122 Ml- Basset, On a Class of Definite Integrals [Nov. 13, 



66. Pebble of quartzite worn by blown sand. Copitz by Pirna. 



67. Do. These are good samples of the stones supposed to have 

 been ground on several sides as they occupied difi'erent positions 

 under the ice. Similar specimens are exhibited in the Dresden 

 Museum as evidence of glaciation. 



68. Glacially striated pebble found by myself below the lignite at 

 Wetzikon. 



69. Do. on the moraine above the lignite of Wetzikon. 



70. A piece of Haffield conglomerate, Haffield. 



71. A slightly worn fragment of close textured mudstone with a 

 shining surface produced by a film of iron oxide. Haffield con- 

 glomerate, Haffield. 



72. Boulder of a green sandstone with shells and masses of the 

 phosphate bed attached and covering striations caused by weather- 

 ing along line of weakness due to rock structure. Compare 

 Nos. 37, 38, 39. ' 



73. Rolled lump of older boulder clay found in newer boulder clay, 

 Clwydian Drift. St Asaph, North Wales. 



74. Lump of newer boulder clay (Clwydian Drift) rolled on shore. 

 Colwyn, North Wales. 



75. Lump of London Clay rolled on shore. Sheppey. 



76. Pebble of Bala Limestone with Halysites catenularius projecting 

 on the surface. In conglomerate at base of Carboniferous. Hol- 

 beck Gill, between Dent and Garsdale, Yorkshire. 



November IS, 1893. 

 Prof. Sir G. G. Stokes in the Chair. 



The following Communications were made to the Society : 



(1) The Application of Newton's Polygon to the Theory of the 

 Singular Points of Algebraic Functions. By H. F. Baker, M.A. 



(2) On a Class of Definite Integrals connected with BesseVs 

 Functions. By A. B. Basset, M.A., F.R.S. 



This paper contains a method for reducing double integrals of 



/.QO 



the form 1 A,"* e~^^^ JJ^'^) ^^ ^^ single integrals ; also various ex- 



io " _ 



pressions for the different kinds of Bessel's functions are found in 

 the forms of definite integrals. 



1. In many investigations connected with the motion of 

 viscous liquids and the conduction of heat, definite integrals occur 

 which depend upon integrals of the form 



»Q0 



j \-e-^'U^(\r)dX^ C(say). 

 Jo 



