Connected with the Earth's Field of Force. 141 



take m = 40 grams and I = 20 centimeters. With known 

 values of e and a the maximmn turning moment (for 

 ^ = 45° and = 0) is 1.67 X lO"'^ dyne-centimeters. In 

 latitude 45° the maximum turning moment is half of this.. 



Fig. 5. — Sections of level surfaces in the meridian (dotted lines) and in 

 the prime vertical (full lines) j shows that the ends of the balance PP' are 

 lowest in the prime vertical. 



This moment is certainly not large^*^ but, given free play, 

 it would swing the rod into the prime vertical. It is 

 opposed by the torsion of the fiber, but fibers may be 

 found strong enough to support the rod and yet so yield- 

 ing that the minute forces of the earth's field will cause 

 a measurable deflection of the rod.^^ The apparatus, 

 torsion-head and all, is turned as a whole into various 

 azimuths and the deflection of the rod in these positions 

 with reference to the position of no torsion is read off on 

 a telescope and scale. From these readings there can be 

 deduced by a process too long to give here the values of 



— — — y where R and N represent now the minimum and 



maximum radii of curvature, which do not always — I 

 might rather say '^do not ever'' — coincide with the radii 



^° Its size may be perhaps made more vivid by the following comparison. 

 A five-eent piece weighs about five grams. Take about a fifth of its weight 

 and you have a gram. Take the weight of about a thousandth of a gram 

 and you have a dyne. Our moment was about one ten thousandth of a 

 dyne-centimeter. The distance factor was forty, so the force factor was 

 only one four-hundred-thousandth of a dyne, one four -hundred-millionth 

 of a gram, one two-billionth part of the weight of a five-cent piece. 



^^ See references on a preceding page. 

 Art. A, p. 368; B, p. 340; E, p. 21. 



