780 Mr. J. C. Buckley on the 



Consider equation (3) applied to a particular strip, C and 

 T are alone variable. Then 



dC 2 b 3 ... 



df=ST < 4 > 



Discussion. 



1. Equation (4) shows that if values of C be plotted as 

 ordinates and valuss of T as abscissae, the graph obtained 

 should be a straight line. In general, the graph is inclined 

 to the T axis, the slope being given by equation (4) . 



2. Now let the straight-line graph showing the relation 

 between C and T be produced backward till it cuts the axis 

 of C. Here T = 0, and therefore equation (3) reduces to 

 equation (2). We thus have a means of obtaining the value 

 of n for a substance in which n is small. 



3. Without using the graph, it is obvious that the value of 

 n can be obtained in any particular case by inserting the 

 value of T in equation (3). 



4. Where n is large, as in the case of steel, the second term 

 on the right of equation (3) approximates to zero. In other 

 words, the restoring couple is due to torsion alone. The 

 strip therefore behaves according to equation (2) and 



^C 



-^p=0. In this case the graph obtained is parallel to the 



T axis. 



Experimental. 



It appeared more hopeful to examine the behaviour of 

 strips of material of small torsional rigidity when subjected 

 to various tensions. 



Preliminary experiments showed that the period of vibra- 

 tion was proportional to the tension in the strip in the case 

 of paper, aluminium, mica, celluloid, and xylonite. 



On the other hand, strips of steel and phosphor-bronze 

 showed no such effect. These are instances in which the 

 C-T graph is parallel to the axis of T as mentioned 

 previously. 



The strips were about 1 cm. wide, with the exception of 

 phosphor-bronze, and the total tension was varied up to 

 2000 grams weight. 



The strip was attached to the end of a beam of circular 

 section, pivoted about its centre, from the other end of which 



