276 Mr. G-. Wilson. On a Method of determining the 

 The equations for the supports are 



16330 = 37*67 Ri + 22'53 R 2 , 

 12034 = 22*47 Ri + 22*69 R 2) 



whence R = 52'0 tons. 



Hi — 2S1-9 

 R 2 = 253-5 „ 

 R* = 12-6 „ 



If I were assumed to be constant then by Clapeyron's theorem of 

 three moments 



B = 53-2 tons. 

 R x = 278-3 „ 

 R 2 = 259-8 „ 

 Ra = 8-7 „ 



The above values of the constants were obtained by dividing the 

 span into twenty equal divisions of 10 feet, and calculating the 

 value of the ordinates to each curve at these points. This is clearly 

 shown in Tables I, II, III, 



Having obtained the ordinates to the M/I curve, in each case the 

 succeeding ordinates could be written down almost by inspection, 

 and employed to find the areas by Simpson's rule, the time occupied 

 being very short. 



If the support at A 1 be supposed to be depressed -J inch below the 

 line A A 3 whilst A 2 is supposed to be elevated § inch above it, the 

 alteration in the supporting forces is easily found. 



For assuming E = 24,000,000 lbs. 



Ec x = —446-4. 

 Ec 2 = 4-669-6. 



Hence the equations become 



16330 — 446-4 = 37*67 R x + 22*53 R 2 , 

 120844-669*6 = 22'47 R x 4-22-69 R 2 , 



whence R = 82*06. 



Rx = 210*2. 

 R 2 = 354-0. 

 R 3 — -46*26, 



indicating that under these conditions the end of the girder at A 3 

 would have to be fastened down in some way. 



Further alterations of level may be investigated in a similar 

 manner. 



