26 G. PL. Williams — Peridotites near PeekskiU, JV. Y. 



to increase, while those on the other side tend to diminish the 

 actual acceleration of the pendulum. 



In (8) the condition a= ■—. — or a = &R'=a', reduces the ra- 

 v J 4 sin a 



dius to zero. This gives the value of a at the center of the 



concentric circles. If the value of - — - R as deduced from (9) be 



sin v 



substituted in (8) it becomes 



a = iR ' ~ W RS (10) 



This is the equation of a parabola, the position of whose 

 vertex is given by the conditions 



y = 



x = W 



z = a' = %R' 



the distance z being, of course, laid off at right angles to the 

 plane of x, y. Eevolving this parabola about its transverse 

 axis, which is parallel to the axes and S, the paraboloid of 

 revolution obtained will represent the relation between a and 

 R for every point in the field. The changes which this surface 

 undergoes during an oscillation of the pendulum, are very 

 curious and interesting, but it is unnecessary to enlarge upon 

 them here, further than to remark that the focus of the parab- 

 oloid is always in the axis x, and its vertex is always in one 

 of two right lines lying in a horizontal plane and making an 

 angle of 30° with the axis x, and intersecting at S. 



These considerations are wholly independent of the maxi- 

 mum amplitude of swing, and also of the geometry of the pen- 

 dulum, excepting so far as it is involved in the distance I. 



The concentric circles which represent the isodynamic lines 

 of the disc pendulum, are of course the right sections of coaxial 

 cylinders, which represent the isodynamic surfaces of any com- 

 pound pendulum. 



When 6 = 0, these consecutive surfaces become a series of 

 vertical and equidistant planes, as is shown by equation (6). 



Art. IV. — The Peridotites of the " Cortlandt Series' 1 on the 

 Hudson River near PeekskiU, N. Y. ; by Geo. H. Williams. 



It is proposed in this paper to give a petrographical descrip- 

 tion of the most basic members of that interesting group of 

 massive rocks which occurs on the southern flank of the 

 Archeean Highlands about forty miles north of the city of New 

 York. 



The writer is under great obligations to Professor James D. 



