1 1\ K-I.I.UI tmucsaca 



as positive and once as negative. Therefore the sum of all 



2 C - 0. (6) 



This formula serves as a check on the values of the eoef- 

 ntM which have been determined either by calculation 

 Of ly graphical measurement. 



e general formula* for the sum of the ordinat*~kd 



products for any influence line fvi/.. with orvrral nalK 



ate MI. -h a- the one *hown in may be arrived 



at hy considering th,- t\\,, .-..nt^uous sloping sides of the 

 influi-ncr line meeting at each salient point as two diverg- 

 ing line-. '!'},. entire influence hn.- i> than made up of paif* 



-in^ lines (see i each pair of which 3 ^ 



inula (5) may be dirr< tly applied. HIUM in Fig 



()rdinatr-lM:i,l product- in 



.. 



-CM* (- 



(-h) 

 ska -C.JT, (-) 



-l torn** - CJtf (-f) 



The signs of the CAT* are -f or - according to tig;' 

 signs of the coefficient*, for the AT are always positive. ST 

 Suininin^ up the above equations and obsen-ing that the^ 

 ordinal e-Umd producU cancel one another except between the 



h: * and it- l:u-4- liiu fttrn. it fillows that 



sum of the ordinate-load products for the influence 

 line, or the H\r-load stress, is 



S - C..V, + C f Af, -h - 2CJ/. . , (7) 



l.-tt.-r > -senU in general any stress or sum of 

 ordinate-load product.* for any influence line, while Z stands 

 for the sum of ordinate-load product.* for any geometrical 

 figure. 



The rate at which S vanes as the load advances a dis- 

 tance dx equals 



