1904.] 



On the Compressibility of Solids. 



801 



Daring an experiment with a rod it contracts while the pressure 

 is being raised, and expands again when the pressure is relieved. The 

 steel tube which holds it, however, acts in the opposite sense, it 

 expands while the pressure rises and contracts while it falls. If the 

 two surfaces were perfectly smooth, one half of the change of length 

 would be measured at the one end and the other half at the other end. 

 As the surfaces are- not perfectly smooth, this does not usually occur. 

 Moreover the steel tubes are prolongations of the central steel block 

 which holds them. The block is bored with holes at right angles to each 

 other in the three principal directions. Consequently for a distance of 

 about an inch and a half in passing through the block the rod is not 

 supported at all. With the exception of this small portion, however, 

 the rod is supported throughout the whole of its length by the steel 

 tube. Now, although it is thus nominally supported equally throughout 

 the whole of its length, we know that in reality this is pretty certain 

 not to be the case. At some place, either in the right arm or in the 

 left arm of the apparatus, the rod is sure to bear more heavily than 

 in any other part. The contraction under pressure and the expansion 

 under relief of pressure will then apparently take place as from this 

 point as origin. Supposing this point itself to be motionless, it is 

 evident that the change of length measured at the two ends will be 

 in the same proportion to each other as would be the arcs which they 

 would describe if the rod were a lever oscillating on the point as a 

 fulcrum. As there is no support at all at the centre, this point must 

 lie on one side or on the other of it and the motions of the ends must 

 be unequal. But the .fixed point of the tubular receiver is the central 

 block; therefore any point in, let us say, the right-hand tube will, 

 when pressure is being raised, move to the right, and, on relief of 

 pressure, retreat by an equal amount to the left. Consequently when 

 we observe and measure the change of position of, for instance, the 

 right-hand extremity of the rod, when the pressure is relieved, that 

 change of position is composed of two motions, the expansion of the 

 part of the rod which lies between the right-hand extremity and the 

 point in it whose motion with respect to the steel carrying tube is nil, 

 along with the proper motion of that point. Similarly, when we 

 measure the change of position of the left-hand end, it also is composed 

 of two parts, the expansion of the part of the rod which lies between 

 the left-hand extremity and the same point in the length of the rod 

 where its motion with respect to the steel tube is nil, along with the 

 proper motion of that point. But at the left-hand end the motion of 

 expansion is to the left, and at the right-hand end it is to the right, 

 while the proper motion of the position of the common point on the 

 rod and on the tube is always in one direction, and in this case, to the 

 left. Therefore the distance measured in the right-hand microscope 

 is the expansion of the portion of the rod which lies to the right of 



