90 An Essay on Rents. [Fbb. 



descend below the other parts of the same strata. But as the ratio 

 of contraction of the parts h, k, m, ?i, of tlie strata B, C, D, E, is 

 as much less than the general ratio of all the strata on the under 

 side of this rent, as that of tliis of the strata below the stratum A 

 is greater than it ; so the elevation of the first stratum above the 

 stratum A would not be so much as tlie elevation of this siratum by 

 the diti'erence of the ratio; nor would the third stratum al;ove the 

 stratum A be so much elevated as the second ; nor the fourth, as 

 the third ; so that the elevations of the strata above the stratum A, 

 a'5 their distances from it increased, would be less ; till at lai^t no 

 alteration in their positions could be observed. Again, as the ratio 

 of contraction of the parts g, i, I, is as much greater than the 

 general ratio as that of this of the strata below the stratum A is less 

 than it; so the first stratum above this stratum would not be suffered 

 to descend so much as it by the difference in the ratio; nor would 

 the third stratum above the stratum A descend so much as the 

 second ; nor the fourth, so much as the third ; so that at the dis- 

 tance above the stratum A which is equal to that between this 

 stratum and the lowest extremity of the rent, no alteration in the 

 general position of the strata would take place. 



Uprf)n this alteration in the position of the strata depend the 

 shape and position of these rents. Let the line b o, fig. 2, Plate 

 XXX., be a continuation of the angular direction of the separated 

 surface of the stratum A on the under side of the rent D ; then as 

 the line y h makes an angle, g i, with the line li m that is greater 

 than the angle b c d, which the line c b makes with the line c fy 

 the IdSt of which is parallel to the line m h : so an angle, o g, is 

 produced, which is the deviation of the stratuin B's surface of 

 separaiions' angular direction from that of the separated surface of 

 the stratum A ; and as the angle / m k is greater than the angle 

 f e d, so the angular direction, e k, of the stratum B on the upper 

 side of the rent makes an angle, k e n, with that of the stratum A, 

 which, being less than the angle o h g, the rent is wider at I i than 

 at d e. Again, the angular directions of the stratum C's separated 

 surfaces deviate as much from those of these of the stratum B as 

 these directions of its surfaces of separation do from the same 

 directions of the separated surfaces of the stratum A. Hence the 

 angular direction a Zi (y 3 is a curved line, the ratio of whose devia- 

 tion from the line b o increases opposite every stratum above the 

 stratum A ; and the angular direction, a e k 2, of the upper side of 

 the rent is a curved line also, which deviates from the line e n with 

 an increasing ratio, but one not so great as that of the under side 

 of the rent ; the width of this rent, there,'"ore, increases upwards. 

 In tliis manner the lower half of the rent, ?i w v, fig. 1, Plate 

 XXIX., was formed; and in a similar manner, with the following 

 exccpiion, its upper half was formed. But as in the upper half, the 

 ratio of contraction on the under side being greater, and on the 

 upper side less, tiian the general ratio of contraction on similar 

 sides of the lower half of the rent, the sectional lines which r**- 



