378 On the CompressibMy of Solids 



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 con- 

 traction 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 



