j540 THE STRENGTH 



of the distances between the supports ; and we 

 should have had W^ = ^Tc^^ ^ ^ut» supposing 

 m and n to be the middles of AB and AG, 

 the strength of the beam is decreased toward 

 the ends (page 470) in the proportion of 

 AmxBmtoAnxBn. If then the above 

 value be reduced in this proportion, we have 



W/ WxAB AnxBn i.AB Am , 



= -^ic- >< ii,r^rBi.> but ]rc = Tz> an4 



X>m _ Am, .. VV — AnxAm2 — ~A^~ ^ 



Cor. If AG = ^, An = ^, and Bn = 

 3An='Am. Whence W = ^i^f? _ | w. 



The conclusion in this Corollary was made 

 use of (pages 475-6 and 494) to ascertain 

 whether the beams were properly proportioned, 

 to bear the same weight toward the ends as 

 in the middle ; and consequently a load laid 

 uniformly over them. 



79. The following experiments are on a large 

 scale and adapted to practice -, they were made 

 on beams of the usual form, by Messrs. Fair- 

 bairn and Lillie, from their models, at different 

 places, where they happened to be supplying 

 beams; and were superintended by Mr. Fair- 



