Properties of rotational terms of the form

B (j^{2} - σ^{2})

.—Evidence is presented to show that the AlH,

{He}_{2}

, and certain other bands involve rotational terms essentially of the form

B (j^{2} - σ^{2})

, and are in agreement with the postulates of a previous

{paper .}^{1}

Since terms of this form have not hitherto been recognized in practice, their chief empirical properties, as shown by the bands discussed below, are now summarized. (1) There are in general two values of the rotational energy term

F (j)

for each

j

value. This type of rotational doubling has previously been confused with that which occurs, due to

\pm ε (where ε = | ρ |)

, when

F (j)

is essentially of the form

B {(j - ρ)}^{2}

. In the special case where

ρ

and

σ

are both zero (

{}^{1}S

states), all rotational doubling is absent. (2) The two sets of

F (j)

values, in doubling of the

σ

type, in general differ in respect to the values of

B

and of a small "secondary"

ρ

whose presence must, at least formally, be admitted; thus

F_{i} (j) = B_{i} [{(j - ρ_{i})}^{2} + \dots (i = A or B)

, with

ε < \frac{1}{2}

, or usually ≪½, in practice; a slight difference in the electronic term values may also occur (as e.g., in the

{He}_{2}

bands). (3) In general, there are six branches in combinations of two

σ

-type terms (cf. Eqs. (2) of text); in the

P

and

R

branches, combinations occur only between like rotational terms (

{F^{'}}_{A} \to {F^{''}}_{A}

, and

{F^{'}}_{B} \to {F^{''}}_{B}

), while in the

Q

branches, "crossing over" always occurs (

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