388 
MR. CHRISTIE ON THE MAGNETICAL OBSERVATIONS 
the observations made by Captain Back are peculiarly well adapted, since in no case 
has so direct a progress been made, to such an extent, towards the magnetic pole, 
whether we consider that point as the point of convergence of magnetic meridians, 
or that at which the direction of the force is vertical. Assuming then the coincidence 
of these points, I had proposed inquiring whether the differential of the dip and the 
differential of the magnetic latitude, taking the increments in observations not very 
distant from each other to express these differentials, had the ratio which the theory 
gave, and had indeed made the requisite computations and comparisons ; but on 
further consideration it appeared to me that this comparison was not so good a test 
of the theory as the more direct one of the dip itself with the magnetic latitude, 
since small errors in the dip would become very sensible in the value of the differen- 
tial, and if these errors happened to conspire at two stations, this value might be 
doubled or reduced one half. I do not propose in the first instance giving the detail 
of that comparison, but it may be proper to mention the general nature of the 
results. 
If X represents the magnetic latitude, and h the dip, then the equation 
tan h = 2 tan X 
gives 
d 8 3 cos 2 8 + 3 
~d\ 4 
In comparing the observations with this formula, I took the sum of the dips at two 
stations as the value of 2 S. The first observations which I employed in this compa- 
rison were those at Musk-Ox Rapid and Rock Rapid ; and here the agreement was so 
marked that I certainly anticipated a general close agreement of the observations 
with the theory. This, however, was the only instance of that agreement which we 
ought to expect in such cases, if a theory be correct. 
As the magnetic polar distances of two stations are determined from their geogra- 
phical position and the observed variations of the needle by the solution of two 
spherical triangles, it would be superfluous to point out the course of calculation 
which I adopted ; but it is necessary that I should state the nature of the comparison 
which I propose instituting between the results of theory and observation. 
If <p is the magnetic polar distance of one station, and <p t that of another, the dip at 
the two stations being h and then if the theory and the observations be both cor- 
rect we shall have 
tan 5 . tan <p = 2 and tan ^ tan <p ; = 2 (15-)? 
and we may judge, by the approximation of these products in all cases to the number 
2, of the degree of coincidence between the theory and the observations. 
In the third column of the following Table are given the distances of the several 
stations from the magnetic pole of convergence, whose position is determined from 
the variations in the second column at the respective stations, combined as indicated 
in the first column; in the fourth column, the dip of the needle at these stations, as 
