258 ON THE DETERMINATION OF THE HORIZONTAL 



V. Magnet away, Scale reading = 495-1 



498-3. 



1-25 

 1-50 

 1-75 

 2-00 

 2-25 

 2-50 



These results verify the conclusions to which we have arrived 

 above. The values of the function D 3 tan u 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. In the 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 furnished 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 coefficient is insensible, as theoretically it should be. 

 From the results of IV. we deduce, by the method of least squares, 



Q = -2148, hQ = - -0017, h = - -0078. 

 We obtain, in like manner, from the results of V., 



Q = -2037, hQ = - -0022, h = - -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, I = I' = -125, the half lengths being expressed in feet. 

 Substituting these values in the expression for h, it becomes 



h = - -0094, 

 agreeing exactly with the mean of the experimental values. 



