THE AID OF THE ACHROMATIC FRINGES. 



121 



shaft of the needle are here possibly associated with a temperature effect. 

 The mean data of each day are consistent and from them the result 2X a = 0.115 

 cm. may be inferred. Thus the deflection due to M = gwg., at 4.2 cm. from 

 the small weight m = o.6ig. is x a = 0.057 cm., a little over a half millimeter 

 when the distance from center of the needle is 1 2 .6 cm. This result has already 

 been used in 91. 



TABLE 7. Maximum static elongations. 



With these data we may inquire as to the time-limits of approximately 

 uniformly varied motion at the outset of the experiment, with the needle 

 (m = o.5 g) in vacuo. We may write for the first departure from equilibrium 



(i) yMtn/R* TX/h t = 2ma 



since x/h is the angular deflection if 2h is the length of the needle, a the acceler- 

 ation, and T the torsion modulus. At the elongation a = o and therefore, 

 statically, using the preceding data and an approximate 7 



IO'XG.SO T 



6 - 7Xl 74~^ = ^- 57 



so that r/7* 2 = 3.3 X io~ 8 . If during a small interval t the motion is apprecia- 

 bly uniformly varied 



= a and x = 



Thus, if t = io 2 sec., 



a = i. 9X10-' cm. /sec.* 



or the error is 



31. 3X io- 8 /i.9Xio-'=i6.5Xio- 2 , or about 17 per cent. 

 Equation (i) may be stated, using the values of a and x, 



yM(m - Tt z /4h 2 )/R* = 2ma 



which shows that to reduce the very large theoretical error t must be much 

 within 100 seconds. Furthermore, m must be made as large as possible com- 



