12 



Proceedings of the Royal Irish Academy. 



and its sides produced to the edges of the card. The points I, c, d, e, and/ 

 are to be pricked through the card itself, from the face, makiDg a slight burr 



A GENERATING POLYGON o? 4 DIAGRAM of the Square Rodts of 



Max. Behdins Moments os a'42-hjot Gisdes due to the 3o-foqt 42-ton 



\ 



CaLEDONIAK RaiLV/AY LocOfc^OTIVE 



T/ii Pol^Qon is fo Ic pruhcd on curd'ooard or 

 celluloid, ,uid a hsU prorUii fir the pencil point 

 at A. It tlrUa out lie fice ara on Oie haer 

 fijure, tic fteelpoijii of Ihe compoisei chtnjinj from 

 one to amther ofthepoinit c, d, ^e., as tJie P,jhjgon 

 rolh ■Jttr. Tlie arc for tlie 12-aheel carers 12 feet 

 of the spm. The i2 fat are needed 1st a 

 leluel go of wlien t}te IS- ion wheel is 

 Sfeet to the right, alien rce haee a max.- „& 



of-maziwa .T/j= IS x IS - 9 x 7, or 

 S61 ft.- torn. With any nwcemenl the 

 one IS decreases, the other niaking 

 a like increase, and their product 

 decreases. Bg choosing a suitable 

 unit, Oie toad can he made to 

 equal the span when one scale 

 suits boihfcei and certieals. 

 With ilii draa-point at 



-r. K 



tons 



i2 tjns 



.^ii'^'^A =B4:i 



the arc of the 12-ton toieel scales Sl-li, 



and M, = {211 i)- = iosi ft -tons'. 



Wi/h a coarser scale the longer span 



trill again scale iSfeet, aiidnow the 



56 is the ic eight of an ideal Locoi. 



heavier in tl,c ratio i : $ and 



sliortcr in ilie ratio S: i. It is 



the real Loco., together with a 



dead load of 28 tons, or ^ oj a 



ton per foot, ichieh in the 



form of a rolling load of 



lU tons has been absorbed 



into Itie ideal Loco., and the 



MUX. IS -W.j = iOS^ft.- 



tons, the joint centre of 



granig being a\ feet 



I'ft of tlie centre. 



ShortSpans tf 

 Clrc/pr er'er- /■/onq 



^eec a-rzd 'y<rrtie:a.h 



^^/ rir Tr 7nc7c/ae a 

 7/C'>y7?ead-Loac/. 



I ' — A'-t 





rsft 



T.C.^. 



-7J^ 



-i-'/fu cJ.-. 



Fig. 10. 



on the back, which allows the card to turn more freely. The draw-point A 

 should be pricked through from the back with a thick needle, to accommo- 

 date the pencil point, and leave the back smooth. The card will lie along 



