INTRODUCTION AND RESULTS. 
257 
nually. We may therefore presume from these instances, that the error in strict 
comparability, arising from the omission of a correction for secular change in the 
observations combined in this survey, the greater part of which differ not more than 
one or two years from a mean epoch, must be within the limits of the ordinary errors 
of observation, including of course those of station error. 
The method of computing the direction of the isoclinal lines, and the geographical 
distance between adjacent isoclinals representing certain differences in the amount 
of the Inclination, by a combination of the observations distributed over a limited 
district of the earth’s surface, was first proposed by Dr. Lloyd in the Magnetic 
Survey of Ireland: it is simple and convenient when the lines conform to the con- 
ditions of being straight, parallel, and equidistant ; but the problem becomes com- 
plicated and the calculation laborious in proportion as these conditions are departed 
from, and the number of indeterminate constants increases ; until at length both 
complication and labour become excessive. In the parts of the continent of North 
America under consideration in this memoir, the variation of the isoclinal lines from 
the simple form above described is considerable : they are not straight lines on any 
projection; they are not parallel, nor are they equidistant. I endeavoured, never- 
theless, to make the method of calculation answer, by breaking up the whole survey 
into several districts, and computing for each the coefficients of latitude and longi- 
tude, together with a central dip : but when districts were taken sufficiently small to 
satisfy approximately the required conditions of straightness, parallelism and equi- 
distance, irregularities of observation arising from station error and other causes be- 
came significant, and materially influenced the results of the combination. I found 
myself obliged therefore finally to revert to the graphical method which I employed 
for the isoclinal lines of the British Survey, and which may be described as follows. 
The observations are first entered in a Mercator’s map on a sufficiently large 
scale, a small cross being made to mark the spot of observation in its proper latitude 
and longitude, with the value of the Inclination written by its side. The isoclinal lines 
corresponding to degrees are then drawn roughly by the eye as the observations ap- 
pear to direct. Lines are next drawn through each place of observation perpendi- 
cular to the direction of the isoclinal lines at the spot, and distances are set off on 
them corresponding to the value in geographical miles of the number of minutes 
which the observed dip is either above or below the full degree to which it is nearest. 
The value in geographical miles corresponding to the odd minutes is computed pro- 
portionally to the distance between the two isoclinals on either side of the place of 
observation ; and it is set off, from the cross which marked the station, towards the 
isoclinal of the full degree which is nearest to the observation. A cross is then made 
in a different coloured ink, to mark the spot where the observation places its nearest 
isoclinal line ; it is obvious that if there were no irregularities in the observations, 
the isoclinal lines would run continuously through these new points. Finally, the 
original rough draft of the lines is revised in reference to these points, and such 
