178 GRAPHIC AND ANALYTIC [CHAP. XII. 



tance, multip ied by the pole distance to scale of force, give the 

 moments at any point. Our construction, therefore, gives the 

 moments also at every point, and we may thus check the re- 

 sults obtained by Art. 114 by the results obtained by the 

 method of moments. 



117. Approximate Construction. It will be readily seen 

 that the portion of the hyperbola in Fig. 81, PI. 21, needed for 

 our construction, is nearly straight. In most cases it will be 

 practically exact enough to lay off f I to the left of A, and \ I 

 also to the left of A at a vertical distance equal to Z, and join 

 the two points thus obtained by a straight line. This line can 

 be taken instead of the curve, and the construction is then the 

 same as above. The error due to thus considering the curve 

 as a straight line is greatest for a weight in the middle of the 

 span, where it does not exceed -riifth of the span for the posi- 

 tion of the inflection vertical, and diminishes from the centre 

 both ways. 



11. Girder continuous over tbree Level Supports 

 Draw Spans. This case is perhaps of the most frequent 

 practical occurrence, and an accurate and simple method of 

 solution is therefore very desirable. 



In the first place, the formulae for the reactions are very 

 simple and easy of application. Thus, for left end support A, 

 the load being in the second span, or to the right of the middle 

 support B, 



for the reaction at middle support, 



for reaction at right end C, 



R = -p(ZaP + 3 d?l- a 8 ); 



where a is always the distance of the weight P from the mid- 

 dle support.* We are therefore already in a position to solve 

 completely the case under consideration. We have only to 



* As already remarked, the development of the formulae assumed in this 

 chapter must be sought for in special treatises on the subject. We assume 

 them as known, and then apply them graphically as above. 



See also Supplement to Chap. XIIL 



