On the Anticlinal Line of the London and Hampshire Basins. 33 



where (P, loA) designates the dihedral angle formed by the 

 plane P and the plane loA. Now in the sohd angle formed by 

 the three planes P, loA, and loH^ perpendicular to P, we have 



' sin loA. cos (P, loA) =cos loH . sin AoH ; 

 and as the angle loH is constant, we see that the accelei'ating 

 couple is proportional to the sine of the deflection of the axis 

 from its position of equilibrium. Hence the law of the oscilla- 

 tions is that of the simple pendulum, and their duration is pro- 

 portional to the square root of the cosine of the angle formed 

 by the earth's axis and the plane P. 



Such is the simple explanation of the observed phtenomena. 

 I ought to observe, however, that after having found the expres- 

 sion for the couple which moves the instrument, it is still neces- 

 sary to explain why the velocity acquired tends to sustain itself; 

 for, properly speaking, there is here no inertia as in the case of 

 a material point. We know, in fact, that the axis oA having a 

 motion in the fixed plane, the instrument does not turn precisely 

 around oA, but around an axis making a small angle with the 

 same, and situated in a plane through oh. perpendicular to P. 

 This axis not being a principal axis of inertia, tends to displace 

 itself, and describe a small cone ; but in order to describe this 

 cone, it would be necessary for it to traverse the fixed plane, 

 which, on its part, resists and produces a couple, whose efi"ect is 

 to raise the axis again, and to sustain, purely and simply, its 

 velocity tangential to the plane P, which latter is increased by 

 the accelerating couple above calculated. 



I may add, lastly, that the small angle formed by the axis of 

 the gyroscope, and the veritable axis of rotation having been 

 neglected, the formulas fou:id are but approximative, and con- 

 sequently do not coincide with the vigorous results obtained by 

 the elaborate, but much more difficult method of Bouz. 



IV. On the Anticlinal Line of the London and Hampshire 



Basins. By P. J. Martin, Esq. 



[Continued from vol. xii. p. 452.] 



BEFORE we leave the great expanse of tertiary drift between 

 the South Downs and the Sussex coast, it will be well to 

 turn our attention again to the nature of its principal ingredient, 

 and to consider the great significance of its presence there. 

 Loam is not an original production, nor is it a common alluvium 

 like the mud silt or sediment of quiet waters, ancient or modern. 

 It is a mixture of sand and clay produced by water in brisk agi- 

 tation ; and when clay predominates in the mixture, it is the 

 " brick-eartli " of geologists. Neither in the form of loam in 

 Phil. Mag. S. 4. Vol. 13. No. 83. Jan. 1857. D 



