Needle No. 2. 

 Lloyd-Creak Circle No. 143 3' -2 5' -7 



These differences have been applied to the observations for Inclination made with the instruments 

 quoted. 



To sum up : The following corrections have been applied to the observed readings in the order given 



below : 



1. Correction for instrumental differences. 



2. ,, ,, unsymmetrical iron. 



3. due to direction of ship's head. 



4. ,, vertical force of ship. 



The resulting values of Inclination are given in Tables XII. and XIII. 



