337 



the roof was only 16^, it was sufficiently evident that the weight of 

 the lead alone could not have caused it to descend. Sheet lead, 

 whose surface is in the state of that used in roofing, will stand firmly 

 upon a surface of planed deal when inclined at an angle of 30*, if 

 no other force than its weight tends to cause it to descend. The 

 considerations which I have stated in the preceding articles led me 

 to the conclusion that the daily variations in the temperature of the 

 lead, exposed as it was to the action of the sun by its southern 

 aspect, could not but cause it to descend considerably, and the only 

 question which remained on my mind was, whether this descent 

 could be so great as was observed. To determine this I took the 

 following data : 



Mean daily variation of temperature at Bristol in the month of 

 August, assumed to be the same as at Leith (Kaemtz, Meteorology, 

 by Walker, p. 18), 8'21 Cent. 



Linear expansion of lead through 100 Cent. '0028436. 



Length of sheets of lead forming the roof from the ridge to the 

 gutter 232 inches. 



Inclination of roof 16 32'. 



Limiting angle of resistance between sheet lead and deal 30. 



Whence the mean daily descent of the lead, in inches, in the 

 month of August, is determined by equation (2) to be 



7=232 x^x '0028436 X tanl6 f 

 100 tan 30 



1= -027848 inches. 



The average daily descent gives for the whole month of August a 

 descent of '863288. If the average daily variation of temperature 

 of the month of August had continued throughout the year, the 

 lead would have descended 10' 19 148 inches every year. And in the 



* This may easily be verified. I give it as the result of a rough experiment of 

 my own. I am not acquainted with any experiments on the friction of lead made 

 with sufficient care to be received as authority in this matter. The friction of 

 copper on oak has, however, been determined by General Morin to be 0'62, and its 

 limiting angle of resistance 31 48'; so that if the roof of Bristol Cathedral had 

 been inclined at 31 instead of 16, and had been covered with sheets of copper 

 resting on oak boards, instead of sheets of lead resting on deal, the sheeting 

 would not have slipped by its weight only. 



2 L2 



