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Volume Article Contents. Oxford Academic. Google Scholar. Cite Citation. Permissions Icon Permissions. Abstract A growing movement courts fear of contemporary popularized forms of modern yoga, warning that yoga is essentially Hindu. Google Preview.

November Comments presented at the annual meeting for the North American Hindu Association of Dharma Studies in conjunction with the annual meeting of the American Academy of Religion. Church of the Holy Trinity v. Congregation for the Doctrine of the Faith. HTM Accessed on May 1, D Magazine. Available at www. Search ADS. Hindu American Foundation. Is Downward Dog the Path to Hell? October 4. Office of the Federal Register.

June Was Hinduism Invented? Britons, Indians, and the Colonial Construction of Religion. The Pew Forum. Praise Moves. December 7. April 2. April December 3. February 6. The Paranormal Pastor, posted on July 1. Van Gennep. A perusal of recent articles in popular yoga publications, such as Yoga Journal , provides evidence that many contemporary practitioners of postural yoga colloquially self-identify as yogis.

In South Asian yoga traditions, the term was not in use until the twelfth- to thirteenth-century emergence of the Nath Yogi tradition. Focusing on English-speaking milieus beginning in the s, de Michelis categorizes modern yoga into three types. Modern Postural Yoga stresses physical exercises, and Modern Meditational Yoga stresses concentration and meditation : These types express little concern for religious and philosophical interpretations of yoga, and instead they often stress that such aspects depend on individual experience rather than doctrinal deliberation de Michelis : — The third type, Modern Denominational Yoga, includes systems that do express concern for religious and philosophical doctrine de Michelis : In this article, I am primarily concerned about postural yoga.

Though some postural yoga teachers combine their teachings on posture and breathing with teachings on the Yoga Sutras , tantra, meditation, and various other aspects of Indian and non-Indian religions, in most postural yoga classes—for example, a postural yoga class at a local university or YMCA—the emphasis remains almost exclusively on posture and breathing.

Scholarly discourse on the question of whether yoga is, in fact, Hindu is not new, as was evidenced by the several papers that addressed this question at the Annual Meeting of the American Academy of Religion. Smith's paper discussed the interplay between the Patanjala Yoga of the Yoga Sutras , Vedanta, and South Asian local practices, suggesting that locally constituted yoga traditions were distinct from textual traditions Mark Singleton's paper pointed out that nineteenth- and twentieth-century transnational constructions of postural yoga are modern reformulations of yoga Most notably, Edwin Bryant argued that yoga cannot be said to be Hindu even from the perspective of the Yoga Sutras , since that tradition requires the practitioner to move beyond identifications of the self with notions tied to the mind—body complex, which includes religious identity.

Christopher Key Chapple suggested that the South Asian yoga traditions betray philosophical underpinnings of pluralism and so cannot be limited by a Hindu definition. This is premised on a narrow vision of religion that defines it in terms of belief. That vision has been privileged among Protestants and Catholics since the seventeenth century Wilfred Cantwell Smith The implication is that a person cannot rationally adopt two religions at the same time because that would require commitment to two different and incompatible belief systems.

Although many contemporary postural yogis assume that their discipline can be traced to a single South Asian lineage going back thousands of years, they represent a variety of yoga systems, and that variety is represented in popular yoga publications, such as Yoga Journal , and in umbrella organizations and conferences, such as Yoga Alliance. Even the most popular postural yoga systems today, most significantly Bikram Yoga, Iyengar Yoga, and Vinyasa, represent different brands that vary dramatically with regard to what they signify for consumers Jain a ; forthcoming.

Furthermore, Singleton points out the absence of any direct lineage between the South Asian precolonial yoga traditions and modern yoga as posture practice : 29— Iyengar Yoga affiliated its form of postural yoga with the yoga tradition presented in the Yoga Sutras , usually attributed to Patanjali, by introducing an invocation to Patanjali at the beginning of each yoga class. Iyengar b. On the reasons Iyengar would link Iyengar Yoga to an ancient yoga lineage, see also Jain forthcoming.

The term fundamentalism dates to the early twentieth century, when the Bible Institute of Los Angeles published a series of booklets called The Fundamentals —15 , which were the impetus for a movement that came to be known as fundamentalism. The term fundamentalist was eventually more broadly applied to institutions or individuals from any religion who seek to return to what they perceive as the unchanging essence of their religions on fundamentalisms, see Marty and Appleby — In the colonial period, orientalism served to legitimate colonial rule by bifurcating the world into the Orient and the Occident.

The Orient and the Occident were defined in terms of perceived essences, and thus each was perceived as a homogenous, static system. Though this article focuses on popular discourse, the critical study of yoga is also threatened by essentialist definitions of yoga. In ways similar to how scholars since the nineteenth century have largely neglected tantra and the narrative and practical traditions of the yogi because of biases in favor of analytical texts, especially the Yoga Sutras , and against what were perceived as degenerate religious forms, such as tantra see Brooks : , note 8; Samuel : 15—16; White : xii—xiii , some contemporary scholars are biased against postural yoga.

Postural yoga is sometimes treated as a mere accretion or commodification that distracts from the purity of the true or original yoga tradition. United States Some contemporary Christians publicly rebuke such attempts, arguing instead that the universal psychological and physical benefits of yoga can be separated from the Hindu, Buddhist, Jain, or other doctrine-specific expressions and then reconstructed as an essential component of the Christian life. They also draw me closer to Christ. Kyria was a Christian digital magazine and web site for women. It was published by Christianity Today , which also publishes the print magazine Today's Christian Woman.

In August , Kyria merged with Today's Christian Woman , which is now a digital magazine and web site as well as a print magazine. The Christian Coalition of America is an evangelical Christian organization that is politically influential on both national and local levels. And people liked to dress up in their best clothes and go there on Sundays and they praised the Lord and it was good. But it came to pass that people grew tired of the Church and they stopped going, and began to be uplifted by new things such as yoga and t'ai chi instead.

We have nothing to do with it here, because its practices are very difficult and cannot be learnt in a day, and, after all, do not lead to much spiritual growth. Many of these practices—such as placing the body in different postures—you will find in the teachings of Delsarte and others. The object in these is physical, not spiritual.

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In , there was a transnational public outcry in response to Choudhury and the BYCI's attempts to enforce copyrights. Bikram Choudhury case No. She points out that, despite settlements out of court, the two cases took almost three years to resolve, from to Fish : , note In , however, the U.

Neither Choudhury and the BYCI nor any other individual or organization could copyright yoga postures or their sequences. These components advocate certain restraints and observances, physical discipline, breath regulations, restraining the sense organs, contemplation, meditation and samadhi. These steps are believed to have a potential for improvement of physical health by enhancing circulation of oxygenated blood in the body, retraining the sense organs thereby inducing tranquility and serenity of mind.

To make sense of such a historical complex and varied phenomenon as yoga, it is, however, essential to retain as much awareness as possible of the social environment and historical specificity of each specific context within which it was adopted and transformed. Examples of this type of Orientalist scholarship include H. Reform movements, including the Brahmo Samaj, the Arya Samaj, and the Ramakrishna Mission founded by Vivekananda , sought to correct the gap between rationalist Hinduism, which was perceived to restore a great and pure Hinduism of the ancient past, and corrupt, ritualistic Hinduism.

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Attempts by some contemporary Hindus to rigidly define Hindu religious identity have served to justify hostilities between communities and political positions see, for example, the essays in Ludden Much of this excludes South Asian folk and popular religious ideas, narratives, and practices that have existed alongside Buddhist, Jain, Hindu, and Islamic ideas and practices see White : xii—xiii; Brooks : , note 8.

These include religious elements, such as polytheism, ritual, devotion, tantra, and yoga's body practices, that are deemed inferior to so-called rational elements. The edited volume, Invading the Sacred: An Analysis of Hinduism Studies in America , provides a substantive selection of the arguments waged against American scholarship on Indian religions Ramaswamy et al.

The argument for yoga's origins in the Indus Valley Civilization assumes that the Indus Valley Civilization has direct ties to later South Asian religious complexes, an issue that is debated. Positions take four forms based on the perceived cultural interaction between the Indus Valley Civilization and Indo-Europeans. Second, scholars argue that the Indo-Europeans gradually migrated into India and settled among those who lived there.

Third, scholars argue that the Vedic people were indigenous to India. Contemporary scholars debate whether or not archaeological artifacts from the Indus Valley Civilization or textual evidence from the early Vedas are evidence of yoga's origins and resist treating any single textual source on yoga as the yoga urtext. Thomas McEvilley points to other Indus Valley seals and suggests they depict early forms of postures found in much later yoga systems, including modern postural yoga, specifically the utkatasana Gheranda Samhita II.

The links between the Indus Valley Civilization and yoga, however, are highly speculative. Doris Srinivasan reviews the artifacts cited for the existence of proto-Shiva forms—most significantly certain characteristics of the Pashupati Seal the most widely cited characteristics are the headdress, the posture, the multiple faces, and the presence of animals; Srinivasan : 78—83 —and concludes that there is nothing that conclusively shows that the seal depicts a proto-Shiva figure. More broadly, yoga refers to wartime itself White : 3.

For example, Haribhadra, in his Yogadrishtisamuccaya , appears to have considerably drawn from Patanjala Yoga, Buddhist sources, and tantric sources in setting forth an eightfold yoga path Dixit ; Chapple Rather, postural yoga functions as a time for the practitioner to undergo psychological and physical healing and transformation through reducing stress and improving physical fitness. According to the Yoga Sutras , for example, the key method for attaining release from suffering is meditation whereby one realizes the self as pure consciousness, distinct from the mind—body complex Larson In the Yoga Sutras , yoga also refers to techniques for transferring the practitioner's consciousness into another body White : 8— In the Nath yoga tradition, on the other hand, hatha yoga methods are used for the transmutation of the subtle and physical bodies in order to acquire bodily immortality, sexual pleasure, and supernatural and sociopolitical powers White , Though postural yoga shares with premodern yoga an emphasis on training and controlling the mind—body complex, it has been repurposed for the sake of modern conceptions of health, beauty, and well-being Alter ; de Michelis ; Strauss ; Newcombe ; Singleton Prior to the twentieth century, posture practice was not central to any yoga tradition see Alter ; de Michelis ; Singleton In nineteenth-century India, the tantric manipulation of the subtle body began to be elided from popular yoga practice because of the negative view of tantra and hatha yoga among Orientalist scholars and Hindu reformers Singleton : 41— Unsurprisingly, the yoga systems that underwent the greatest degree of popularization were those postural varieties that elided tantric elements completely, such as Iyengar Yoga and Bikram Yoga.

Though hatha yoga is the traditional source of postural yoga, equating them does not account for the historical sources, which include British military calisthenics Sjoman , modern medicine Alter , and the physical culture of European gymnasts, body-builders, martial experts, and contortionists Singleton All of these influenced figures responsible for constructing postural yoga, including Tirumalai Krishnamacharya — and, in turn, his three most influential students—Iyengar, K.

Pattabhi Jois — , and T. Desikachar b. Such an equation would also fail to account for the variety of methods and aims that hatha yoga systems themselves have embraced since their emergence in the tenth to eleventh centuries that are usually not present in postural yoga. Their presence is explained by Singleton's argument that nineteenth- and twentieth-century constructors of postural yoga wanted to prescribe this form of fitness as something that was indigenous to India Singleton and by Jain's suggestion that efforts to tie certain yoga brands to an ancient lineage served to elaborate those brands forthcoming.

Furthermore, the aims of postural yoga do not reflect the soteriological systems of premodern Hindu traditions, including the use of the body as a means to a nondualist enlightenment experience as found in many tantric traditions. Rather, postural yoga's aims include modern conceptions of self-development. Scholars, however, agree that this dichotomy is based on a mistaken historical understanding.

Yoga, for example, was a term used in some sections of the Mahabharata to refer to a dying warrior's attempts to transfer himself to the sun White : 7. Groothuis, on the other hand, conflates postural yoga with the yoga of Vivekananda even though Vivekananda boldly disavowed those body techniques and aims that became central to postural yoga.

All rights reserved. For permissions, please e-mail: journals. Issue Section:. Download all figures. View Metrics. Email alerts New issue alert. Advance article alerts. Article activity alert. As things stand thus, accept my intercession for the prince, my benefactor, and pardon him. Thy wish is granted to thee. Thy master has already received what is due to him. The latter had been for- nasty, and tunate, in so far as he had found by accident hidden Brahman treasures, which gave him much influence and power.

In consequence, the last king of this Tibetan house, after it had held the royal power for so long a period, let it by degrees slip from his hands. Besides, Laga- turman had bad manners and a worse behaviour, ou account of which people complained of him greatly to the Vazir. Now the Vazir put him in chains and imprisoned him for correction, but then he himself found ruling sweet, his riches enabled him to carry out his plans, and so he occupied the royal throne.

The latter was killed A. This Hindu Shahiya dynasty is now extinct, and of the whole house there is no longer the slightest, rem- nant in existence. We must say that, in all their grandeur, they never slackened in the ardent desire of doing that which is good and right, that they were men of noble sentiment and noble bearing. If you wish, I shall come to you with horsemen, 10, OCX foot-soldiers, and elephants, or, if you wish, I shall send you my son with double the number.

In acting thus, I do not speculate on the impression which this will make on you. Therefore each planet makes within a kalpa a certain number of complete revolutions or cycles. These star-cycles as known through the canon of Thetradi- Alfazari and Ya'kub Ibn Tarik, were derived from cl zdri and Hindu who came to Bagdad as a member of the politi- " cal mission which Sindh sent to the Khalif Almansur, A. If we compare these secondary statements with the primary statements of the Hindus, we discover discrepancies, the cause of which is not known to me. Is their origin due to the translation of Alfazail and Ya'kub?

For, certainly, any scholar who becomes aware of mistakes in astronomical computations and takes an interest in the subject, will endeavour to correct them, Muhammad as, e. Muhammad Ibn Ishak of Sarakhs has done. Then he added to the cycles of Saturn one cycle more, and compared his calculation with the actual motion of the planet, till at last he found the calculation of the cycles completely to agree with astronomical observa- tion. In accordance with this correction he states the star-cycles in his canon.

Aryabhata Brahmagupta relates a different theory regarding the cycles of the apsides and nodes of the moon, on the authority of Aryabhata. The planets. Number of their revolutions in a Kalpa. Number of the revolutions of their apsides. Number of the re- volutions of their nodes. Sun Bralimagupta. See the notes. Mars 2,,, Mercury 17,,, Jupiter.

Likewise, if we divide the cycles of the table by 10,, the quotient is the number of the star-cycles in a haliyuga, for this is one-tenth of a caturyuga. The fractions which may occur in those quotients are raised to wholes, to caturyugas or kaliyugccs, by being multi- plied by a number equal to the denominator of the fraction. The following table represents the star-cycles speci- ally in a caturyuga and kaliyuga, not those in a man- vantara.

Although the manvantarccs are nothing but multiplications of whole caturyugas, still it is difhcult to reckon with them on account of the sarhdhi which is attached both to the beginning and to the end of them. The names of the planets. Their revolutions in a Caturyuga. Their revolutions in a Kaliyuga. Sun 4,, , , His apsis Star-cycUs of a kalpa and catur- yuga, ac- cording to Pulisa. Tlie names of the planets. Their revolutions ill a Caturyuga.

Venus 7,, , These numbers are contained in the following table : — Tlie Yugas according to Pulisa. The names of the pl. Number of their revolu- tions in a Caturyuga.

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Number of their revolutions in a Kalpa of Caturyugas, Number of their revolutions in a Kalpa of Caturyugas. Her apsis. Her node. They apparently did not understand him properly, and imagined that dryahhata Arab, drjabhad meant a thousandth part. The Hindus pronounce the d of this word something between a d and an r. So the consonant became changed to an r, and people wrote drjabhar. Afterwards it was still more mutilated, the first r being changed to a z, and so people wrote dzja- hhar.

If the word in this garb wanders back to the Hindus, they will not recognise it. I shall represent them in the table such as I have found them, for I guess that they are directly derived from the dictation of that Hindu. Possibly, therefore, they give us the theory of Aryabhata. Some of these numbers agree with the star-cycles in a catur- yuga, which we have mentioned on the authority of Brahmagupta ; others differ from them, and agree with the theory of Pulisa ; and a third class of numbers differs from those of both Brahmagupta and Pulisa, as the examination of the whole table will show.

The names of the X lauets. The Hindus call the year in which a month is repeated in the common language malamdsa. Mala means the dirt that clings to the hand. As such dirt is thrown away, thus the leap month is thrown away out of the calculation, and the number of the months of a year remains twelve. However, in the literature the leap month is called adhimdsa. That month is repeated within which it being con- sidered as a solar month two lunar months finish.

If the end of the lunar month coincides with the beginning of the solar month, if, in fact, the former ends before any part of the latter has elapsed, this month is re- peated, because the end of the lunar month, although CHAPTER LI. If a month is repeated, the first time it has its ordinary name, whilst the second time they add before the name the word durd to distinguish between them. If, e. The first month is that which is disregarded in the calculation.

The Hin- dus consider it as unlucky, and do not celebrate any of the festivals in it which they celebrate in the other months. The most unlucky time in this month is that day on which the lunation reaches its end. Saura is greater than candra by eleven days, which gives in two years and seven months the supernumerary adkimdsa month.

This whole month is unlucky, and nothing must be done in it.

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We shall now describe it accurately. Tiiis difference sums up to the thirty days of an adhimdsa in the course of V7W lunar days, i. As the religious reason of this theory of intercala- Quotation tion the Hindus mention a passage of the Veda, which redo. For a month has thirty- lunar days, and a twelfth part of the solar year has 3o? It may even happen that the sun enters two consecutive signs on the same month-day e. Therefore the quotation from the Veda is not correct. Proposed I suDpose, liowevcr, that it may have the following explanation r r?

The reason is that the month misses just that moment which is particularly adapted to earn in it a heavenly reward, viz. In the books of Ya'kub Ibu Tarik and of Alfazaii this name is written padamdsa. Pada in the orig. P-Dh means end, and it is possible that the Hindus call the leap month by both names ; but the reader must be aware that these two authors frequently misspell or disfigure the Indian words, and that there is no reliance on their tradition.

I only mention this because Pulisa explains the latter of the two months, which are called by the same name, as the supernumerary one. The month, as the time from one conjunction to the Explanation following, is one revolution of the moon, -which revolves universal or through the ecliptic, but in a course distant from that STonths and of the sun.

This is the difierence between the motions of the two heavenly luminaries, whilst the direction in which they move is the same. If -w-e subtract the revolutions of the sun, i. All months or days which reckon as parts of whole kalpas we call here universal, and all months or days wliich we reckon as parts of a part of a kalpa, e. The lunar year is complete with mouths, twelve months, -whilst the solar year, in consequence of the difference of the two year kinds, has, with the addition of the adhimdsa, thirteen months. How many solar, lunar, and civil days are re- quired for the forma- tion of an adJiimoia niontb.

The compu- tation of adhimdsa according to Pulisa. These, therefore, are the universal adhimdsa months. Multiplying each of these numbers by 30, we get days, viz. In order to reduce these numbers to smaller ones we divide them by a common divisor, viz. Thus we get as the sum of the days of the solar months ,; as the sum of the days of the lunar months, ,; and as the sum of the days of the adhimdsa months, If we further divide the universal solar, civil, and lunar days of a halpa, each kind of them separately, by the universal adhimdsa months, the quotient represents the number of days within which a whole adhimdsa month sums up, viz.

This whole computation rests on the measures which Brahmagupta adopts regarding a halpa and the star- cycles in a halpa. According to the theory of Pulisa regarding the caturyuga, a caturyuga has 51,, solar months, 53,, lunar months, 1,, adhimdsa months. Accordingly a caturyuga has 1, If we reduce the numbers of the months by the common divisor of 24, we get 2, If we, lastly, divide the universal solar, lunar, and civil days of a caturyuga, each kind separately, by the uni- versal adhimdsa months of a caturyuga, the quotient represents the numbers of days within which a whole adhimdsa month sums up, viz.

These are the elements of the computation of the adhimdsa, which we have worked out for the benefit of the following investigations. Eegarding the cause which necessitates the 'Anardtra, lit. O If we have one year or a certain number of years, and reckon for each of them twelve months, we get the corresponding number of solar months, and by multi- plying the latter by 30, the corresponding number of solar days. It is evident that the number of the lunar months or days of the same period is the same, phis an increase w'hich forms one or several adhimdsa months.

If we reduce this increase to adhiundsa months due to the period of time in question, according to the relation between the universal solar months and the universal adhimdsa months, and add this to the months or days of the years in question, the sum represents the partial lunar days, i. This, however, is not what is wanted. Therefore, in order to find that which is sought, we must subtract some- thing from the number of lunar days, and this element which must be subtracted is called 'dnardtra.

Computa- tion of the Unardtra according to Pulisa. Cii'icisms on Ya'kub Ibu Tarik. The universal lunar days of a kalpa are 1,,,, This number is larger than the number of universal civil days by 25,,,, which represents the uni- versal xinaratva. Both these numbers may be diminished by the com- mon divisor of , Thus we get 3,, uni- versal lunar days, and 55, universal xinardtra days.

According to Pulisa, a caturyuga has 1,,, lunar days, and 25,, unardtra days. The com- mon divisor by which both numbers may be reduced is Thus we get 4,, lunar days and 69, unardtra days. The word means sum of days ; for dll means day, and argana, sum. Ya'kub Ibn Tarik has made a mistake in the compu- tation of the solar days ; for he maintains that you get them by subtracting the solar cycles of a kalpa from the civil days of a kalpa, i.

But this is not the case. We get the solar days by multiplying the solar cycles of a kalpa by 12, in order to reduce them to months, and the product by 30, in order to reduce them to days, or by multiplying the number of cycles by In the computation of the lunar days he has first taken the right course, multiplying the lunar months of a kalpa by 30, but afterwards he again falls into a mistake in the computation of the days of the 'dnardtra. For he maintains that you get them by subtracting the solar days from the lunar days, wdiilst the correct thing is to subtract the civil days from the lunar days.

The general method of resolution is as follows : — The complete years are multiplied by 12; to the product are added the mouths which have elapsed of the current year, [and this sum is multiplied by 30 ;] to this product are added the days which have elapsed of the current month. The sum represents the saurdliargana, i. You write down the number in two places.

In the one place you multiply it by , i. The product you divide by ,, i. The quotient you get, as far as it contains complete days, is added to the number in the second 'place, and the sum represents the candrdliargana, i. The latter number is again written down in two different places. In the one place you multiply it by 55,, i. Tile quotient you get, as far as it represents complete days, is subtracted from the number written in the second place, and the remainder is the sdvandhargana, i.

Morede- However, the reader must know that this computa- tailed rule. If, therefore, a given number of years commences with the beginning of a halpa, or a caturyuga, or a haliyuga, this computation is correct. But if the given years begin with some other time, it may by chance happen that this computation is correct, but possibly, too, it may result in proving the existence of adhiradsa time, and in that case the computation would not be correct.

Also the reverse of these two eventualities may take place. However, if it is known with what particular moment in the Icalpa, caturyuga, or Icaliyuga a given number of years commences, we use a special method of com- putation, which we shall hereafter illustrate by some examples. The latter We shall Carry out this method for the begiu- methnd. First we compute the time from the beginning of the life of Brahman, according to the rules of Brahma- gupta.

We have already mentioned that Icalpas have elapsed before the present one. Multiplying this by the well-known number of the days of a Iccdpa 1,,,, civil days, vide i. Dividing this number by 7, we get 5 as a remainder, and reckoning five days backwards from the Saturday which is the last day of the preceding kalpa, we get Tuesday as the first day of the life of Brahman. We have already mentioned the sum of the days of a caturyuga 1,,, days, v. A manvantara has seventy-one times as much, i. The days of Page If we divide this number by 7, we get a remainder of 2.

Therefore the six manvantaras end with a Monday, and the seventh begins with a Tuesday. Of the seventh manvantara there have already elapsed twenty-seven caturyugas, i. Therefore the twenty-eighth caturyuga begins with a Thursday. The days of the yugas which have elapsed of the present caturyuga are 1,,, The division by 7 gives the remainder i. Therefore the kaliyuga begins with a Friday. Now, returning to our gauge-year, we remark that the years which have elapsed of the kalpa up to that year are 1,,, Multiplying them by 12, we get as the number of their months 23,,, In the date which we have adopted as gauge-year there is no month, but only complete years ; therefore we have nothing to add to this number.

By multiplying this number by 30 we get days, viz. As there are no days in the normal date, we have no days to add to this number. Multiply this number by and divide the pro- duct by , The quotient is the number of the adhimdsa days, viz. If, in multi- plying and dividing, we had used the months, we should have found the adhimdsa months, and, multi- plied by 30, they would be equal to the here-mentioned number of adhimdsa days. If we further add the adhimdsa days to the partial solar days, we get the sum of ,,,, i. Dividing it by 7, we get as remainder 4, which means that the last of these days is a Wednesday.

Therefore the Indian year commences with a Thursday. If we further want to find the adhimdsa time, we divide the adhimdsa days by 30, and the quotient is the number of the adhimdsas which have elapsed, viz. This is the time which has already elapsed of the adhimdsa month of the current year. To become a complete month, it only wants i day, 8 minutes, 30 seconds more. The same We liave here used the solar and lunar days, the applied to a adliividsa and unardtra days, to find a certain past Lcordiifg to portion of a halpa.

The former term means a mxdtiplicator in all kinds of calculations. In our Arabic astronomical hand- books, as well as those of the Persians, the word occurs in the form guncdr. The second term means each divisor. It occurs in the astronomical handbooks in the form bahcdr. We should only have to shorten the above-mentioned numbers by three ciphers, and in every other respect get the same results. Therefore we shall now give this computation according to the theory of Pulisa, which, though applying to the caturyuga, is similar to the method of computation used for a Icalpa.

According to Pulisa, in the moment of the beginning of the gauge-year, there have elapsed of the years of the cattiryuga 3,,, which are equal to 1,,, solar days. Further, the past 3,, years of the caturyuga are 1,,, liyiar days. We multiply this number by the number of the caturyugas of a kalpa, i. Thus we get the product 6,, These are the years which have elapsed before the present kalpa.

We further multiply the latter number by 12, so as to get months, viz. We write down this number in two different places. In the one place, we multiply it by the number of the adhimdsa months of a caturyuga, i. The quotient is the number of adhimdsa months, viz. Multiplying this number by 30, we get the product 9,,,,,, viz. This number is again written down in two different places.

In the one place we multiply it by the 'dnardtra of a caturyuga, i. Thus we get as quotient 1 53,,,,, i. Unardtra days. We subtract this number from that one written in the second place, and we get as remainder 9,,,,,, i. Dividing this sum of days by 7, we get no remainder. This period of time ends with a Saturday, and the present kalpa commences with a Sunday. This shows that the beginning of the life of Brahman too was a Sunday.

Of the current kalpa there have elapsed six manvan- Page2i9. Therefore six manvantaras have 1.

Thereby we find as the number of days of six complete manvantaras, ,,, Dividing this number by 7, we get as remainder 6. Therefore the elapsed manvantaras end with a Friday, and the seventh man- vantara begins with a Saturday. Of the current manvantara there have elapsed 27 caturyugas, which, according to the preceding method of computation, represent the number of 42,,, days. The twenty-seventh caturyuga ends with a Monday, and the twenty-eighth begins with a Tues- day. Of the current caturyuga there have elapsed three yugas, or 3,, years.

These represent, according to the preceding method of computation, the number of 1,,, days. Accordingly, the sum of days which have elapsed of the hal'pa is ,,,, and the sum of days which have elapsed between the beginning of the life of Brahman and the beginning of the present kaliyuga is 9,,,,, To judge from the quotations from Aryabhata, as we The method have not seen a book of his, he seems to reckon in the following manner : — The sum of days of a caturyuga is 1,,, The time between the beginning of the kalpa and the beginning of the kaliyuga is ,,, days.

The time between the beginning of the kalpa and our gauge-date is ,,, The number of days which have elapsed of the life of Brahman before the present kalpa is 9,65 1,,,, This is the correct method for the resolution of years into days, and all other measures of time are to be treated in accordance with this.

We have already pointed out on p. The ahar- gana as given by Ya'kilb Ibu Tdrik. A second method given by Ya'kiib. As he translated from the Indian language a calculation the reasons of which he did not understand, it would have been his duty to examine it, and to check the various numbers of it one by the other. He mentions in his book also the method of aliargana, i.

Divide the product by the solar months. The quotient is tlie number of complete adhimdsa months plus its fractions which have elapsed up to the date in question. The quotient is the number of adhimdsa months toge- ther with the number of the months of the years in question.

The sum represents the lunar days. As, now, the lunar months are the sum of solar and adhimdsa months, we multiply by them the lunar months and the division remains the same. The quo- tient is the sum of that number which is multiplied and that one wliich is sought for, i. However, the civil days in a Tcalpa are less than the lunar days by the amount of the unardtra days. Now the lunar days we have stand in the same relation to the lunar days minus their due portion of 'dnardtra days as the whole number of lunar days of a halpd to the whole number of lunar days of a kalpa minus the complete number of 'dnardtra days of a kalpa ; and the latter number are the universal civil days.

If we, therefore, multiply the number of lunar days we have by the universal civil days, and divide the product by the universal lunar days, we get as quotient the number of civil days of the date in ques- tion, and that it was which we wanted to find. In- stead of multiplying by the whole sum of civil days of a kalpa , we multiply by 3,,, and instead of dividing by the whole number of lunar days of a kalpa , we divide by 3,, The Hindus have still another method of calculation. Explication of the latter methid. The latter method applied to the gauge- year.

The double of the remainder they divide by Then the quotient represents the partial adhimdsa months. This number they add to that one which is written down in the uppermost place. They multiply the sum by 30, and add to the product the days which have elapsed of the current month. The sum represents the partial solar days. This number is written down in two different places, one under the other. They multiply the lower number by ii, and write the product under it. Then they divide it by ,, and add the quotient to the middle number.

This number they subtract from the number written in the uppermost place, and the remainder is the number of civil days which we want to find. If we divide by this number the double of the months of the given years, the quotient is the number of the partial adhimdsas. How- ever, if we divide by wholes plus a fraction, and want to subtract from the number which is divided a certain portion, the remainder being divided by the wholes only, and the two subtracted portions being equal por- tions of the wholes to which they belong, the whole divisor stands in the same relation to its fraction as the divided number to the subtracted portion.

If we make this computation for our gauge-year, we get the fraction of y. Thereby we get 89 as the multiplicator, and as the divisor. In this the inventor of the method has shown his sagacity, for the reason for his computation is the intention of getting partial lunar days and smaller multiplicators. Thus we get 63! If we change this fraction into eleventh parts, we get and a remainder of which, if expressed in minutes, is equal to o' 59" 54'".

Therefore, according to the Hindus, one iinardtra day sums up in 63 W lunar days. For if we multiply the universal iinardtra days by , we get the product And if we multiply the universal lunar days by 1 1, we get the product 17,,,, Jfetliod for the compu- tation of the iinardtra days accord- ing to Brahma- gupta. The difference between the two numbers is 43,, If we divide by this number the product of eleven times the universal lunar days, we get as quotient , If he uses this divisor without the fraction, and divides by it the product of eleven times the partial lunar days, the quotient would be by so much larger as the dividendum has increased.

The other details of the calculation do not require comment. One of their methods of finding the ad- liimdsa for the years of a kalpa or caturyuga or kaliyuga is this : — They write down the years in three different places. They multiply the upper number by 10, the middle by , and the lower by Then they divide the middle and lower numbers by , and the quotients are days for the middle number and avama for the lower number.

The sum of these two quotients is added to the number in the upper place. The sum represents the number of the complete adhimdsa days which have elapsed, and the sum of that which remains in the other two places is the fraction of the current adlmndsa. Dividing the days by 30, they get months. Ya'kub Ibn Tarik states this method quite correct! The latter We write down this number in three different places, pifedto tL The upper number we multiply by ten, by which it gets a cipher more at the right side.

The middle number we multiply by and get the product 4,,,, The lower number we multiply by Page The latter two numbers we divide by ; thereby we get for the middle number as quotieut ,, and a remainder of , and for the lower number a quo- tient of 1,,, and a remainder of The sum of these two remainders is 17, Thereby the sum of the numbers in all three places is raised to 21,, Eeducing these days to months, we get ,, months and a remainder of twenty-eight days, which is called Sh-D-D.

This is the interval between the beginning of the month Caitra, which is not omitted in the series of months, and the moment of the vernal equinox. Further, adding the quotient which we have got for the middle number to the years of the Tcalpa, we get the sum of 2,,, Dividing this number by 7, we get the remainder 3. Therefore the sun has, in the year in question, entered Aries on a Tuesday. The two numbers which are used as multiplicators Explanatory for the numbers in the middle and lower places are to latter me- be explained in the following manner : — Dividing the civil days of a kalpa by the solar cycles of a halpa, we get as quotient the number of days which compose a year, i.

Simplifica- tion of the same me- thod. Dividing the universal ilnardtra days by the solar years of a Icalpa, the quotient is the number of Unardtra days which belong to a solar year, viz. Deducing this fraction by the common divisor of ,, we get days. The fraction may fur- ther be reduced by being divided by 3. The measures of solar and lunar years are about days, as are also the civil years of sun and moon, the one being a little larger, the other a little shorter. The one of these measures, the lunar year, is used in this computation, whilst the other measure, the solar year, is sought for.

The sum of the two quotients of the middle and lower number is the difference between the two kinds of years. The upper number is multiplied by the sum of the complete days, and the middle and lower numbers are multiplied by each of the two fractions. If we want to abbreviate the computation, and do not, like the Hindus, wish to find the mean motions of sun and moon, we add the two multiplicators of the middle and lower numbers together.

This gives the sum of 10, If we, therefore, want to have the same quotient which we get by the first division, we must divide by of the divisor by which we divided in the first case, viz. In the one place multiply it by nil, and divide the product by 67, Sub- tract the quotient from the number in the other place, and divide the remainder by The quotient is the number of the adhimdsa months, and the fraction in the quotient, if there is one, represents that part of an adhimdsa mouth which is in course of formation.

Mul- tiplying this amount by 30, and dividing the product by 32, the quotient represents the days and day-frac- tions of the current adhimdsa month. If you divide the months by this number, you get the com- plete adhimdsa months of the past portion of the catur- yvga or halya. Therefore he had to subtract something from the dividendum, as has already been explained in a similar case p. We have found, in applying the computation to our gauge- year, as the fraction of the divisor, -s-. Pulisa has, in this calculation, reckoned by the solar days into which a date is resolved, instead of by months.

In the one place you multiply it by from Pulisa. The quo- tient you subtract from the number in the other place and divide the remainder by The quo- tient is the number of adhimdsa months, days, and day-fractions. The common divisor for this number and for the divisor is The matter is this : — Those days which are divided by the adhimdsa months are of necessity solar days. The quotient con- tains wholes and fractions, as has been stated.

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  7. Both denominator and numerator have as common divisor the number A divisor common to both this denominator and its numerator is Eeducing the fraction thereby, we get o-. Vstt- If we now multiply the number which Pulisa adopts as devisor by the just-mentioned common divisor, i. But it is quite impossible that this number should, in this part of the calculation, be used as a divisor. If we want to base this method on the rules of Brahmagupta, dividing the universal solar months by the adhimdsa months, the result will be, according to the method employed by him, double the amount of the adhimdsa.

    Purther, a similar method may be used for the com- putation of the 'dnardtra days. Write down the partial lunar days in two different places. In the one place, multiply the number by 50,, and divide the product by 3,, Sub- tract the quotient from the number in the other -place, and divide the remainder by 63 without any fraction. In the further very lengthy speculations of the Page If we want to find the years, the days being given, the latter must necessarily be civil days, i. If we multiply the given days by 55,, and divide the product by 3,,, the quotient repre- sents the partial unardtra days.

    Adding hereto the civil days, we get the number of lunar days, viz. These lunar days stand in the same relation to the adhimdsa days which belong to them as the sum of the uni- versal solar and adhimdsa days, viz. If you, further, multiply the partial lunar days by , and divide the product by ,, the quotient is the number of the partial adhimdsa days.

    Subtract- ing them from the lunar days, the remainder is the number of solar days. Thereupon you reduce the days to months by dividing them by 30, and the months to years by dividing them by 1 2. This is what we want to find. AppUcation our gauTC-vear are ,,, This number is othegauge- giveii, aud wliat we want to find is, how many Indian years aud months are equal to this sum of days. The quotient is 1 1,45 5,, Unardtra days.

    We add this number to the civil days. The sum is ,,, lunar days. We multiply them by , and divide the product by ,1 1 1. The quotient is the number of adhimdsa days, viz.


    We subtract them from the lunar days and get the remainder of ,,,, i. We divide these by 30 and get the quotient of 23,,,, i. Dividing them by 12, we get Indian years, viz. Write down the quotient in two different places. The quotient gives the adhimdsa months. The remainder is the number of partial solar days. You further reduce them to months and years. These two measures stand in a constant relation to each other. Therefore we get the partial lunar days which are marked in two difterent places. Now, these are equal to the sum of the solar P;ige Therefore the partial and the universal adhimdsa days stand in the same relation to each other as the two numbers written in two different places, there being no difference, whether they both mean months or days.

    The quotient is added to the adhimdsa. The sum is the number of the past idnardtras. Multiplying this number by the unardtra of the caturyuga. Adding this to the adhimdsa, we get the sum 1,, And this is not what we wanted to find. On the contrary, the number of 'dnardtra days is 18,, Nor is the product of the multiplication of this number by 30 that which we wanted to find.

    On the contrary, it is 53,,