Regarding the use of the word 'affirmative' in this context

Solution 1:

In this context, "affirmative elements" means those characteristics that define a social group as a tribe and distinguish it from others. The full paragraph containing the sentence in question is:

It is difficult to describe an Indian tribe by the Affirmative elements of its composition. Nevertheless it is clearly marked, and the ultimate organization of the great body of the American aborigines. The large number of independent tribes into which they had fallen by the natural process of segmentation, is the striking characteristic of their condition. Each tribe was individualized by a name, by a separate dialect, by a supreme government, and by the possession of a territory which it occupied and defended as its own. The tribes were as numerous as the dialects, for separation did not become complete until dialectical variation had commenced. Indian tribes, therefore, are natural growths through the separation of the same people in the area of their occupation, followed by divergence of speech, segmentation, and independence.

"Element" can be used to describe a component or part of something. ("Element," OED 4b.) The elements of a chair would include a seat, back and legs. In certain contexts, "element" may be definitional. (I.e. "element" is synonymous with "essential element.") For example, in legal usage, the "elements" of a crime are the things that must have happened for that crime to be committed. (The elements of first degree homicide might be (1) killing, that is (2) unlawful, (3) committed with an intent to kill, and (4) committed with deliberation and premeditation.)

"Affirmative" here may mean characteristics that describe the existence, as opposed to the non-existence of something. That is the interpretation in a more recent discussion:

Severin Fowles, "From Social Type to Social Process: Placing 'Tribe' in a Historical Framework," in The Archeology of Tribal Societies (2002)

Solution 2:

It is difficult to describe an Indian tribe by the affirmative elements of its composition.the affirmative elements of its composition.

The phrase in question can be rephrased as "the elements that affirm its composition as a tribe."

and paraphrased as

"the elements that positively define it as, or demonstrate it to be, a tribe."