Chemistry and Physics. 217 



the strip in the form of a helicoid, when the bifilar couple (the 

 second term) is negligible. 



The influence of the bifilar term would be most pronounced 

 when the torsional rigidity is small. Preliminary experiments 

 showed that the period of vibration was proportional to the ten- 

 sion for strips of aluminium, celluloid, mica, paper, and xylonite. 

 On the other hand, ribbons of steel and phosphor-bronze did 

 not show this effect. Plotting values of T as abscissae and 

 the corresponding values of C as ordinates, the points for 

 a xylonite strip (1575 X 3 X 0*05 cm ) fall close to a straight 

 line. This is consistent with the above equation. The slope 



dC 

 of the line gives irr — 0*1425, which is in excellent agreement 



Ct J. 



2b 3 

 with — - = 0*1429. The intercept of the line on the axis of 



ot 



ordinates (T= 0) gives C = 132 000 dyne-cm., or n = 1*589 X10 5 . 

 It is thus seen that this method affords a means of obtaining the 

 value of the coefficient of rigidity for suitable substances. Very 



e dC . 2b 3 . . 

 good agreement between the values or y^, and — — is shown by 



Ct -L ot 



the data tabulated for five different widths of paper and two of 

 celluloid. Aluminium behaved similarly but gave trouble because 

 of the rapid damping of its vibrations. [ C was always obtained 

 from the period, P = 2ir*J I\ C.~\ The straight lines in the first 

 diagram for paper practically pass through the origin. This is 

 due to the very small value of w, for when T= we would ex- 

 pect to find C oc b. The lines on the second diagram for paper 

 intersect the axis of ordinates at finite distances above the origin. 

 In this case, the paper was cut in another direction. In fact, it 

 was found that two ribbons of paper cut from the same sheet, 

 but in perpendicular directions, showed a considerable difference 

 in rigidity, though the bifilar effect was the same for both strips. 

 "This means that the distribution of tension producing the bifilar 

 effect is independent of the fibrous structure of the material of 

 the strip ; whereas the rigidity depends greatly upon the 

 structure." As a further test of the formula I and T were kept 

 constant for paper so cut as to make n negligible. The experi- 



C 

 mental data verified the relation — = constant. 



b 3 



When the ribbon is made of a very thin piece of material hav- 

 ing a large coefficient of rigidity the two terms of the right 

 member of the general equation may attain comparable values. 

 For a steel tape of dimensions 41*9 X 1*26 X 0*01 CIn the data 



, . , dC 2b 3 



obtained were -y™= 0*007, —r = 0*008, n = 8*351 X 10 11 ,- and 



Ct -L Ot/ 



C = 25 000 for T '= 0. With another specimen of steel, 



Am. Jour. Sci.— Fourth Series, Vol. XXXIX, No. 230.— February, 1915. 

 15 



