36 On ihi Straiijtsatien of Matlock in Derhy shire, 



?©<!, expresses both the effort which it exercises upon the ma- 

 chine, and the quantity of movement which it loses itself by 

 the reaction it undergoes : if, therefore, we call F that force, 

 this quantity F will be the same thing with that which is 

 expressed by m U in our equations*. Thus, if we call Z 

 the angle comprehended between this force F, and the ve- 

 locity u, which the point would have where we suppose it 

 applied, if we make the system assume any geometrical 

 movement, the general equation (F) will become s Y u co- 

 sine Z = (AA). It is therefore under this form that we 

 shall immediately employ this equation, by means of which 

 we may apply whatever we can mention, to any imagi- 

 nable kind of force ; and the principles exposed in this first 

 part will serve us to develop the general properties of ma- 

 chines properly so called, which are the object of the en- 

 suing division of the present work. 



[To be continued.] 



VI. On the Stratification of Matlock in Derbyshire, point- 

 ing oiU a Mistake of the late Mr. John Whitehurst, 

 relative thereto; afid on the Trunamutation of Lime to 

 Silex. By Mr. John Farky, Mineralogical Surveyor, 



To Mr, Tillnch. 



SIR, 



A. HK hleMr. John JFhitehurst, in his " Inquiry into the 

 original State and Formation of the Earth," has given sec- 

 tions of the strata to be found in various parts of Derbyshire, 



• It is evident that the quantity of movement lost m V, is the result of the 

 movement which the body •:) would have had the instant afterwards, if it 

 had been free, and of the movement equal, aird directby opposed to that 

 which it will reallv assume : now the first of these two movements is itself 

 the result of the actual movement of m, and of its absolute motive force; 

 therefore m U is the result of three forces, wTiich are : its absolute motive 

 force, its actual quantiy of movement, and the quantity of movement equal 

 and directly oppo^ed to that which it should have the instant after : but ac- 

 eoiding- to the preceding note, these two last q^iantities of movement have 

 for theii result the vis iiurliu' : therefore m U or F is the result of the motive 

 force of TO and of its vis inertux ; i. e the force exercised iy any i^ivcn bixly, at 

 tdv'i instant, is the result of its ahoiute ittutive force and nfils vis inertiac, 



which, 



