62 Royal Society : — 



If we conceive the bar now to return to its former temperature, 

 contracting by the same amount (A) per linear unit ; then the point 

 B (fig. 2) will by this contraction be made to ascend through the 

 space 



BX.X=.r\ 



L\ 



L tan </) J 



(1) 



Total descent / of B by elongation and contraction is therefore 

 determined by the equation 



/=L\^ (2) 



tan^ 



To determine the pressure upon a nail, 

 driven through the rod at any point P 

 fastening it to the plane. P^ 



It is evident that in the act of exten- 

 sion the part BP of the rod will descend 

 the plane and the part AP ascend ; and 

 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 extension 

 T, sin(0 + j) / .sin((i> — e) 



P=t/p )J—1—L —y.(a — p) ii ^, 



COS^ COS0 



and in the case of contraction 



P=z({a—p) 



sin(0 + O_ sin(^— 



Reducinc 



cos (f) cos (j> 



these formulae become respectively 



COS(^ 



P= 



< 2p sin ^ cos 2 — ft sin((/) — ^) > 



< asin (i^ + i) — 2psinri< cosi > 



(3) 



(4) 



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 

 Cathedra], 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 



