The upasthāna ritual is performed to let the sacrificial fire remain in residence after the primary oblations are complete. In the triple-fire śrauta rite this is done at the āhavanīya altar with several incantations specified in the saṃhitā-s of the Yajurveda, e.g. Taittirīya-Saṃhitā 1.5.5. Among those incantations the following is recited:
indhānās tvā śataṃ himā dyumantaḥ samidhīmahi ।
vayasvanto vasyaskṛtaṃ yaśasvanto yaśaskṛtaṃ ॥
suvīrāso adābhyam agne sapatna-dambhanaṃ varṣiṣṭhe adhi nāke ॥
Kindling you, may we kindle [you] in luster through a hundred snows [winters].
The strong one the maker of strength, the famous one the maker of fame.
With good heroes, the undeceived, O Agni, the deceiver of foes in the highest heaven.
The Taittirīya-Saṃhitā furnishes the following brāhmaṇa passage for the above mantra-s (In TS 1.5.7):
indhānās tvā śataṃ himā ity āha । śatāyuḥ puruṣaḥ śatendriya āyuṣyevendriye prati tiṣṭhati । eṣā vai sūrmī karṇakāvatī । etayā ha sma vai devā asurāṇāṃ śatatarhāṃ stṛṃhanti । yad etayā samidham ā dadhāti vajram evaitac chataghīṃ yajamāno bhrātṛvyāya pra harati stṛtyā achaṃbaṭkāram ।
He recites: “may we kindle [you] through a hundred snows [winters]”. He lives a hundred years and has a hundred senses. Verily he is stable in life and senses. This is a red-hot tube with cutting edges. By this indeed the deva-s have struck hundreds of piercings on the asura-s. When he takes up the fire-stick with this [incantation], the ritualist hurls the śataghnī like the vajra for his enemy’s overthrow without fail.
The text is notable in being, what to our knowledge, the earliest mention and description of the weapon frequently encountered in the itihāsa-s and purāṇa-s and also found in the Arthaśāstra of Viṣṇugupta Cāṇakya. The weapon is described as being a sūrmī, which tradition holds to be a red-hot hollow cylinder. It is described as being karṇakāvati, i.e. with prongs or cutting edges. As its name goes, śataghnī, and from the description of the attack by the deva-s on the asura-s in this brāhmaṇa, it is clear that it was intended to be a weapon of “mass destruction”. Thus, it is reminiscent of what the braḥmaṇa-s are described as having deployed on the Egyptian Herakles by Flavius Philostratus in his biography of Apollonius of Tyna. It is in this context that he says that if Alexander had penetrated beyond the Vipāśā river he might have not been able to take the fort of Indians even if he had 10000 Achilles-es and 30000 Ajax-es with him. Given that the itihāsa-s mention it as being used as a mechanical device for the defense of forts it is likely that it was indeed some form a siege engine of the early Arya-s.
For the same incantation the Maitrāyaṇī-Saṃhitā (in MS 220.127.116.11) gives a rather different explanation:
manor ha vai daśa jāyā āsan । daśaputrā । navaputrā । aṣṭaputrā । saptaputrā । ṣaṭputrā । pañcaputrā । catuṣputrā । triputrā । dviputrā । ekaputrā । ye nava āsan tān eka upasamakrāmat । ye aṣṭau tān dvau । ye sapta tān trayaḥ । ye ṣaṭ tān catvāraḥ । atha vai pañca eva pañca āsan । tā imāḥ pañca । daśata imān pañca nirabhajan । yad eva kiṃ ca manoḥ svam āsīt । tasmāt te vai manum eva upādhāvan । manau anāthanta । tebhya etāḥ samidhaḥ prāyacchat । tābhir vai te tān nirādahan । tābhir enān parābhāvayan । parā pāpmānaṃ bhātṛvyaṃ bhāvayati ya evaṃ vidvān etāḥ samidha ādadhāti ।
Manu indeed had 10 wives. [Respectively,] with 10 sons, with 9 sons, with 8 sons, with 7 sons, with 6 sons, with 5 sons, with 4 sons, with 3 sons, with 2 sons, with 1 son. The 1 son [of the wife with 1] joined with the 9 sons [of the wife with 9]; Those of the she with 2 sons with those of she with 8 sons; 3 sons with 7 sons; 4 sons with 6 sons. The 5 [of she with] 5 remained that. They were just 5. The 10s (i.e. 50) dispossessed these 5. Now Manu had some [possession] of his own. Therefore, those  indeed ran to Manu himself. The sought protection in Manu. He gave each these fire-sticks. With those [fire-sticks] the [5 sons] indeed burnt up those . They defeated those . He who knows this and offers the fire-sticks defeats his evil enemies.
This brāhmaṇa is notable for more than one thing: We know that the Hindus were aware of the formula for the sum of natural numbers from the famous citation of the sage Śākapūṇi in the Bṛhaddevatā regarding the hidden Āgneya ṛk-s associated with the “jātavedase sunavāma…” sūkta (Ṛgveda 1.99). There he gives the sum of 1+2+3…+1000=500500. This brāhmaṇa gives the derivation of the formula for the sum of such a series cryptically and is reminiscent of how Carl Gauss said he computed such a sum as kid. Both brāhmaṇa-s from the two YV saṃhitā-s importantly play on the power of the word śata (100) in the incantation. Once Manu gives his 5 dispossessed sons the samidh-s they are said to have beaten their 50 rival half-brothers. How does this come about? Again it seems to rely on an arithmetic symbolism. When he gave them the samidh-s, as the TS states that samidh makes you śatendriya. Thus, it seems to imply that the 5 become thereby beating their half brothers.
That apart it also provides a clue regarding the origin of the story formula of the Mahābharata. We have remarked several times before that when old history was composed it was poured in the bottles of preexisting myth and thereby took their shape. Thus, when we encounter formulaic numbers like 100 (Kaurava-s) and 5 (Pāṇḍava-s) one is immediately alerted to the use of a preexisting mythic frame. Indeed, such a formula related to the count and the differentiation of the Pāṇḍu-s extends beyond the Indo-Iranian horizon. In the Secret History of the Chingizid Mongols we hear the tale of their legendary ancestress Alan Qo’a bearing 5 sons. Notably, there too 2 of her sons are of different father from the from other 3. A birth through a divine non-human father is implied for 3 of them (all 5 in the case of the Pāṇḍu-s). Further, Alan Qo’a specifically instructs her 5 sons to be united despite their being half-brothers. So there is a hint of the need of unity in face of conflict fraternal conflict. These motifs echo what are seen far away in time and space in the Mahābhārata of the Hindus. Hence, we were curious as to whether we might find earlier echoes of the Mahābhārata story formula in earlier Indo-Āryan tradition. We believe that the above brāhmaṇa is indeed the “essentialized” motif of fraternal conflict featuring the number of 5 against 50 that became 5 versus in the Mahābhārata where the party of 5 prevailed in the end despite being initially dispossessed as in this case.
Now we move on to an entirely different theme from a brāhmaṇa passage from the Kapiṣṭhala-kaṭha-Saṃhita 35.8.
sā eṣā anuṣṭup । tasyāḥ saptākṣaram ekam pādam aṣṭākṣarāṇi trīṇi । teṣāṃ saptānāṃ yāni trīṇi tāny aṣṭāv upayanti । tany ekādaśa । sā triṣṭup । yāni catvāri tāny aṣṭāv upayanti । tāni dvādaśa । sā jagatī । yāny aṣṭau sā gāyatrī ।parā pāpmānaṃ bhātṛvyaṃ bhāvayati ya evaṃ vidvān etāḥ samidha ādadhāti ।
There was this Anuṣṭubh. 1 of its feet had 7 syllables, the [remaining] 3 had 8. Of the [foot] which had 7, 3 of them went to the 8. That made 11. This was the Triṣṭubh. The [remaining] which were 4 [of that foot] went to the 8. That made 12. This was the Jagatī. The [remaining] feet which had 8 [syllables became] the Gāyatrī (Kapiṣṭala-kaṭha-saṃhitā 35.8).
The model being proposed here is something comparable to what we see in evolution of nucleic acid and protein sequences. The original Anuṣṭubh is conceived thus:
There is fission and fusion with deletion shown by :
(1 foot of Triṣṭubh) or
(1 foot of Jagatī)
What remains is:
Of course, no surviving regular Anuṣṭubh from the earliest Vedic tradition has a 7-syllabled final foot. So is this merely a case of brāhmaṇa numerology or does it reflect some early development in prosody? Now the existence of a basic 8-syllabled unit is something mentioned early in Vedic tradition e.g. by Kurusuti Kāṇva:
vācam aṣṭāpadīm ahaṃ navasraktim ṛtaspṛśam ।
indrāt pari tanvam mame ॥ (RV8.076.12)
An eight-[syllable]-footed, nine-cornered utterance, touching Ṛta
I have measured out its body from Indra.
Being a Gāyatrī with 3 feet of syllables each, the ṛk is testimony for what it states. Further, what is the “nonagonal” form of the utterance? The sūkta in question is composed as sets of tṛca-s of Gāyatrī-s. Thus each tṛca has 8-syllabled feet giving us the navasrakti structure the ṛṣi mentions. Thus, we can be sure that 8 was definitely a recognized unit of the foot from early one. Further, the very term pāda as a metrical foot has a Iranian cognate paa used in the same sense. Further, πούς (poús) as used by Aristophanes suggests that this was indeed the originally the Greek cognate of the Vedic pāda. Thus a comparable metric foot was recognized early in Indo-European. By comparing Sanskrit, Avestan and Greek, Martin West proposed that there are reconstructible proto-feet of Indo-European prosody with 8 syllables and other versions of them with 6 and 7 syllables. If this were true then the brāhmaṇa might be recalling or reconstructing an origin mechanism wherein the shortened 7-syllabled element fragments and merges with adjacent 8-syllabled feet to give rise to the Triṣṭubh and Jagatī.
In any case this irregular hypothetical Anuṣṭubh is not the standard Anuṣṭubh of Sanskrit which since the earliest Vedic record came to be of syllables. Indeed, this form of the Anuṣṭubh was the basis of a child’s mathematical problem presented by Bhāskara-II in his Līlāvatīː
samānām ardha-tulyānām viṣamāṇām pṛthak pṛthak ।
vṛttānām vada me saṃkhyām anuṣṭubh-chandasi drutam ॥
Tell me quickly what are the counts of the variations of Anuṣṭubh meter with:
(i) same [configuration of feet]
(ii) half-equivalent [feet]
(iii) dissimilar [feet]
Each syllable can take a short (0) or a long state (1) . If every foot has the same configuration of 0,1 then we only have to look for combinations of one 8-footed element. If it has half-equivalent feet the two syllable configurations are the same. But we have remove all instances where all 4 feet are same for a strict definition. Now if all feet are dissimilar then we have 32 syllables available but we have to remove all those where either all or a pair of feet are the same. Thus we get the answers as:
Interestingly, these numbers make an appearance in modern computing e.g. as in 16-bit and 32 bit computing and the largest 32 bit number.