18 Frederic Guthrie on certain 



ones and had the normal length. Or if we have a half-free 

 lath having one artificial and, say, four natural nodes, and 

 then set it quite free and cause it to vibrate, only the last seg- 

 ment will be affected, breaking up into two parts respectively 

 equal to the first and second at the other end. 



§ 4. The lengths of segments and consequent vibrating- 

 periods or notes are independent of the length of the part of 

 the lath on the other side of the vice's jaws. This appears 

 from two experiments with B. This lath was shortened by 

 pushing it through till its effective length was 220 millims. 

 The tail from the front edge of the vice was now 85 millims. 

 The lath divided into two segments S! = 172 and-s 2 = 4:8. Their 

 ratio is 3*51. The analogous ratios when the length was 280 

 was 3*51. The next segmentation gave 



^=29-5, s 2 = 80-5, * 8 = 110, ^=2-73, - 3 =l-36. 



s l s 2 



The analogous ratios with the 280-millims. lath were 2*77 

 and 1'37 respectively. 



II. Torsional and torsio-transverse vibrations. 



§ 5. The laths A, B, and C are, when clamped as before, 

 easily set vibrating torsionally so as to have a single central 

 longitudinal node (fig. 3). 



With A and B the nodal line is perfectly straight. With 

 C it was slightly curved, touching the central line near the 

 middle, and bending down at both ends to the amount of 

 •5 millim. As this was not a condition of bowing (for the 

 line did not shift when the lath was bowed on the other side), 

 it must result either from some slight variation in the quality 

 of the lath or want of perfect symmetry in the clamping. It 

 has no present interest. 



§ 6. The simplest combination of the torsional with the 

 segmental as exhibited by all three laths is shown in fig. 4. 



The same figures are obtained on whichever side the lath is 

 bowed ; so that whether the form of A and C, or that of B is 

 produced must depend upon some indefinitely small difference 

 of condition either of quality or clamping. With B, however, 

 it is possible to obtain a state of vibration by means of very 

 hard clamping, which is perfectly symmetrical about the axis. 

 This is shown in fig. 5. The actual condition of the sand 

 about the cross nodes is interesting. 



The next combination is fig. 6, and then fig. 7. Again, 

 PL III. fig. 8. Further, fig. 9. 



And finally one can with some difficulty produce fig. 10. 



