322 Mr Searle, Apparatus for Measuring the Extension of a Wire. 



would be free to move horizontally East and West, or North and 

 South, or vertically (when the wire is stretched) and to turn about 

 a vertical axis. It thus possesses four degrees of freedom. The 

 two links destroy three degrees of freedom by preventing the 

 frame from (1) rotating about its own wire A', (2) rotating about 

 the wire A, (3) moving towards or away from the frame CD. 

 The frame CD' has thus but one degree of freedom remaining, 

 viz. that which enables it to follow the stretching of the suspend- 

 ing wire. 



One objection to the use of the links K, K' arises from the 

 fact that when the wire A' is stretched so that the ends of the 

 links on CD' are lower than the ends on CD, the tensions of 

 the two wires are not the same as if the links were absent. It 

 is here supposed that the two wires are vertical when the links 

 are horizontal. The error due to the obliquity of the links is 

 easily found. If a be the length of the links, I the length of the 

 wires, and P and Q the tensions in the absence of the links, 

 then when the links make an angle 6 with a horizontal plane, 

 the ends corresponding to P being the lower, the tensions of the 

 wires are approximately 



In my apparatus a= 5 cm., I = 300 cm. approximately. Hence, 

 when there is a difference of level of 1 cm. between the ends of 

 the links, 6 = $ and a8 3 /U = ^^ . Since 2PQ/(P + Q) is roughly 

 the mean of the two loads, we see that the obliquity of the links 

 in this case only alters the tensions by 3 0| 1 000 of the mean load. 

 This error is therefore negligible. 



Since increasing obliquity of the links brings the two frames 

 closer together, it is necessary that the surface of that part of 

 the level-holder which rests upon the screw should be part of 

 a plane which passes through the axis of the pivots H, and is 

 such that it is horizontal when the bubble is at its fiducial 

 mark. 



With this apparatus the students at the Cavendish Laboratory 

 find it easy to investigate the deviations from Hooke's Law for 

 copper wire. When a copper wire of '01186 square cm. in section 

 is put slowly through a series of cycles of loading and unloading, 

 well-marked hysteresis curves are obtained, even though the 

 range of load is but 2 kilogrammes. The maximum extension 

 in this case is only "037 cm. in a length of 286 cm. The gradual 

 extension due to a continued load and the gradual contraction 

 consequent on the removal of a load are also easily measured 

 by means of the apparatus. 



