Beams, &c. ; and on the Polygon of Forces. 327 

 ©f the four blocks AE "j ^ill respectively f ^ 9"] with fp e) Cq 



. r, ' he at the inter- j l- . ^i J /-I, .J _ 



. . AF > ,,,,;,,„ „f ,y,A fr > the < gf>^''{ r 



f .1 r 1- A r-> V he at the inter- ! >. 



9f the five ditto . . AF > ,^,,-^^„ ^f th^i /' 



of the whole .... AG J """'"'* U jJ lines 



If it be desired to continue this archiform combination 

 by a seventh block AZ, fig. 3, adjoininn; to the first so as 

 to extend to the horizontal line ZG, draw fron) A the line 



AZ, any where between the direction A g of" the sustaining 

 force there, and a vertical kt fall from A. The length of the 

 block will be thus ascertained, Froni S, fig. 2, parallel to 

 ZA, fio-. 3, conceive the line Sz to be drawn ; and z, w ill 

 therefore be the representative point of the centre of gravity 

 of this additional block ; its weight niay be of any practical 

 amount greait.r than Az, so that its centre of gravity shall 

 in the line AZ, fig. 3, be at such a distance from Z in pro- 

 portion to ZA, as the weight represented in fig. 2 by A z, 

 is to the whole weight oT the block. Therefore if it be 

 homogeneous and prismalicai, its weight will be double 

 that represented bv Az; if it be wedge-form, with its 

 broad end towarils A, fig. 3, its weight will be f of A z, 

 fig. ti. And from the given length and weight thus 

 found, and its density, its other dimensions may be readily 

 calculated*. 



It will appear, on consideration of tiiis problem, that if 

 the spire block, CD had had its base line at right angles to 

 the sjiire, and had been uniform in its figure, that is, if the 

 spire had arisen from the middle of and perpendictdar to its 

 base, its re|)reseritaiive in fig. 2, Sc would have been at 

 right angles, to the vertical AG ; and blocks similaT to DIl, 

 EF, and FG, but reverse, being placed in lieu of AH and 

 BC. would not only have made the whole figure umtorm, 

 having a middle and two side spires, but (attending to the 

 directions of the problem in aseertaining the positions) the 

 whole would also have been in equiiibrio. Further, if the 

 centre-block of this unih)rm combination be now made 

 twice as heavy, it is ])lain that it uill require, in order 

 to be supported in equiiibrio, the side blocks to be also 

 twice as heavy — or, which will be equally cHicacious, that 



♦ 1 have made a model of wood mucl> like (\g 3, vvliose span 7.G h about 

 15 feet, the eiinme blocks are wedges, with their edges downward, on which 

 tlie whole siaiids. The planes .at the joinings arc about 1^ iudi deep and 

 :i to 4 inclieii in the horizontal direction (hi ri;;ljt anj!;lc's to the plant of the 

 fi;;urc)- Wiien a moderate prcisiire is applied to any of the bloc k*, and 

 then Muldirily withdrawn, the whole vibrates on the edges of the two ex- 

 ti'triac biucki. 



X 4 another 



