1888.] 



The Radio-Micrometer. 



97 



I have shown that — 



Twice the best length, 21 



The best sectional area, a 



v<$s> 



■V® 



and that the best number of turns of wire is 1. 



The numerical values for a particular bar 10 X 5 X J mm. are — 



If the breadth be also a variable, the best rectangle is a square of 

 infinite size made of the same wire, which is always the best, what- 

 ever shape, size, or number of turns the circuit may have. 



The best circuit with respect to moment of inertia is that which 

 is practically required, because a convenient period of oscillation must 

 be made use of, and so the torsion must be supposed to vary as the 

 moment of inertia. A difficulty was found in working the expression 

 for this, which was entirely overcome by supposing the wire where it 

 crosses the axis to have a sectional area proportional to its distance 

 from the axis, except in its immediate neighbourhood. On this sup- 

 position the resistance and the moment of inertia of the upper side of 

 the rectangle are each equal to that of half the same length of copper 

 wire on the sides, and thus not only has the best variation been 

 found, but, what is more important, the coefficients for resistance 

 and moment of inertia have been made identical, which is required 

 in order to put the equations into a simple form. 



The expressions found with respect to weight are now applicable to 

 moment of inertia if certain changes are made. Thus, the figure 1 

 in the expression for length must be replaced by \ . The moment 

 of inertia of the active bar K must replace its weight W, and the 

 moment of inertia of a unit piece of copper at 5 mm. from the 

 axis u must replace its weight u'. 



It is thus found that the expressions for 



And this is true whatever length or number of turns the circuit 



a = 0-002007 sq. cm., 



I = 4-621 cm. 



The best sectional area, a = 



may have. 



Twice the best length, 21 = 



As before, the best number of turns is 1. 

 The numerical values are — 



a = 0-00102 sq. cm,, 



I = 2-337 cm. 



ii 2 



