Rev. G. Phillips on the Summation of Series. 339 



short period of twenty-three days, produced an induration 

 which was sufficient to maintain almost any weight brick-work 

 was capable of for openings in buildings. The effect probably 

 would have been the same with Parker's had the materials not 

 set before the bricks were fixed in it: further, that pozzolano 

 had not in that period produced an equal adhesion, and that 

 common mortar had produced hardly any. And it appears 

 from the splitting of the large piers thrown down on the 21st 

 of April, that an increasing induration took place ; this was 

 evident from the nearly equal fracture of the bricks and ce- 

 ment. . 



The incompressibility of mortar being one of its most va- 

 luable qualities, it results that Parker's, and Mulgrave's ce- 

 ments, and pozzolano, are so far equally useful, that brick-work 

 constructed with them will bear on each superficial foot be- 

 fore the bricks will crack, about twenty-three tons ; that fifty 

 tons will totally crush such brick-work ; that Portland-stone, 

 of the best quality, will not split with less than one hundred 

 and seventy-three tons and a half; and that a bedding or joint 

 of pozzolano mortar is not destructible with that weight. 



John White. 



IX. Extract from the Memoirs of Savary, Bulce of Rovigo. 

 {Vol. ii. page 53.) 



<« The bridge of Ratisbon is the only stone bridge on the 

 Danube, from Ulon where the river is not of any great width, 

 to the sea. It is of Roman origin, and is constructed of gray 

 freestone and thin bricks bound together with pozzolano ce- 

 ment. This monument will stand the ravages of time. 



« He informed me that Marshal Davoust had left that very 

 morning with his whole army, in consequence of its being re- 

 ported to him that the Archduke was manoeuvring to turn 

 Ills right ; that every effort had been made to destroy the 

 bridge, but the masonry work resisted every attempt to break 

 it down; it had therefore been necessary to give up the idea." 



XLVII. On the Summation of Series. By the Rev. George 

 Phillips, B. A. Fellow of Queen's College, Cambridge*. 



THE summation of infinite series, from its connexion with 

 some of the most difficult branches of physical science, 

 has always been regarded as a subject of great importance. 

 In these pages are summed some very general series by means 

 of definite integrals; their sums are made to depend upon 



• Communicated by the Author. 



2X2 the 



