9^ OfeSERVAflONS ON THE 



wall and counterfort given by Mr. Mullf.r In his ^<\ 

 prob: from whence arifes 4/^ + 2zwX.v''4-4^+ iwXzn 



•^T:0-\--^-^'wXa^z:i\^ba"-s^y which tranfpofed and divided 



b—%hn^ — : 



oy4^ + 2'<x',giyesA'* + 2««-f |-fiX;cz=tf^X- 4^ + 2^,; 

 ^ T « — tV; and beins^ reduced, gives x z=. a 



^^^ H 4T4.2.-:;; — TT^-^+T-s-^wbichisagenc- 

 ral equation for flone walls ; and by comparing the 

 fpecific gravities, as in the former cafe, then xzz 



^v/«'X 



'^,rb—\o^2r.,\Y.n' 



T-l-ff— ^^+ iV> ^ general equa- 



4/4--"^'' 

 tion fdr brick walls. 



No\V in order to obtain the value of w, let Q_re- 

 prefent the niafs of the wall and counterfort together, 

 fufpended 'to a line paffing ^ r^ r- 



through their common center 

 of gravity, and which will cut 

 the line AE, we will fuppofe, 

 in the point H. Then, from 

 the 'principles of mechanics, if 

 c arid d be the points in the 

 line i\ E, where lines paffing 

 throiifdi thx refr.ective centers 

 'ot - i^'rtivitv m m^- -two miiHes 

 A B (; D; and B C F E, vviilF^"' ^_^ 



inter fca that line, we have Q^ -*- A b + 1 B K 

 (-cd) : : B E -i-£B C (CIS ihe mafs B C F M] : 



I A h-\- , iii X Br.X.^i'C_l4-* X -^r.^ ■>. . 



'X3+i\— f'5^ 



:cU. 



lie nee 



All 



—-j-Vt -{--'- =-,>'.-. 'i hen again, by the laws ot mecha- 

 nics ; as 4-?- (= A B 4-^1 BE + BS) : ,V^ (zr. AH) :: ^^ ( =^ Q) : 

 4^-|| — \\' • — and confequently, .;y— 7^*|=,2:4near- 



ly. Nov/ b- -^--- =,V5=,379, near- 

 ly, and if ;/=', and the angle CBF =45'^, fo that 

 S'=,c;; — and their different values fubftituted in tlie 

 general expreflions above, we Ihall get xzz ,0815 X^? 

 nearly, for ftone walls, and >:— ii;^Xa nearly, tor 

 brick walls. 



