5A" + 15B" + 10G" - 10D" - Y ( G ' 2 + 2D' 2 ) “ 150 V5 (O' + 2D') - 1600 + 20000 = 0. 
As to the first of these, we have A + B + G + D = 156000, A' + D' — B' — C = — 280 \]5, 
and the equation thus is 
156000 + 40 V-5 (- 280 V5) - 100000 = 0, 
which is right. 
For the second equation, if in the calculation we keep the radicals in the first 
instance distinct, we have 
5A" +15B" +10G" -10D" = - 18800 + 3000 V5 + (-1500 + 300 V5) VQ + (500 + 100 V5) V&, 
- 150 V5 (G' + 2D') = {- 450 - 70 V5 
+ (20 + 4 + Vo) VQ + (-10 + 2 V5) VQi} (~ 150 V5) 
-1600 + 20000 =18400 
(O' 2 + 2D' 2 ) = -~ {282000 + 416800 V5 
+ (- 8800 - 4000 V5) VQ + (4400 - 2000 V5) VQi}- 
Substituting in the equation, we ought to have 
0 = -18800+ 3000 V5+ (-1500 + 300 V5) VQ + ( 500+ 100 V5) VQi 
+ 52500 + 67500 V5 + (- 3000 - 3000 V5) VQ + (- 1500 + 1500 V5) V& 
+ 18400 
- 52100 - 70500 V5 + ( 5000 + 2200 V5) VQ + ( 2500 - 1100 V5) VQi, 
that is, 
0 = (500 - 500 V5) VQ + (1500 + 500 V5) VQi > 
r-go 
and 
but 
solul 
R. 
pp.