n 



Royal Society : — 



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

 descent is represented by 



E\ cos 



t. 



7,} 



$a 



{«■ 



■O^+d+O 



}• 



2/4 L(l+XO sin (0-0 (1-UJsin fo + t) 



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

 contracts, the descent is 



tan i f-ia sin ((J)-\-i) sin (0 — i) tan i 

 tan E sin 2 cos t 



The first case passes into the second. 



If E be very great as compared with /j.a, the second term in the 

 above formula may be neglected. It then corresponds with the for- 

 mula 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 lbs., 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 16th of February to the 28th of 

 June, 1858. 



A Table is given showing the descent for every day of that period, 

 from 7 a.m. to 6 p.m. and from 6 p.m. to 7 a.m. 



In the months when there was no sunlight from 6 p.m. to 7 a.m., 

 there was no descent in that interval. The descents from 7 a.m. to 

 6 p.m. were very different on different days. Sometimes they 

 amounted to a quarter of an inch in the day, and sometimes were 

 not appreciable. The greatest descents were on sunny days, and 

 especially when with a warm sun there was a cold wind. The least 

 were on days of continual rain. The average daily descents were, in 

 inches, — 



February. 



March. 



April. 



May. 



June. 



•10000 



•1380G 



•16133 



•21500 



•21888 



These descents were not due to the extreme temperatures of the 

 periods in which they took place, but to the aggregate of the variations 

 up and down during each interval. The difference of the highest and 

 lowest temperatures in any interval may have been small, and yet the 

 changes of temperature up and down may have been many, and their 

 aggregate great. It is upon this aggregate that the descent depends. 



The dilatation of ice was measured in the years 1845, 1846, at the 

 Observatory of Pultowa, by Schumacher, Pohr, and Moritz ; and the 

 particulars of their experiments were communicated to the Academy 

 of St. Petersburgh, by W. Struve, in 1848, and published in its 

 Memoirs (Sciences Mathem. et Phys., eer. 6. t. iv.). By exposing 



