COMPARISON OF THE UNIFILAR WITH THE BIFILAR. 67 



the correction amounts then to shortening the wire by a quantity 

 independent of its length. 



If T' be the practical tenacity of the metal that is to say, the load 

 which a wire a square centimetre in cross section can support with- 

 out inconvenience we may put 



p = 2Trr 2 T' = 27rr 2 aT, 



a being a coefficient less than unity. The correction is then ex- 

 pressed by r^l - or r\ assuming a = -. The value of the 



7 \ 20,T \ T 2 



root is found in the last column of the table in (711). 



Assuming r= 0*005 an< ^ /=ioo, we find that the correction 

 amounts to 0-28 cm. for iron, to 0-22 cm. for copper, to o'lycm. 

 for silver, 0^25 cm. for platinum ; it is, then, far from being 

 negligable. 



The torsion couple of the bifilar will most frequently ^be deter- 

 mined by methods of oscillation, and the experimental value will thus 

 at once contain all the corrections. The preceding formulas will only 

 be useful when it is desired to calculate the absolute value of the/ 

 coefficient of the bifilar by means of its dimensions. 



718. INFLUENCE OF TEMPERATURE. The bifilar "suspension has 

 the advantage over the unifilar of being far less sensitive to changes 

 of temperature ; the only effect resulting from rise of temperature is 

 the expansion, which alters the length of the wires, and the distances 

 of the points of support. The sensitiveness being proportional to 

 the first of these quantities, and inversely as the product of the two 

 others, it would be possible by a suitable choice of the nature of the 

 bodies used, to produce a complete compensation, but this precaution 

 is superfluous. If the wires and the cross-pieces are of the same 

 metal, the change of sensitiveness is proportional to the coefficient of 

 expansion, from the numbers cited above (712), and the mean values 

 of the coefficients of expansion (656), this variation is not the 

 thirtieth of that which would be produced in the unifilar by the 

 change of elasticity corresponding to the same change of temperature. 



719. COMPARISON OF THE UNIFILAR WITH THE BIFILAR. Let 

 us assume that we suspend a body of p grammes, giving it a definite 

 directive force. 



For a bifilar with parallel wires of diameter d, and at a distance 

 of 20, we shall have 



F 2 



