# General Report on Tunny

22H Page 69

Putting      j = 6            δi6 = Πi6
 ∴ PB(ΔDi + lim = cross) = Πi.β ∴ (for Χ2 = lim) PB(ΔD2 + → x) = Π2.β (H9)

 Now [illegible] → dot (nearly always) [illegible] → cross (for punctuation)

 ∴ ΔD2 → dot ΔD2 + Lim → dot    (R1 p. 9) (H10)

Figs. 22 (VI)(VII)(VIII) give scores [illegible] for the various ΔD counts shown.

The following table gives values for two impulse ΔD proportional bulges against limitation dots and crosses.

 δ..≡ PB(ΔDi = .    ΔDj = . | L = .) δ..≡ PB(ΔDi = .    ΔDj = . | L = x) δ..≡ PB(ΔDi = .    ΔDj = .) and so on

 δ.. δxx δx. δ.x
 {β(Π.. + Πxx) - β(Π.. - Πxx)} {β(Π.. + Πxx) + β(Π.. - Πxx)} {-β(Π.. + Πxx) - β(Πx. - Π.x)} {-β(Π.. + Πxx) + β(Πx. - Π.x)}
 δ.. δxx δx. δ.x
 (1+β) {-β2(Π.. + Πxx) + 2βΠ.. + (3Π.. + Πxx)} (1+β) {-β2(Π.. + Πxx) + 2βΠxx + (3Πxx + Π..)} (1+β) {+β2(Π.. + Πxx) + 2βΠx. + (3Πx. + Π.x)} (1+β) {+β2(Π.. + Πxx) + 2βΠ.x + (3Π.x + Πx.)}
 δ.. δxx δx. δ.x
 +½β(Π.. + Πxx) +½β(Π.. + Πxx) -½β(Π.. + Πxx) -½β(Π.. + Πxx)

Fig. 22(XII)

The workings are left to the reader (similar workings are given on R4 p. 80)

Two results should be noticed.

(i) δ.. = δxx and δ.x = δx.. Whatever the relative values of Π.. and Πxx. This shows that the benefits of counting against Χ2 limitation