The first chapter of the third or supplementary part consists of fifteen sections, which are often quite short, are mostly unconnected in matter, and appear to be of very different age. The second chapter, however, forms a long and important treatise (identical with that found in the Chhāndogya) on the doctrine of transmigration. The views here expressed are so much at variance with those of Yājnavalkya that this text must have originated in another Vedic school, and have been loosely attached to this Upanishad owing to the peculiar importance of its contents. The preceding and following section, which are connected with it, and are also found in the Chhāndogya, must have been added at the same time.

Not only is the longest Upanishad attached to the White Yajurveda, but also one of the very shortest, consisting of only eighteen stanzas. This is the Īçā, which is so called from its initial word. Though forming the last chapter of the Vājasaneyi Saṃhitā, it belongs to a rather late period. It is about contemporaneous with the latest parts of the Bṛihadāraṇyaka, is more developed in many points than the Kāṭhaka, but seems to be older than the Çvetāçvatara. Its leading motive is to contrast him who knows himself to be the same as the Ātman with him who does not possess true knowledge. It affords an excellent survey of the fundamental doctrines of the Vedānta philosophy.

A large and indefinite number of Upanishads is attributed to the Atharva-veda, but the most authoritative list recognises twenty-seven altogether. They are for the most part of very late origin, being post-Vedic, and, all but three, contemporaneous with the Purāṇas. One of them is actually a Muhammadan treatise entitled the Alla Upanishad! The older Upanishads which belong to the first three Vedas were, with a few exceptions like the Çvetāçvatara, the dogmatic text-books of actual Vedic schools, and received their names from those schools, being connected with and supplementary to the ritual Brāhmaṇas. The Upanishads of the Atharva-veda, on the other hand, are with few exceptions like the Māṇḍūkya and the Jābāla, no longer connected with Vedic schools, but derive their names from their subject-matter or some other circumstance. They appear for the most part to represent the views of theosophic, mystic, ascetic, or sectarian associations, who wished to have an Upanishad of their own in imitation of the old Vedic schools. They became attached to the Atharva-veda not from any internal connection, but partly because the followers of the Atharva-veda desired to become possessed of dogmatic text-books of their own, and partly because the fourth Veda was not protected from the intrusion of foreign elements by the watchfulness of religious guilds like the old Vedic schools.

The fundamental doctrine common to all the Upanishads of the Atharva-veda is developed by most of them in various special directions. They may accordingly be divided into four categories which run chronologically parallel with one another, each containing relatively old and late productions. The first group, as directly investigating the nature of the Ātman, has a scope similar to that of the Upanishads of the other Vedas, and goes no further than the latter in developing its main thesis. The next group, taking the fundamental doctrine for granted, treats of absorption in the Ātman through ascetic meditation (yoga) based on the component parts of the sacred syllable om. These Upanishads are almost without exception composed in verse and are quite short, consisting on the average of about twenty stanzas. In the third category the life of the religious mendicant (sannyāsin), as a practical consequence of the Upanishad doctrine, is recommended and described. These Upanishads, too, are short, but are written in prose, though with an admixture of verse. The last group is sectarian in character, interpreting the popular gods Çiva (under various names, such as Īçāna, Maheçvara, Mahādeva) and Vishṇu (as Nārāyaṇa and Nṛisiṃha or “Man-lion”) as personifications of the Ātman. The different Avatārs of Vishṇu are here regarded as human manifestations of the Ātman.

The oldest and most important of these Atharvan Upanishads, as representing the Vedānta doctrine most faithfully, are the Muṇḍaka, the Praçna, and to a less degree the Māṇḍūkya. The first two come nearest to the Upanishads of the older Vedas, and are much quoted by Bādarāyaṇa and Çankara, the great authorities of the later Vedānta philosophy. They are the only original and legitimate Upanishads of the Atharva. The Muṇḍaka derives its name from being the Upanishad of the tonsured (muṇḍa), an association of ascetics who shaved their heads, as the Buddhist monks did later. It is one of the most popular of the Upanishads, not owing to the originality of its contents, which are for the most part derived from older texts, but owing to the purity with which it reproduces the old Vedānta doctrine, and the beauty of the stanzas in which it is composed. It presupposes, above all, the Chhāndogya Upanishad, and in all probability the Bṛihadāraṇyaka, the Taittirīya, and the Kāṭhaka. Having several important passages in common with the Çvetāçvatara and the Bṛihannārāyaṇa of the Black Yajurveda, it probably belongs to the same epoch, coming between the two in order of time. It consists of three parts, which, speaking generally, deal respectively with the preparations for the knowledge of Brahma, the doctrine of Brahma, and the way to Brahma.

The Praçna Upanishad, written in prose and apparently belonging to the Pippalāda recension of the Atharva-veda, is so called because it treats, in the form of questions (praçna) addressed by six students of Brahma to the sage Pippalāda, six main points of the Vedānta doctrine. These questions concern the origin of matter and life (prāṇa) from Prajāpati; the superiority of life (prāṇa) above the other vital powers; the nature and divisions of the vital powers; dreaming and dreamless sleep; meditation on the syllable om; and the sixteen parts of man.

The Māṇḍūkya is a very short prose Upanishad, which would hardly fill two pages of the present book. Though bearing the name of a half-forgotten school of the Rigveda, it is reckoned among the Upanishads of the Atharva-veda. It must date from a considerably later time than the prose Upanishads of the three older Vedas, with the unmethodical treatment and prolixity of which its precision and conciseness are in marked contrast. It has many points of contact with the Maitrāyaṇa Upanishad, to which it seems to be posterior. It appears, however, to be older than the rest of the treatises which form the fourth class of the Upanishads of the Atharva-veda. Thus it distinguishes only three morae in the syllable om, and not yet three and a half. The fundamental idea of this Upanishad is that the sacred syllable is an expression of the universe. It is somewhat remarkable that this work is not quoted by Çankara; nevertheless, it not only exercised a great influence on several Upanishads of the Atharva-veda, but was used more than any other Upanishad by the author of the well-known later epitome of the Vedānta doctrine, the Vedānta-sāra.

It is, however, chiefly important as having given rise to one of the most remarkable products of Indian philosophy, the Kārikā of Gauḍapāda. This work consists of more than 200 stanzas divided into four parts, the first of which includes the Māṇḍūkya Upanishad. The esteem in which the Kārikā was held is indicated by the fact that its parts are reckoned as four Upanishads. There is much probability in the assumption that its author is identical with Gauḍapāda, the teacher of Govinda, whose pupil was the great Vedāntist commentator, Çankara (800 A.D.). The point of view of the latter is the same essentially as that of the author of the Kārikā, and many of the thoughts and figures which begin to appear in the earlier work are in common use in Çankara’s commentaries. Çankara may, in fact, be said to have reduced the doctrines of Gauḍapāda to a system, as did Plato those of Parmenides. Indeed, the two leading ideas which pervade the Indian poem, viz., that there is no duality (advaita) and no becoming (ajāti), are, as Professor Deussen points out, identical with those of the Greek philosopher.

The first part of the Kārikā is practically a metrical paraphrase of the Māṇḍūkya Upanishad. Peculiar to it is the statement that the world is not an illusion or a development in any sense, but the very nature or essence (svabhāva) of Brahma, just as the rays, which are all the same (i.e. light), are not different from the sun. The remainder of the poem is independent of the Upanishad and goes far beyond its doctrines. The second part has the special title of Vaitathya or the “Falseness” of the doctrine of reality. Just as a rope is in the dark mistaken for a snake, so the Ātman in the darkness of ignorance is mistaken for the world. Every attempt to imagine the Ātman under empirical forms is futile, for every one’s idea of it is dependent on his experience of the world.

The third part is entitled Advaita, “Non-duality.” The identity of the Supreme Soul (Ātman) with the individual soul (jīva) is illustrated by comparison with space, and that part of it which is contained in a jar. Arguing against the theory of genesis and plurality, the poet lays down the axiom that nothing can become different from its own nature. The production of the existent (sato janma) is impossible, for that would be produced which already exists. The production of the non-existent (asato janma) is also impossible, for the non-existent is never produced, any more than the son of a barren woman. The last part is entitled Alāta-çānti, or “Extinction of the firebrand (circle),” so called from an ingenious comparison made to explain how plurality and genesis seem to exist in the world. If a stick which is glowing at one end is waved about, fiery lines or circles are produced without anything being added to or issuing from the single burning point. The fiery line or circle exists only in the consciousness (vijnāna). So, too, the many phenomena of the world are merely the vibrations of the consciousness, which is one.