that do not burst with Frost. 245 



Mr. Powell's plan is to make the piping elliptical — either 

 before it is laid, in which case it may be made of that form ori- 

 ginally or by passing round pipe through rollers, or afterwards, 

 when suitable hand-squeezers will effect the result without the 

 necessity of removal. As will afterwards be seen, it is not 

 necessary that the pipe should be elliptical throughout ; if 

 left round under staples and in other inaccessible places, the 

 adjacent elliptical portions ensure safety. The principle, of 

 course, is obvious. As is well known, the Bourdon pressure- 

 gauge depends on the fact that the area of an elliptical pipe is 

 less than that of a circle of equal perimeter : therefore during 

 increased pressure its section becomes more circular; increased 

 circularity of section produces diminished curvature in the form 

 of the pipe ; and so the movements of the end of the pipe are used 

 to measure pressure. Thin brass is used for this purpose, and is 

 so elastic that it returns to its original form when the pressure is 

 removed; and so an indefinite number of increments and de- 

 crements of pressure may be measured by it. The case of the 

 elliptical water-piping is different. Here there is not a defi- 

 nite pressure to withstand, but a definite increase of volume ; 

 and, moreover, if this increase of volume is resisted, a practi- 

 cally infinite force arises to break down the resistance. The 

 question then is, how best to allow of this increase of volume. 

 The method of the indiarubber pipes I have already mentioned. 

 The other plan is to make them of an elliptical or other-than- 

 round section. There is, however, far more in this suggestion 

 than one would be likely to see at first. Consider the case of 

 a round pipe in which water is beginning to freeze. Increase 

 of volume must take place somewhere. No pipe can be abso- 

 lutely uniform in strength everywhere. So wherever a place 

 occurs which happens to be a little weaker than the rest, no 

 matter how little, that place will stretch, and necessarily 

 stretch more than other places. But when a round pipe 

 stretches, two things happen — its diameter increases and its 

 thickness decreases ; therefore, as the strength of a tube to 

 resist bursting is inversely as the diameter and directly as the 

 thickness, each of these effects makes the stretched portion 

 still weaker than the neighbouring parts ; therefore a round 

 pipe under the action of frost is in a state of unstable equili- 

 brium ; the consequence is, knobs form on the pipe, and ulti- 

 mately burst. 



Now consider the'case of an elliptical pipe, of such strength, 

 of course, as to stand the ordinary water-pressure. As before, 

 suppose some portions are weaker than others. When expan- 

 sion takes place they will suffer most, and will begin to give 

 way. But an elliptical pipe on giving becomes more circular, 



Phil. Mag. S. 5. Vol. 13. No. 81. April 1882. X 



