112 Canon Moseley on the Descent of a Solid Body on an 

 increase of temperature of t° is represented by 



1 + t t \ " 



And similarly the strain with which it tends to contract under 

 a diminution of temperature / 2 is 



KEt 2 \ . 

 1-* 2 X ' 



Whence it follows that the opposite resistances at X and X T arc 

 respectively greater than the elasticity of the plate, so that a por- 

 tion only dilates and contracts, when 



and 



or, since 



and 



when 





1 cos t sin 9 



sin (£ + 

 J - cos <f> 



KE/A 



l awK sin (^~0 . sin (<£ + /•) 1 + X^ 

 cos t sin cos KE/ 2 \ 



> T-aV 



* If no resistance were opposed to the dilatation of the element Ax, it 

 would become, by an increase of temperature t lf (\ + t-,\)Ax. To bring it 

 back, therefore, to the length from which it has dilated, each foot must be 



compressed by 7T~TTTT7~ ' Since, therefore, its section is K, the thrust 



(1+WA. KEt L XAx KEf.A 



necessary to compress it is represented by 7TT~* \\^ x > orD y TX7V 



t If R represents the resistance to crushing per square inch of section, 

 and S similarly represents the tensile strength, the bar will crush at X if 



1+Xf 

 and will tear asunder at X x if 



l-Xt 2 



