. American engineer and railroad journal . ) + () ,„, , ,J =: ^ = 573 491 J- — /? = — 380= 193 4gi -f — {R— AJ = — = 379 791 yi? = ar. comp j^ —/?= ar. comp 9992921 Extracting sq. root 2)19 ^ A^= 87° 41 sin. from which the angle CBN= 175 22and the angle180= - 175° 22 „ , ; = 2 19. A B AI =Then, ^ which A-^ H = 30 Si. The length of the arc // A may be found in the samemanner as described for Eq 7. To find the frog angle D A E = R .1 C. fig. 11, ofth
. American engineer and railroad journal . ) + () ,„, , ,J =: ^ = 573 491 J- — /? = — 380= 193 4gi -f — {R— AJ = — = 379 791 yi? = ar. comp j^ —/?= ar. comp 9992921 Extracting sq. root 2)19 ^ A^= 87° 41 sin. from which the angle CBN= 175 22and the angle180= - 175° 22 „ , ; = 2 19. A B AI =Then, ^ which A-^ H = 30 Si. The length of the arc // A may be found in the samemanner as described for Eq 7. To find the frog angle D A E = R .1 C. fig. 11, ofthe first frog, given the radius of main track = R, theradius of the turnout = R and the standard gauge = ^. In the triangle B A Cwe have given the side A C ^ R— ^ g. A B = R + io; — R. , , (/?->) + (R-iff) + (R + ig)Let s = > then, from trigonometry, we have Sin. i B A C: ig)][s-(R+ig)] (13) (/? - ig) {R + i^)It will be noted that in this case the result is not affectedby the width of the narrow gauge R and BN = R\ Example : Given the radius of the main track, R =573,69, the radius of the turnout A = 380 00, and thestandard gauge = 4 ft. 8A in. = to find the frogangle £> A E = B A C, fig. n : ■f = f573 69-3So)-f ()+ () = 573,69 s-{R- ig) = s - (R + ig) = - ... A — i _^ = ar. com p R + Ig = 3^ ar. ,.Extracting sq root i B A C= 2° 36 9 sin. 72)17 3718065281796724310844175343 31424596571229 VoL LXVI, No. 5.] ENGINEERING JOURNAL. 233 whence the angle /?. / C is 5° 13 18—the required an-swer. To find the frog angle D .1 E =z n A C, fig. 12. ofthe second frog, given the radius of the main track = A,the radius of the turnout — A, (he standard gauge = g,and the narrow gauge = g. In the triangle ./ /> C we have the side ./ C = A* + A^ — tr, the side A J> = A + i g, and the side li C =A? -/?. , . (/?-/?) + (A- + i^ - g) + (A- + ig)Let J = ^ « then, from trigonomet
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