170 



The former neutral line is nearer the top than the bottom, the 

 other nearer the bottom than the top. The one is at the same di- 

 stance from the top as the other is from the bottom. This distance 

 is represented by the formula 



Ig sin (0-Q 

 2 sin cos i* 



"When the plate is dilated, it is the longer portion which dilates 

 downwards ; and when it is contracted, it is the shorter portion 

 which contracts upwards. The lower end of the plate descends 

 therefore by a given increase of temperature more than it ascends 

 by an equal fall ; and on the whole the plate descends. 



If we suppose the temperature first to be increased by t y and 

 then diminished by t ; then 



1st. In the case in which a portion only of the plate dilates, the 

 descent is represented by 



EX 2 cos f t? ___ f a a "I 



2^ l(l+AO sin (0-t) (1-A* 2 ; sin (0 + t) J ' 



2ndly. In the case in which the whole plate dilates and the whole 

 contracts, the descent is 



tan J^ sin cos t 



The first case passes into the second. 



If E be very great as compared with pa, the second term in 

 the above formula may be neglected. It then corresponds with 

 the formula given by the author in a former communication to the 

 Society. 



To verify the fact of the descent of a plate of metal under the 

 conditions supposed, a deal board 9 feet long and 5 inches broad, was 

 fixed at an inclination of 18^ against the wall of a house having a 

 southern aspect, and a sheet of lead was placed upon it one-eighth 

 of an inch thick and weighing 28 Ibs., and having its edges turned 

 over the edges of the board so as not to bind upon it. Near the 

 lower extremity a vernier was constructed, by which the position of 

 the lead on the board could be determined to the 100th of an inch. 

 Its position was observed daily between 7 and 8 in the morning and 

 6 and 7 in the evening, from the 1 6th of February to the 28th of 

 June, 1858. 



