108 Dip and Variation of the Magnetic Needle. 
The annual motions shewn in this table indicate discrepancies 
which must be ascribed to local attraction and errors of -observa- 
tion. This is particularly true of the Ohio observations, some of 
the results being more than double of those at other stations 
moderately distant. The above results should be combined in 
such a manner as best to eliminate these errors. Within moderate 
limits, the motion at each locality may be presumed to be in 
versely as the distance between the lines of equal variation. This 
hypothesis is known to be untrue for the earth at large, yet it is 
worth inquiry whether the error is sensible within the limits of 
the United States. I have therefore multiplied each annual mo- 
tion by the distance between the nearest lines of equal variation 
expressed in geographical miles. Column ninth of the preceding 
table shows the multipliers, and column tenth the products. 
These products, according to our hypothesis, should be constant. 
They are indeed quite variable, yet the extreme fluctuations oc- 
cur in Ohio, at places where the mean motion of the needle must 
be supposed nearly the same. There is no decided inequality 
in the mean of these products for the different parts of the Uni- 
ted States. I ascribe these inequalities then mainly to acciden- 
tal causes and not to the hypothesis assumed. They probably 
arise in part from the employment of different years in determin- 
ing the annual motion. The mean of all the products is 163.14, 
which divided by the distance between the lines of equal varia- 
tion should give the annual motion. Column eleventh of the 
table shows the result of this computation. These numbers are 
alternately above and below those in column eighth ; and in my 
opinion represent tolerably well the annual motion in this coun- 
try. We may now proceed to discuss the absolute variation. - In 
order to obviate as far as possible any objection arising from the 
uncertainty of the annual motion, I have confined myself to re- 
cent observations. Of the one hundred and ninety three observa- 
tions employed, none were made before 1825, but ten before. 
and one hundred and twenty were made since 1838. The 
observations are all reduced to January 1, 1840, by applying the 
annual motion computed in the manner just explained. 
