General Report on Tunny


25Y Page 193

are to be distinguished, multiplied by 23.

In the following table the number of legal wheels is exact: other entries to four figures only.

  Total no.
of wheels.
Δ'd wheels with the
correct no. of crosses.
Legal
wheels.
Χ1 2,193,000,000,000 271,900,000,000 23,314,226,716
Χ2        21,43,000,000        304,000,000        73,241,034
Χ3           535,800,000          78,320,000        14,524,128
Χ4             66,990,000          19,544,000          2,869,568
Χ5               8,434,000            1,364,000             556,416

From this table the factor in favour of a wheel because it is spontaneously legal can be calculated. It should be noticed that any supposed ΔΧ wheel corresponds to two Χ wheels or to none, so that e.g. a ΔΧ5, constrained to have the correct number of crosses gains a factor if it is spontaneously legal.

(R5 p 4; for factor given by integration R3 p 30.)


25Y     PROPORTIONAL BULGES RELATING TO

These will all be derived using (22D(g))

The following notation will be used for proportinal bulges
  (. . x) ≡ β . . x denoted the P.B. of 1 = ., 2 = ., 6 = x in ΔΨ
  {. . x} ≡ δ . . x " " " " 1 = ., 2 = ., 6 = x in ΔD
    Πx   " " " "   2 = x,   ΔP
    Π..   " " " " 1 = ., 2 = .,   ΔP
    Π1+2   " " " " 1 + 2 = .,   ΔP
    θ   " " " " = .    
  PB(ΔZ2 = .) = PB (ΔZ2 + ΔZ6 = .)
  = PB(ΔΨ'2 + ΔΨ'6 + ΔΧ2 + ΔΧ6 + ΔP2 + ΔP6 = .)
  = PB(ΔΨ'26 + + ΔP2 = .)
  = βθΠx
       
  PB (ΔD1 = ., ΔD26 = .) = ½[{...} + {.xx}]
  =..(... + .xx) + Πxx(xx. + x.x) + Πx.(x.. + xxx) + Π.x(.x. + ..x)]


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