As I discuss in this question, by far the most popular school of Hindu philosophy is the Vedanta school, which bases its tenets on the doctrines laid out in the Brahma Sutras, a work by the sage Vyasa which summarizes and systematizes the philosophical teachings of the Upanishads. (You can read the Brahma Sutras here.) But the Vedanta school didn't always have the dominant position in Hindu philosophy; before the time of Adi Shankaracharya the dominant school of Hindu philosophy was the Purva Mimamsa school, which I discuss here. In contrast to the Vedanta school which is devoted to analyzing the Jnana Kanda of the Vedas, i.e. the Upanishads, Purva Mimamsa focuses on analyzing the Karma Kanda of the Vedas, i.e. the Samhitas and Brahmanas.
Now in this excerpt from Jaimini's Purva Mimamsa Sutras, the defining text of the Pyrva Mimamsa school, Jaimini discusses the question of whether Sanskrit words used in the Vedas have the same meaning that they have in ordinary usage, or whether they mean something entirely different. The Purvapakshin or opponent makes the argument that they have a completely different meaning, because the Vedas speak of the cows of the gods walking on their backs, whereas the word "cow" in ordinary usage refers to an animal that walks on its feet:
Further we meet with the statement that 'Uttana vai devagava vahanti' (Apastamba-Shrauta Sutra 11.7.6) which means 'that cows that belong to the deities move on their backs'; and from this it follows that the animals spoken of by the word 'go' (in 'gava') are those that walk on their backs; and thus it is clear that the word 'gauh' in the Veda is different from that spoken of by that word in common parlance.
Jaimini refutes this by saying that this quote is an Arthavada. For those who don't know, the Purva Mimamsa school believed that the Vedas consist primarily of two kinds of statements, Vidhis or injunctions concerning Dharma, and Arthavadas or statements that were just intended to glorify the actions prescribed in the Vedas. The Purva Mimamsa school even classified the Upanishads' statements about Brahman as Arthavada, as I discuss here and here. So Jaimini thinks that the statement about cows of the gods were just intended to glorify some action, perhaps Yagnas done in honor of the gods.
But my question is, what is the original source of this quote about the cows of the gods walking on their backs?
As you can see, the translator attributes the quote to Apastamba Shrauta Sutras, but I think it must have originally come from somewhere in the Vedas, for multiple reasons. First of all Shrauta Sutras are a type of Kalpa Sutra, and in another excerpt from the Purva Mimamsa Sutras Jaimini states in no uncertain terms that he does not consider Kalpa Sutras to be a scriptural authority. And given that Jaimini analyzes the quote in the Vidhi and Arthavada framework, he must consider it as a scriptural authority. And more importantly, the entire subject under discussion is the meaning of words in the Vedas, so it wouldn't make sense to discuss a quote that's not in the Vedas.
On a side note, I should add that this excerpt from the Tantra Vartika, one of Kumarila Bhatta's commentaries on the Purva Mimamsa Sutras, gives an alternative interpretation of the quote, namely that it refers to how as the Earth makes its revolution, sometimes it appears to the residents of Devaloka like the cows that are on Earth are upside down:
Or, the passage [of the Purva Mimamsa Sutras] may refer to the fact that it is the ordinary cows of the Earth that are referred to in this [Vedic] passage, as as appearing to walk on their backs, owing to the revolutions of the Earth together with all the three worlds, as described in the Puranas. That is to say, just as we see the gods above us, so too, when in the course of revolution the Earth reaches a point above the abode of the gods, they see the things on the Earth as above them; hence it is only natural that to them the cows walking on the Earth should appear to be walking on their backs.
Kumarila Bhatta, by the way, was the guru of Mandana Mishra, the Purva Mimamsaka whom Adi Shankaracharya defeated in a debates as I discuss here. And apparently he's considered by some to be an incarnation of Shiva's son Kartikeya, aka Skanda or Muruga.
