of the Earth’s magnetic Force in absolute Measure. 15 
Series V. Time 1555" p.m.... 3°16" P.M. 
Magnet away, Scale reading = 495-7... 498-3. 
| D 4 (Me — Mp) u | p°tanu 
1:25 368-46 6°54/52"-5 | +20233 
1-50 211-99 3°26’ 8” -20261 
1°75 133-41 2°10’ 6” | -20292 
2-00 + 89°39 1927/16" — | ~ -20313 
2°25 63-00 i° 1739" | .-20390 
| 2-50 45°99 0°44/55"-5 |  +20420 | 
These results verify the conclusions to which we have arrived above. The 
values of the function p* tan w are constant for all distances in the first three 
series, the differences in the resulting values being less than the probable errors 
of observation ; and consequently, the coefficient of the inverse fifth power of the 
distance is insensible. Inthe fourth and fifth series, on the other hand, in which 
the lengths of the magnets are equal, the values of this function form an increasing 
series, as D increases; and therefore, in this case, the coefficient of the inverse 
fifth power of the distance has a sensible negative value. 
We may further employ these results to test the accuracy of our conclusions, 
by deducing from them the values of the two coefficients, in the expression for 
the tangent of the angle of deflection, and comparing their ratio with that fur- 
nished by theory. It is needless to make this computation for the numbers of 
the first three series; for it is manifest from the results, that the second coef- 
ficient is insensible, as it theoretically should be. From the results of Series IV. 
we deduce by the method of least squares, 
2148). ha=—r0017;,” = —coo07s 
We obtain, in like manner, from the results of Series V., 
o=-2057) ho = —-0022) i — —- 0110: 
And the mean of the resulting values is —-0094. Now, in these two series, 
the length of each of the magnets was three inches ; that is, / = /'= ‘125, the 
half lengths being expressed in feet. Substituting these values in the expression 
for h, it becomes 
h = —-0094, 
exactly agreeing with the mean of the experimental values. 
