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



The part Xj x will thus have remained unmoved either by the 

 increment or the decrement of the temperature, and the plate 

 will not descend. The strain will be greatest on the points Xj 

 and x x when the plate suffers a diminution of temperature; and 

 it is a possible case that the tensile strength may not be suffi- 

 cient to bear this strain. The plate will then be torn asunder 

 at those points. Although the plate was before too long to be 

 made to descend by the given alternation of temperature, yet the 

 parts into which it is thus separated may not. The points X 

 and x are those which sustain the greatest thrust when the tem- 

 perature is raised ; they are therefore those at which there is the 

 greatest tendency to crush. The distances X A, x B, X } A 1? x x B x 

 are independent of the length of the plate. 



If the plate adhere to the plane, so that, besides the resistance 

 of friction to its descent, there is that of its shearing upon it, and 

 if in any new position into which it is sheared the adhesion be 

 supposed to be reestablished as perfectly as it was in the position 

 from which it was sheared, and if, lastly, the thrust and strain of 

 expansion and contraction due to an alternation of temperature be 

 sufficient to overcome the resistance to shearing of the surfaces in 

 contact, then for a given weight of the plate and inclination of the 

 plane the resistance to shearing will be the same as it would be 

 if a given addition were made to the resistance of friction ; and 

 taking for the coefficient of friction one equal to the sum of the 

 actual coefficients of friction and the coefficient of this equivalent 

 imaginary friction, the cases of friction and adherence may be 

 treated as one of friction only. 



Let the plate be rectangular and of uniform thickness, and let 

 it rest lengthwise upon the plane. 



Let its dimensions and weight, and the conditions of its dila- 

 tation and contraction, be represented as follows : — 



a = length in feet at the given temperature T° Fahr. 



K= transverse section in square inches. 



E*=' modulus of elasticity. 



X = dilatation or contraction per foot for every variation of 

 1° F. in the temperature of the plate or bar. 



/j = 1 +X£j = length to which each foot in the length of the 

 bar is dilated when (dilating freely) it is heated from 

 the temperature T° by t° F. 

 I 2 =l—\t^= length to which each linear foot of the bar is 

 shortened, when from the temperature T° it is cooled by 

 / 2 °, contracting freely. 



* The modulus of elasticity is here assumed to be that weight in pounds 

 which, if applied as a tension to a bar of the metal 1 square inch in section 

 and 1 foot long, would lengthen it by one foot, or which, if applied as a 

 thrust, would (if the same law obtained, however great was the compression) 

 compress it by one foot. 



