1880.] Mr Keeping, Neocomian deposits of Potton and Upware. 377 



Lord Rayleigh in his paper On the numerical calcidation of the 

 roots of fluctuating functions (Proc. London Math. /Soc, Vol. v. 

 p. 122) has calculated the least root of the equation J^i^) =0, 

 his result being 2'404!826. Denoting this by z^, the least root of 

 the equation (1) 



= (iz^y = (1-202413)' = 1-445797, 



which confirms the value found above. 



May 3, 1880. 



Professor Newton, President, in the Chair. 



E. B. Tawney, M.A., Trinity College, was ballotted for and duly 

 elected a Fellow of this Society. 



The following communications were made to the Society : — 



(1) W. Keeping, M.A., On the included pebbles of the Neoco- 

 mian deposits of Potton and Upware, and their hearing upon the 

 physical features of the lower cretaceous period. 



The Lower Greensand (Upper Neocomian) beds beneath the 

 Gault at Potton in Bedfordshire, Upware near Cambridge, and 

 elsewhere, include various pebble beds and conglomerates. The 

 majority of the pebbles are phosphatic nodules or " coprolites," for 

 which the beds have been worked during the last ten or twelve 

 years. These were all of them derived as pebbles from older 

 Neocomian and Jurassic rocks, and saturated with phosphate 

 during the formation of the Upware and Potton beds. Besides 

 these there are many other pebbles which are not phosphatised, 

 and which are therefore picked out by the work-people and 

 accumulated in rubbish heaps at the diggings. They belong to 

 various ages, namely-: I. Lower Cretaceous; ii. Jurassic (impure 

 limestone, chert, and sandstone) ; and ill. more ancient rock frag- 

 ments. These latter are considered under two first headings 

 according to their sizes. The smaller pebbles, which make up 

 regular conglomerates, consist of quartz, apparently vein quartz, 

 and subangular fragments of hard, highly silicious, fine-grained 

 rocks, many of which are chert, the rest being highly indurated 

 argillites (Lydian stone, etc.). The larger pebbles (diameter more 

 than an inch) are vein quartz, vein breccia, quartzite, altered 

 sandstone, probably of carboniferous age, and altered grits. 



Amongst the more interesting pebbles are [a) the angular and 

 subangular fragments of indurated shale and Lydian stone ; (6) a 

 very angular, joint- hacked piece of Cambrian or Silurian pale 

 slate, in which a group of fossils was found ; and (c) the masses of 



