General Report on Tunny

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22H Page 69

Putting      j = 6            δ_i6 = Π_i6.β

	∴ 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_.. = δ_xx and δ_.x = δ_x.. Whatever the relative values of Π_.. and Π_xx. This shows that the benefits of counting against Χ₂ limitation

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