12 The Rev. H. Luoyp on the Determination of the Intensity 
Finally, substituting in the value of h above given, and designating the half 
lengths of the deflecting and of the suspended magnets by / and /’, respectively, 
h=3(2r—3!”); 
a quantity whose value may be exactly known, independently of experiment. This 
quantity vanishes, when 7 = 31”, or 
J = 1-2241'; 
a result which is independent of the magnetic state of the bars.* 
As the preceding results depend, in part, upon an empirical law of magnetic 
distribution, which is only approximately true in the case of small magnets, it 
seemed desirable to obtain a confirmation of their accuracy by direct experiment. 
The nature of such confirmation will be immediately understood from the form 
of the relation between the angle of deflection and the distance. For since, in 
the method of deflection employed by Gauss, p*tanu=Q(1-+/n~*), the 
function pb’ tan w will be constant for all values of p, when 4 = 0; while, if the 
coefficient of the fifth power of the distance have a sensible value, it will vary 
with p, its values forming a decreasing or increasing series, as D increases, ac- 
cording as h is positive or negative. Hence we have only to observe the deflec- 
tions produced at different distances, when the two magnets have the relative 
lengths pointed out above, and to compare the results with those obtained under 
other circumstances. 
Several series of experiments were accordingly made in the beginning of 
the present month, in some of which the lengths of the two magnets were the 
same, while in others they were in the deduced ratio of the number 1-224 to 1. 
The form of the magnets was cylindrical, their lengths being 3 inches, and 
* If the centre of the deflecting magnet be in the magnetic meridian passing through the centre 
of the suspended magnet, and its axis perpendicular to the same line, we find, by a process similar to 
that above given, that the condition to be fulfilled, in order that the term involving the fifth power 
of the distance may vanish, is 
M, __ ,Ms'. 
MM?’ 
and accordingly that the corresponding relation between the lengths of the two magnets is, in that case, 
oil 
