290 



in its different parts inversely to its thickness in these parts. 



In figure 2 let A Ai be a part of the thick side, 



and B Bi a part of the thin side, so that when 



the tube is empty A B and Ai Bi are parallel 



lines, and at right angles to the central axis C 



Ci, If the wall at A is twice as thick as at B, y 



and A Ai be elongated by a water pressure to a 



ai, B Bi will be elongated twice as much, or to b 



bi, and the lines a b and ai bi will no longer be 



6 



i 

 ft 



^» 



I 



I 



A 



A. 



iX< 



at right angles to C O! But not only will the 

 wall strive, in opposition to the pressure, to 

 regain Its former dimensions, but also the rel- 

 ative position of its parts. To regain the former 

 is not possible as long as the pressure lasts; to 

 regain the latter, only the rigidity of the walls 

 has to be overcome. This disturbance of the 

 relative position of the parts which manifests itself in the unequal 

 stretching, is in direct proportion to the pressure. If w^e let this 

 latter be represented by the line a b, that part which will tend to 

 bring a and b into a line at right angles to C Ci can be repre- 

 sented by b d, where a d b is a right angled triangle. Shice the 

 thickness of the wall varies graduallv from one side to the other, 



%\^^ 



the 



same reasoning applies to all parts of the wall 



between 



A Ai and B Bi, and since A Ai B Bi is any part of the tube, it 

 must apply to the whole tube. But in order that all such lines 

 as a b can arrange themselves at right angles to C Ci, or nearly 

 so, it is necessary that C Ci became a curve, and since B Bi elon- 

 gates more than A Ai, the former must He on the longer periph- 

 ery; in other words, the tube must bend, and its concave side is 

 the side of the thicker wall. To illustrate this take a rubber 

 tube 5 mm. thick and 60 mm. long, fit into one end a closed 

 lass tube for a stopper, into the other end an open glass tube, 

 pointed at one end to enter the small rubber tube, otherwise 

 considerably larger, to fit a larger rubber tube or bulb. Fill this 

 apparatus with water and apply pressure. The tube will be 

 slightly dilated but will not bend. Take out the small rubber 

 tube, push a glass rod through it, and shave one side of the free 

 portion of the tube. Rearrange the apparatus and again apply 



fc> 



