Table 2 



^i 



6lj-30 



sin 0j 



cos 0j 



cos (0j - 30) 



^i' 



O I II 



68 59 14.676 



O » II 



38 59 14.676 



0.93350166 



0.35857308 



0.77728423 



5.40961166 



102 41 05.226 



72 41 05.226 



0.97559289 



-0.21958714 



0.29762840 



1.88057496 



142 37 42.676 



112 37 42.676 



0.60698032 



-0.79471687 



-0.38475484 



13.015729 



288 55 52.126 



258 55 52.126 



-0.94590914 



0.32443167 



-0.19198850 



4.86994806 



Xj = 3 + Tj COS 0j 



yj = rj'sin d- 



rj = r/±2 



^i + 4 = ''i'±4 



tan 0j 



4.93974111 



5.04988146 



Tj 



= 3.40961166 



r^ = 9.40961161 



2.60337906 



2.58704992 



1.83467556 



^2 



= 3.88057496 



r, = 5.88057496 



- 4.4428508 



- 7.34381941 



7.90029135 



h 



= 15.015729 



r, = 9.015729 



- 0.76376927 



4.57996538 



- 4.60652838 



1-4 



= 6.86994806 



r^ = 8.86994806 



- 2.91558822 



Checks of the computations of Table 2 were made as follows: 

 1. Using (x- - 3)^ + yj^ = rj^ and values from Table 2: 



(xj-3)^ 



yi^ 



(xi - 3)^ + y.' 



^i^ 



3.762 59557 



25.501 30276 



29.263 89833 



29.263 89831 



0.170 52777 



3.366 03441 



3.536 56218 



3.536 56218 



106.994 59999 



26.414 60341 



169.409 20340 



169.409 20140 



2.496 29060 



21.220 10372 



23.716 39432 



23.716 39410 



2. From the formulas of (2) and (3) find A = 2, B = 2v''3, C = 0, D = - 6( V^ + 2), E = -6(V3'+l), 

 F = 9(2V'3'+ 3), § = BEG = - 60 (V"3 + 3), ^„ = a'A + CG = 8, L = p„' - a' GB= - - 11 x 2" 



H » - 2^- 48 (V'3"+ 2) + 60 {yjj + 3)] /ll x2^ = + (2/11) [26.1961524] =-4.76293680. 

 From Table 2, Sxj = 4.76293700 = - H = 4.76293680. Again computing N from equations (3), 

 find N = - 429.826515. From Table 2 find Hx. = - 429.826494 and IIxj = N. 



3. From equation (6), compute the quantities: 



U = B/A = Vs; V = C/A = 0, W = D/A = - 3 ( V'3 + 2), R = E/A = - 3(V"3 + D, T = F/A 

 = 9 (2^/3 + 3)/2, = c' + cW + T = 9/2, 6^ = R + cV = - 3, p'= a' + T = % (ISy/S + 35), 



Q = aV(c^ - a^) = 4/5, k, = (GV + <^ Q)^ - a^ 6,' = - 2' 3V5^ K 



a'W'=+(1189+684V3)/2' 



Now from equation (6), Dm. = H tan d^ = k^/k, = - 5' (1189 + 684 V3)/2'3' = - 25.756540. 

 Now forming 11 tan d- from the values in Table 2, find 

 n tan e- = - 25.756539. 



107 



