(4) Then bathe in waters prepared for the purpose; rub over the hairs fragrant oil, thus removing disagreeable scent of mixture; pleasures of royalty may then be enjoyed by a king by means of various kinds of perfumes.
(5) Mix together equal quantities of cinnamon, Kushtha, Renu, Nalika, Sprikka, Myrrh, Valaka, Tagara, Kesara and Patra and grind them on a stone forming them into a paste; rub it over the head and then bathe; such a bath is suited to kings.
(6) Mix together in oil the powder of Manjishtha, Vyaghranakha, Sukti, cinnamon, Kushtha, and myrrh; heat the mixture in Surya. It is known as Champakagandhi oil.
(7) Grind together equal quantities of Patra, Turushka, Vala and Tagara and you will get a perfume provoking sexual passion. Add to this perfume Prianguka and expose mixture to the smoke of Katukarohini and Hingulika. You will get a perfume which is known as Vakulagandha. To this add Kushtha and you will get a perfume known as Utpalagandha. Add to this sandal, you will get again perfume known as Champakagandha. Add to this nutmeg, cinnamon and Kustumbari; you will get a perfume known as Atimuktagandha.
(8) Mix together 1/4 parts of Satapushpa and Kunduruka, 1/2 parts of Nakha and Thurushka, and 1 part of Sandal and Priangu; grind them well and expose mixture to the smoke of Guda and Nakha.
You will then get an excellent perfume.
(9) Grind together equal quantities of Jatamamsi, Valuka, Thurushka, Nakha and Sandal and form a paste; expose it to the smoke of bdellium, Valuka, lac, Musta, Nakha and Sarkara;
(10) 1 part of Haritaki, 2 parts of Sankha, 3 parts of Kshudramusta, 4 parts of Drava, 5 parts of Ambu, 6 parts of Guda, 7 parts of Utpala, 8 parts of Sylaka and 9 parts of Musta give you a perfume.
Numerous kinds of perfumes may be similarly prepared by mixing together different parts of each substance.
314 For an explanation of various botanical terms occurring in this Chapter reader is referred to the glossary at the end.
» CHAPTER XXX Contents PART 2 ON PERFUME MIXTURES «
Notes: Text gives an instance of proportion in which ingredients are to be mixed. Similarly, of 9 substances we can take from 1 to 9 parts of each, and no mixture ought to contain same number of parts of any 2 substances. The question is to find the number of different varieties of mixtures.
Suppose 9 substances to be represented by 9 letters from A to I, proportion of parts being from 1 to 9. As each substance may be taken from 1 to 9 parts and as no 2 substances shall be taken the same number of parts, number of mixtures required is the number of ways in which figures from 1 to 9 may be written under the letters from A to I. This is the number of permutations of 9 things taken altogether, which is equal to 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 = 362,880. Stanza gives us therefore 362,880 different varieties of perfumes.
(11) Mix together 4 parts each of Sita, Syla, and Murta, 2 parts each of Sree and Sarja, and 1 part each of Nakha and bdellium, grind them all on a stone with honey; add to the mixture Camphor.
You will then get a perfume known as Kopachada (destroyer of anger), fit only for kings.
(12) Mix together cinnamon, Usira, and Patra, 1 part each, and Sakshmaila, 1/2 a part; powder them well; add to the mixture equal parts of Musk and Camphor. You will get an excellent perfume.
(13) Of 16 substances Ghana, Valaka, Syleyaka, Karpura, Usira, Nagapushpa, Vyaghranakha, Sprikka, Agaru, Damanaka, Nakha, Tagara, Dhannya, Takkola, Chora and Sandal, any 4 mixed in proportion of 1, 2, 3, and 4 parts will form a perfume.
(14) As the number of 4 substances out of 16 is large and as each of 4 substances may be mixed from 1 to 4 parts, number of mixtures will be very large. The process is known as Gandharnava - ocean of perfumes.
(15) Dhannya and Karpura being substances of strong scent, a part of the former and a little less than a part of the latter shall be added - these 2 substances shall never be mixed in 2, 3, or 4 parts.
(16) Mixtures shall be exposed first to the smoke of Sreevatsa, secondly, to that of Sarjara, thirdly, to that of Guda, and lastly to that of Nakha. Add to mixture both Camphor and musk.
(17) The process gives us 174,720315 different varieties of perfumes.
(18) 1 part of a substance can be mixed with 2, 3 or 4 parts of 3 other substances in 6 ways. Similarly, 2, 3 or 4 parts of same substance can be mixed respectively with 1, 3, 4 / 1, 2, 4 / 1, 2, 3 parts of 3 other substances, each in 6 ways.
(19) Thus beginning with a single substance we get 24 varieties of perfumes; beginning with each of 3 other substances we shall get 72 varieties316; or 96 varieties in all.
(20) The number of 4 substance out of 16 substances is 1820.
(21) Every set of 4 substances gives us 96 varieties; by multiplying 1820 by 96 we shall obtain the number already stated, viz. 174,720.
Notes: Above number has been obtained on supposition that 2 substances, Dhanya and Karpura, enter into mixtures in 2, 3 and 4 parts also, which however is not the case. Actual number will therefore be less than the number stated above. We shall first explain how number was arrived at by author, pointing out an error committed by him which has permanently crept into text and then find out actual number of mixtures under conditions given.
In Chapter on combinations in algebra, we learn that the number of combinations of n things taken r at a time
… the number of combinations 16 things taken 4 at a time
Again, take one of these sets of 4 substances. Call substances by letters A, B, C, D; each of these enters into mixture in 1, 2, 3 and 4 parts; but no 2 substances enter in same number of parts.
Question now is to find out the number of mixtures that can be formed of each set of 4 substances.
315 Wrong. Vide notes which follow.
316 Wrong. Vide notes which follow.
» CHAPTER XXX Contents PART 2 ON PERFUME MIXTURES «
The number required is the number of ways in which figures 1, 2, 3 and 4 may be written under letters A, B, C, D. This is number of permutations of 4 things taken all together, which is equal to 1 × 2 × 3 × 4 = 24. Author is therefore wrong when he says that the number of such mixtures is 96.
We shall show his error by actually putting down proportions of various mixtures.
A B C D A B C D A B C D A B C D
1 2 3 4 2 1 3 4 3 1 2 4 4 1 2 3
- // - 2 4 3 - // - -1 4 3 - // - 1 4 2 - // - -1 3 2
- // - 3 2 4 - // - -3 1 4 - // - 2 1 4 - // - -2 3 1
-- // -- 3 4 2 - // - -3 4 1 - // - -2 4 1 - // - -2 1 3
-- // -- 4 2 3 - // - -4 1 3 - // - -4 1 2 - // - -3 1 2
-- // -- 4 3 2 - // - -4 3 1 - // - -4 2 1 - // - -3 2 1
Total 6 Total 6 Total 6 Total 6
In all, 24 varieties for each set.
Now author says that we shall get another 24 varieties beginning with several parts of B and 24 beginning with several parts of C and 24 beginning with several parts of D, thus 96 varieties in all. It is clear that Varaha Mihira must have "dozed a little" when he wrote Stanza 19; for the number of varieties in reality is only 24 and not 96. For 24 varieties we have given above include and are identical with 72 more varieties of author. We will begin for instance with several parts of B. These are:
B A C D B A C D B A C D B A C D
1 2 3 4 2 1 3 4 3 1 2 4 4 1 2 3
- // - 2 4 3 - // - -1 4 3 - // - 1 4 2 - // - -1 3 2
- // - 3 2 4 - // - -3 1 4 - // - 2 1 4 - // - -2 3 1
-- // -- 3 4 2 - // - -3 4 1 - // - -2 4 1 - // - -2 1 3
-- // -- 4 2 3 - // - -4 1 3 - // - -4 1 2 - // - -3 1 2
-- // -- 4 3 2 - // - -4 3 1 - // - -4 2 1 - // - -3 2 1
Total 6 Total 6 Total 6 Total 6
In all, 24 varieties beginning with several parts of B. Now comparing these with 24 varieties already given, it will be found that 2 lists are identically the same. So that 4 substances mixed in proportion of 1, 2 3, 4 parts each, give us only 24 mixtures, and not 96. Therefore, total number of mixtures is 24 × 1820 = 43,680 and not 96 × 1820 or 174,720 as stated by author. It is strange that Utpala, commentator, has not noticed the error.
As 2 of 16 substances do not enter into mixtures in 2, 3 and 4 parts, we will find actual number of varieties under conditions given - a point which author has omitted. Keeping aside 2 substances, number of sets of 4 substances out of 14 is the number of combinations of 14 things taken 4 at a time.
This is equal to
As before, each set will give us 24 mixtures. Total number on mixtures therefore is 1001 × 24 = 24,024 (I).
Again the number of 3 substances out of 14
We will now find out number of varieties of mixtures, which each set of 3 substances will give us, taking them in 2, 3 and 4 parts. Let letters A, B, C denote 3 substances, and figures 2, 3, 4 denote the parts. The number required is number of ways in which figures 2, 3, 4 can
» CHAPTER XXX Contents PART 2 ON PERFUME MIXTURES «
be written under letters A, B, C. This is the number of permutations of 3 things taken all together = 1
× 2 × 3 = 6. Therefore total number of mixtures of 3 substances out of 14 = 364 × 6 = 2184. Adding to each of these mixtures 1 part of Dhanya we get 2184 mixtures of 4 substances (II).
Adding to the same a little less then a part of Karpura we get 2184 mixtures of 4 substances (III).
Now as under the conditions of the case no 2 substances shall enter into a mixture in same number of parts, and as 2 substances Dhanya and Kurpura are only to be added in one part each; it is evident that these 2 do not enter into a mixture together - otherwise we shall have to find out the number of sets of 2 substances out of 14 and number of mixtures of each set, each substance being taken from 2 to 4 parts and to each mixture thus obtained add a mixture of 1 part of Dhanya and a little less than a part of Karpura. Such however does not appear to be the object of author. He evidently wants that each mixture shall contain 10 parts.
Total number of mixtures under conditions given is 24,024 + 2184 + 2184 = 28,392.
(22) Beginning from unity form several series of numbers by adding together each figure with next and the sum with next and so on omitting only the last. Last of the series will represent number of combinations required.
Notes: In this Stanza, author lays down a rule for finding the number of combinations of n things taken r together when n and r are known. For instance, required number of combinations of 7 things taken 4 together. Write in a line figures from 1 to 7 and call it first series, thus:
1, 2, 3, 4, 5, 6, 7 ... (1). Form second series from first as follows:
1 + 2 = 3; 3 + 3 = 6; 6 + 4 = 10; 10 + 5 = 15; 15 + 6 = 21. So that second series is 1, 3, 6, 10, 15, 21 … (2). Form third series from second as follows:
1 + 3 = 4; 4 + 6 = 10; 10 + 10 = 20; 20 + 15 = 35. So that third series is 1, 4, 10, 20, 35 ... (3). Form fourth series from third thus:
1 + 4 = 5; 5 + 10 = 15; 15 + 20 = 35, so that fourth series is
1, 5, 15, 35 … (4) and so on. The number of combinations, therefore, of 7 things taken 4 together is the last number of fourth series, viz. 35.
The above may appear to be a somewhat clumsy process. Bhaskarachariar in his Lilavati (Arithmetic) gives identical rule now found in Western works on algebra. He says: Form fractions with figures, say, from 7 to 1 for numerators, and from 1 to 7 for denominators thus:
.
The number of combinations of 7 things taken 2 together is product of first 2 fractions = 21.
The number taken 3 together is the product of first 3 fractions = 35. The number taken 4 together is the product of first 4 fractions = 35 and so on. This process is also mentioned in Aphorisms of Pingala, known as Chandas Sutra, a very ancient work.
(23) Agaru, Pattra, Turushka and Syleya shall be mixed in 2, 3, 5 and 8 parts, and Priyangu, Musta, Rasa and Kesa shall be mixed in 5, 8, 2, and 3 parts.
(24) Sprikka, Cinnamon, Tagara and Mamsi shall be mixed in 4, 1, 7 and 6 parts; and Sandal, Nakha, Sreeka, and Kunduruka shall be mixed in 7, 6, 4, and 1 parts.
(25) Each set of 4 substances may be mixed in all possible ways in parts mentioned - the number of parts being always 18 in case of each mixture. Mixtures form perfumes, ointment, and the like.
Note: As before, each set of 4 substances will give 24 varieties of mixtures.
(26) To the mixtures mentioned above, add equal parts of Nakha, Tagara, Turushka, nutmeg, camphor and musk and expose them to the smoke of Guda and Nakha. You will get what are known as Sarvatobhadra perfumes.
» CHAPTER XXX Contents PART 2 ON PERFUME MIXTURES «
(27) If, to same mixtures, you add equal parts of nutmeg, musk and camphor, and drench resulting mixtures in Sahakara and honey, you will again get what are known as Sarvatobhadra perfumes.
(28) Whenever substances Sarjarasa and Sreevasaka are mentioned with other substances for giving perfumed smoke, remove the two and use instead Valaka and cinnamon. Resulting mixture will serve for bath.
(29) Mix together any 3 out of 9 substances, Lodhra, Usira, Nata, Agaru, Musta, Malaya, Priyangu, Dhana and Pattya.
(30) Add to the mixture 1 part of Sandal, 1 part of Turushka, 1/2 a part of Nakha and a 1/4 part of Satapushpa; expose the mixture to the smoke of Katuka, Hingula and Guda; we thus get 84 different varieties of mixtures.
Notes: Number of combinations of 9 substances taken 3 at a time is equal to .
(31) Allow the toothbrush317 to soak in the urine of cow mixed with powder of Haritaki for 7 days.
Then put it in fragrant water prepared as described below.
(32) Fragrant water shall be prepared with cardamom, cinnamon, Pattra, Anjana, honey, Maricha, Nagapushpa and Kushtta and allow toothbrush to remain in water till it becomes fragrant.
(33) Mix together powder of 4 parts of nutmeg, 2 parts of Patra, and 1 part of cardamom and camphor; smear it over toothbrush and dry it in Surya.
(34) Toothbrush prepared as stated above shall be used by Brahmins, Kshatriyas, and Vaysias only.
By its use appearance of a person will become bright, his countenance will become agreeable, his mouth pure and of good smell, and his voice sweet.
(35) Chewing of Tamboola318 excites sexual passion, brightens personal appearance, promotes prosperity, causes mouth to smell sweet, increases strength, removes phlegmatic affections and produces many other benefits.
(36) A due admixture of lime reddens the lips. If nut exceed its measure it will bring down the color; if lime exceed its measure, mouth will smell ill and if leaves exceed their measure, mouth will be of good smell.
(37) If leaves exceed their measure at night or nut exceed its measure by day, effect will be good; if case be otherwise, Tamboola will not be found sweet. If Tamboola contain as its ingredients Takola, arecanut, Lavaliphala and Parijata, it will exhilarate the spirit and excite sexual passion.
317 This is a piece of stick or small twig of particular trees (vide Chapter 85 [Chapter XXXVIII]) used as toothbrush.
318 This consists of Arecanut and betel mixed with lime.
» CHAPTER XXX Contents PART 2 GLOSSARY OF MEDICAL AND BOTANICAL TERMS «
Chora - a kind of perfume; plant, Chrysopogon Aciculatus.
Ghana - bulbous root of plant, Syperus Hexastychus Communis.
Gokshuraka - plant, Asteracantha Longifolia.
Guda - a kind of bdellium.
H
Haritaki - fruit of Terminalia Chebula.
Hinguka - prickly night shade, Solanum Jacquini.
I
Katuka - a fragrant grass, Trichosanthes Dioeca.
Kesa - plant, Andrapogon Schoenanthus.
Kesara - Mimusops Elengi.
Kodrava - a species of gram eaten by the poor, Paspalum Scrobiculatum.
Kunduruka - resin of plant, Boswellia Thurifera.
Kushtha - a medicinal plant, Costus Speciosus or Arabicus.
Kustumburi - coriander seeds.
L
Lavaliphala - fruit of Averrhoa Acida.
Lodhra - tree, Symplocos Racemosa, the bark of which is used in dyeing.
Musta - a species of grass, Cyperus Rotundus.
N
Priyangu - a medicinal plant and perfume.
R
Renu - a drug or medicinal substance, fragrant but bitter and slightly pungent taste, and of a greyish color.
S
Sahakara - sort of fragrant Mango tree.
Sailaka - bitumen.
Sarja - resinous exudation of Sal tree.
Sarkara - grit.
Satapushpa - a sort of dill or fennel, Anethum Sowa.
Sukti - a sort of perfume in appearance like dried shell fish.
T
Tagara - seed of Cassia Tora.
Takkola - tree, Pimenta Acris.
Triphala - three, Myrobalans; fruits of Terminalia Chebula, Terminalia Bellerica, Phyllanthus
Usira - fragrant root of plant, Andropogon Muricatus.
Vyaghranakha - a kind of medicinal herb, with a fragrant root.
[Tamil characters at the end of each line have been omitted.]
» CHAPTER XXXI Contents PART 2 ON SEXUAL UNION «
(1) King Vidurattha was killed by his queen who concealed a weapon in her plaited hair; and king of Benares was killed by his queen, who disliked him, with poison which she carried in her anklets.
(2) Thus wives who do not love their husbands have killed them. Of what use is it to quote more instances. Husbands shall therefore ascertain in various ways whether they have secured the affection of their wives.
(3) A loving wife shows her love in various ways. She will, in presence of her Lord, show, as if by accident, her navel, arms, and ornaments and will adjust her garments; will allow the hairs of her head to fall loose as if by accident, will raise her eyebrows, will tremble, and will cast a side-look at her husband.
(4) She will spit aloud; laugh openly; get first into the bed; crack her joints; yawn; beg for the gift of trifles; embrace a child and kiss it; will for a time look at her friend; look at her husband when his look is turned from her; scratch her ears; and will speak in his praise in his absence.
(5) A loving wife will, besides, speak affectionately to her husband, assist him with her money, will give up her anger at the sight of her Lord and will be filled with pleasurable sensations; will meet any calumnious attacks on him by recounting his virtues.
(6) She will show due respect to the friends of her Lord and hate his enemies; she will feel grateful to him for his helps; will feel distressed during his absence.
(7) An unloving wife will contract her eyebrows; turn her look away from her Lord; will be wanting in gratitude; will not move from her place at the sight of her husband; will never feel cheerful; her lips will be dull and motionless; she will befriend the enemies of her Lord and will be harsh in her speech.
(8) She will shake with fear at the sight or touch of her Lord; will feel haughty; will not attempt to pacify her Lord when he leaves her company in anger; she will wipe off her face after sexual enjoyment; will go to bed before her Lord and rise after him.
(9) Begging women, female devotees, maid servants, the nurse, girls, laundress, flower woman, harlot, a friend, barbaric woman, these generally serve as messengers or go-betweens for women and bring disgrace and ruin on respectable families;
(10) It is therefore necessary to protect family women from intrigues of these persons and to maintain the honor, fame, and respectability of family.
(11) To go out at night, to keep awake on the pretense of a religious observance, to excuse herself on false plea of illness, to be found forever in houses of other persons, to attend plays and the like, to consult astrologers, to frequent mourning houses or festivals are acts from which women should be kept back.
(12) A modest wife is one who out of shame does not first exhibit an inclination to sexual embrace;
who throughout is nevertheless subject to sexual passion.
(13) Virtues of a woman are young age, beauty, decoration with ornaments, being agreeable to her Lord, being learned in matters which will make married life happy and being of a playful nature. A lady possessing these virtues is known as a female gem. A woman not possessing these virtues is loathed by a man of taste as a disease.
Notes: Vyasa says: A woman who is chaste and innocent, who eats pure meals, who is of sweet speech and who is fondly attached to her husband is known as a Lakshmi (goddess of wealth).
» CHAPTER XXXI Contents PART 2 ON SEXUAL UNION «
Again, a woman who has ugly eyes, who is dirty, quarrelsome, talkative, is known as a Rakshasi (fury).
(14) A woman shall not indulge in low language; nor shall she wear bad colored clothes; nor be of a dirty body.
(15) A good wife is one who breathes unlike men; who extends her arms to her Lord to serve as a
(15) A good wife is one who breathes unlike men; who extends her arms to her Lord to serve as a