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1L. On the EquUiirium of a Comlination of Beams, Blocks^ 

 l2fc. ; and on the Polygon of Forces. By John 

 Southern, £35, of Solw near Birmingham. 



to Mr. Tilloch. 



Sir, — Although several authors, who have written on 

 Arches, Roof's, &c. have treated iht- subject or Eqir.librii m 

 very exlcnsivelv and uiih great adroitness, I have not set- a 

 in any work a prol)1em of the pretie nature of that \vh;ch 

 herein follows; and which I conceive may be of consider- 

 able utility in practice, being easy of application. 



Jn all those problems btaring on the present point, that 

 I have noticed, the centre of gravuv of each block or beam 

 is supposed to be in the right line that joins ih.e points of 

 abutment; l)ut cases occur ni practice in which that does 

 not take place, and to these is the present problem pecu* 

 Jiarly adapted, though it is advantageou-.ly so to others: 

 for instance, the rafters and slates of roofs have their com- 

 non centre of gravity higher than the rafters, though it is 

 these which sustain the svhole; and fig. 3. herein referred 

 to will point to other cases; and it will be seen thai this 

 circumstance is material to their position of equilibrium. 



The language of authors on this subject is not always 

 distinct, and is very likely to have been mistaken in regard 

 to the words l<ars and teams, which are frequently used ia 

 problems of the kind in question under the sui)positioix 

 of their possessing vo ueigkt, without its being so ex- 

 pressed ; and even when it is, it does not appear to me to 

 have been properly treated. 



All the authors 1 have consulted, speaking of a numi^er 

 of beams supportuig each oiher in equilibrio, say the forces 

 are in the diitclions of the beams ; and, certainly, whea 

 these have no weight, but are merely props sustaining 

 ■weights at their ancles, this proposition is true; but al- 

 low the bars or beams to gravitate, and to be the only gra- 

 vitating matter, and their forces exist at the angles, which 

 the propositions do not develop : for though some of the 

 authors alluded to show what portion of the weight of eacli 

 beam lies on the angle, and then direct the consideration to 

 follow as if actually united weights were substituted for 

 them ; yet it must be allow(d that this is not matter of fact, 

 and that neither the quantum of force, nor its direction, 

 with which each btam presses on its contiguous ones, is 

 shown, as I trust will soon appear. 



Vol. 4 1 . iNy. 1 S 1 . May 1813. X Ixl 



