494 KEPOET — 1891. 



value of X, which satisfies both equations, and consequently 

 gives the value of x required. 



The process of design is illustrated in the drawings ap- 

 pended by an application to the design of a wall 50ft. high, 

 2ft. 6in. wide at the top, and composed of masonry whose 

 weight IS 1441b. per cubic foot. The width of the wall is 

 determined at intervals of 5ft. 



The first equation to be solved is thus — 



jr + Cx - a) a = 62-5 - = 10-85. 



w 



We proceed accordingly to measure off OAi = 1'085. AiBi = a 

 = 2-5, and AiCi = -^^yO^ = 0-625. The line GJi^ is then drawn ; 

 and the point where it intersects the curve, i.e., D in figure, 

 gives .3-03 as the value of b, the width of the wall 5ft. from 

 the top. 



Next OA., is measured off = (2=^ - 1'^)62-5- = 7-59 ; AoBo = 3-03 ; 



w 



and A.,C., = j\, 3-03 x (2a + 36) = 4-26. The line C.,B., then inter- 

 sects the curve at E, which gives 5-86 as the next width of the 



wall. 



The distances to be measured off in order are thus — 



0A,= 3^.62-5^. 

 w 



x\iBi = a. AjCi = Jjy ^^• 



ID 



A^B, = h . A.A = tV ^ (2a + 36) . 



Q:\, = ^-^(:6'-T)Syl-b 



10 



A3B3 = c. A3C3 = 1^0 c (2a + 46 + 3c) . 



&c. &c. A,C4 = Jo ^ (2a + 46 + 'k + M) . 



&c. 



I found it convenient in making the drawing to change the 

 scale of the curve at this point, and consider the typical 

 equation, a:* + ix — p) q = r, as the resultant of the two 

 equations, — 



100// = x' - r \ 



100// + {x —p) q = o\ 

 but othervs'ise the process is exactly the same. 



In making the drawings, the distances OAi, OA., &c., are 

 measured off first of all, and red lines drawn through these. 

 In calculating the value of A3C3 we have to add on 6 -f 3c to 



