522 Geological Society. 



tions which he has given of this question, the terms involving the 

 square of the velocity being found to have no effect on its value. The 

 difference between his result and that obtained by other writers on 

 the same question, is shown to be entirely owing to his adopting a 

 new principle m the application of analysis to fluid motion, which 

 may be thus stated. If u, v, w be the velocities resolved in the di- 

 rections of three rectangular axes of a fluid particle situated at the 

 point whose coordinates are a', y, z, then, in order that the motion 

 may admit of determination by the integral of a partial differential 

 equation, it is necessary to suppose that ud x + v dy + wd z is an 

 exact differential of a function oi x,y, and z. This supposition must 

 therefore be true, independently of the particular mode of disturbance 

 and of the form of the arbitrary function by which it is expressed. 

 The quantity in question is an exact differential, for reasons drawn 

 from the nature of curve surfaces, and independently of all that is 

 arbitrary, if the variation of the coordinates from one point to another 

 at a given instant be in the direction in which the motion is impressed 

 by the arbitrary disturbance, and not otherwise. Hence the varia- 

 tion of the coordinates in the partial differential equation to which 

 that supposition conducts, must be subject to the same limitation. 

 It is plain that this principle, if true, must materially aflfect the man- 

 ner of treating many hydrodynamical problems, and would seem 

 therefore to merit the attention of mathematicians *. 



GEOLOGICAL SOCIETY. 



June 10, 1840. — A notice of a mass of trap in the mountain 

 limestone on the western extremity of Bleadon Hill, Somersetshire, 

 and on the line of the Bristol and Exeter Railway, by the Rev. D. 

 WilUams, F.G.S. 



This is the first discovery of trap in situ in the Mendip Hills or in 

 Somersetshire, with the exception of the Hestercombe granite, de- 

 scribed by Mr. Horner f. and a slate porphyry, observed by Mr. Wil- 

 liams, a little north of Simmon's birth, in JExmoor. The rock varies 

 in character from a granular to a porphyritic and amygdaloidal 

 greenstone. It occurs near a line of fault, which has brought the 

 lias on a level with the carboniferous limestone ; and when first ex- 

 posed on the eastern side of the railway cutting, it appeared to be 

 conformablj'^ interstratified with the limestone ; but the cutting of 

 the western side (the line of railway ranging north and south) has 

 subsequently proved that the trap is clearly intrusive, intersecting at 

 a considerable angle the limestone beds. On the east side the 

 trap is in contact with the lias, but no change appears to have been 

 produced in that formation, though the mountain limestone is stated 

 to be considerably altered. The trap at the lower part presents a 

 broad bed-like mass, but it rapidly diminishes in its upward course 

 through the limestone thinning away entirely. Mr. Williams states, 

 that the limestone appears to have yielded along the line of one of 



* [On the subject of this communication see L. E. and D. Phil. Mag., 

 vol. xvii. p. 465 : also present vol. pp. 132, 321, and Mr.Chaliis's communi- 

 cation in the present Number. — Edit.] 



I Geol. Trans., 1st Series, vol. iii. p. 348. 



