11G Canon Moscley on the Descent of a Solid Body on an 



■ — - EX^ cos 6 



AX=— 7T-T Tl\— ^"/ 



In like manner, 



Bx 



w(l+X/J sin(^ + t) 



EX* 2 cos <fi 

 1 "w(l-\gsin(0 + 4 ) : 



AX 



whence 



_ EX£ 2 cos 

 1_ ~w(l— X/ 2 ) sin((£ — t) 



^ r , EX^ sin 26 cos t 



w(l+X^) sin (<£ + 1) sin (<£ — *) 

 X,#. =« — 



EX^ 2 sin 2<p cos 6 



(1— Xy sin ((/> + £) sin (<£ — t) 



If these expressions vanish or become negative, there is no 

 partf of the plate which does not dilate by the assumed increase, 

 and contract by the assumed decrease of temperature. 



The fact of the descent of a solid body upon an inclined plane 

 when subjected to alternations of temperature was first observed 

 in the descent of the lead on the southern side of the roof of the 

 choir of Bristol Cathedral, and was communicated to the Royal 

 Society { in April 1855. I have since verified it by the fol- 

 lowing experiment. I fixed a deal board 9 feet long and 5 inches 

 broad to the southern wall of my house so as to form an inclined 

 plane, and upon it I placed a sheet of lead, turning its edges 

 down over the side edges of the board, and taking care that it 

 should not bind upon them, but be free to move with no other 

 obstruction than that which arose from its friction. The incli- 

 nation of the board was 18° 32', the thickness of the lead l 

 of an inch, its length 9 feet, and its weight 28 lbs. The lower 

 end of the board was brought opposite to a window, and a ver- 

 nier was constructed which could be read from within, and by 

 which the position of the lead upon the board could be deter- 

 mined to the 100th of an inch. I began to measure the descent 

 of the lead on the 16th of February, 1858, and recorded it every 

 morning between 7 and 8 o' clock, and every evening between G 

 and 7 o'clock until the 28th of June. 



* If a sheet of lead rest on a plane of oak inclined at 22|°, 



X#=e- 30-63*i, X 1 a? 1 =a -30*63 * 2 , 



where the length is measured in feet, and the temperature in degrees of 

 Fahrenheit, and the modulus of elasticity of lead is assumed to be 720,000, 

 its coefficient of expansion ^aVo frj anf ^ tnc limiting angle of resistance be- 

 tween it and oak 22^°. 



t This agrees with inequality (18). 



t Proceedings of the Royal Society, vol. vii. p. 341. 



