ON THE MAGNETIC INTENSITY OF THE EARTH. 31 
Notice of the manner in which the results in the above table 
have been computed.—There are five stations in North Ame- 
_ rica at which Mr. Douglas observed the dip. ‘The number of 
_ separate observations is 21 distributed as follows: 
Cape Disappointment . . . 38 
Pont George: FR 
Hore. Yancoirver 0s es SG 
Sie Bran@isto 3 po. SS 
Money Blk ee OT 
To compute from these the dip at the eighteen stations where 
_ it was not observed, we require the direction of the isoclinal 
lines, and the rate at which the dip increases in the perpendi- 
cular to them. 
The relative position of the five stations, being nearly on the 
same geographical meridian, is unfavourable for determining 
the direction of the lines; but, on the contrary, extremely fa- 
vourable for a deduction of the rate at which the dip increases 
in the perpendicular to them; and as the horizontal stations 
are all nearly under the same meridian also, the rate of increase 
is the element of calculation, which it is most important to ob- 
tain correctly. ‘ 
To compute, therefore, the rate of increase from the observa- 
tions themselves, we may take the direction of the lines from 
a general map, as a small uncertainty in this respect has little in- 
fluence on the result. In M. Hansteen’s map of the lines of 
dip in 1780 we find their direction in that part of the globe to 
be from N. 74° W. to S. 74° E.* If we express by r the rate 
of increase corresponding to a geographical mile, and make 
8 = the dip at a central geographical position, say 45° N. 
lat., and 124° W. long., and 9,, 8,, 65, &c., the observed dip at 
the five stations, we shall have 
8, = 8 + (a, cos 74° — b, sin 74°) r 
é 8, = 8 + (a, cos 74° — b, sin 74°) r, &e., 
_ the coefficient a being the difference of longitude between the 
ie central station and that at which the dip was observed, ex- 
__ * When I wrote the above I had not seen M. Erman’s more recent mag- 
| _‘ netic map from his own observations in 1828, 1829 and 1830, in which are de- 
_ lineated the dip lines of 60°, 65°, and 70°, which pass through the district in 
_ which Mr. Douglas’s observations were made. Their direction in the meridian 
| _ of 124° W. measured on M. Erman's map is, as nearly as the measurement can 
be made, from N. 743° W. to 8. 743° E. I add this note to explain the reason 
| __ why the direction in the text was not taken at once from the more modern and 
_ cotemporaneous map, and to express the satisfaction I feel in this confirmation 
| _ of the element I had ventured to introduce for the calculation of Mr. Douglas’s 
_ results,—the only element in the calculation which was not furnished by his 
___ own observations. 
