336 



conversely in the act of contraction ; and that in the former case 

 the nail B will sustain a pressure upwards equal to that necessary 

 to cause BP to descend, and a pressure downwards equal to that 

 necessary to cause PA to ascend ; so that, assuming the pressure to 

 be downwards, and adopting the same notation as before, except 

 that AP is represented by p, AB by a, and the pressure upon the 

 nail (assumed to be downwards) by P, we have in the case of ex- 

 tension 



p _,, x 



COS (f> C 



and in the case of contraction 



sin 



T, , N 



P=u(ap) - vy ' up 



cos ty > 



Reducing, these formulae become respectively 



P= - < 2p sin <p cos i asin(^> i) > ... (3) 

 cos ffl L J 



P= - <csin(d + z) 2p sin 6 cost > (4) 



cos 0L J 



My attention was first drawn to the influence of variations in 

 temperature to cause the descent of a lamina of metal resting on an 

 inclined plane, by observing, in the autumn of 1853, that a portion 

 of the lead which covers the south side of the choir of the Bristol 

 Cathedral, which had been renewed in the year 1851, but had not 

 been properly fastened to the ridge beam, had descended bodily 

 18 inches into the gutter; so that if plates of lead had not been in- 

 serted at the top, a strip of the roof of that length would have been 

 left exposed to the weather. The sheet of lead which had so de- 

 scended measured, from the ridge to the gutter, 19 feet 4 inches 

 and along the ridge 60 feet. The descent had been continually 

 going on, from the time the lead had been laid down. An attempt 

 made to stop it by driving nails through it into the rafters had failed. 

 The force by which the lead had been made to descend, whatever it 

 was, had been found sufficient to draw the nails*. As the pitch of 



* The evil was remedied by placing a beam across the rafters near the ridge, 

 and doubling the sheets round it, and fixing their ends with spike nails. 



