Islamic Civilization

Al-Khazini’s Balance of Wisdom

Al-Khazini (fl. 1115-1130) lived and worked under the patronage of the Seljuk court.[1] He was an ascetic character, handing back 1000 Dinars sent to him by the wife of an Emir, living instead on 3 dinars a year, sharing his house with a cat.[2] Apart from the Balance of Wisdom, which will receive focus in this outline, another treatise of his is on instruments (Risalat fi'l-alat), found by Sayili in codices 682 and 681 of the library of the Sipahsalar Mosque  in Tehran. It includes 17 folios in the manuscript.[3] The treatise has seven parts, each devoted to a different instrument: a triquetrum; a dioptra; a triangular instrument; a quadrant; devices involving reflection; an astrolabe; and simple helps for the naked eye. Apart from describing the devices and their use, the treatise also demonstrates their geometrical basis.

Al-Khazini like Al-Quhi and Ibn al-Haytham before him, sought to unify the two concepts of gravity in relation to the centre of the universe, and in relation to an axis of suspension of a lever.[4] Al-Khazini was first to make the proposition, that:

‘For each heavy body of a known weight positioned at a certain distance from the centre of the universe, its gravity depends on the remoteness from the centre of the universe. For that reason, the gravities of bodies relate according to their distances from the centre of the universe.’[5]

This proposition was adopted only six centuries later in Europe, in the 18^th century following developments in the theory of gravitation.[6]

As a student of statics and hydrostatics, Al-Khazini borrowed immensely from al-Biruni and al-Asfizari.[7] Using the same instrument as al-Biruni, he made repeated trials with several metals and gemstones. He also measured the specific gravities of other substances: salt, amber, clay etc, noting whether the substance sank or floated on water. The accuracy of such measures is evident, showing hardly any deviations from modern values.[8] In the process, Al-Khazini was also able to show that both water at the freezing point and hot water were of lower density than water at an intermediate temperature.[9] He also observed that the buoyancy of the air must affect the value of the weight of an object weighed in it.[10] The bulk of Al-Khazini’s findings are summed up in his treatise Kitab Mizan al-Hikma (The Balance of Wisdom).

Al-Khazini’s Kitab Mizan al-Hikma was written in 1121-1122 for the Seljuk Sultan Sanjar's treasury, and has survived in four manuscripts, of which three are independent.[11] It was partly translated and edited by the Russian envoy Khanikoff in the mid 19^th century.[12] Though the work deals principally, and in great detail, with the practice of accurate weighing and the determination of specific gravities, it also discusses gravitation, flotation, and geodesy.[13] It studies the hydrostatic balance, its construction and uses and the theories of statics and hydrostatics that lie behind it and other topics, altogether eight subjects:

1.Theories of centres of gravity according to various Greek and Muslim scholars.

2. Further discussion on centres of gravity, mechanism of the steelyard.

3. Comparative densities of metals and precious stones, according to al-Biruni.

4. Balance designed by some Greek and Muslim scholars.

5.The water balance of Umar al-Khayam, its adjustment, testing and use.

6.The comprehensive balance; determination of the constituents of alloys.

7. Weights of coinage.

8. The Steelyard clepsydra.

The eight books are very informative.[14] First, by looking at his predecessors’ science, al-Khazini provides crucial records of their contributions that could have remained unknown or lost. In dealing with their theories of centres of gravity, Al-Khazini most particularly draws attention to the Greeks' failure to differentiate clearly between force, mass and weight, and shows awareness of the weight of the air, and of its decrease in density with altitude.[15] In Book Three, for instance, Al-Khazini brings to knowledge Al-Biruni ’s measurements of weights, instruments and procedures, which would otherwise have been lost. Interestingly, the treatise also includes other matters, little to do with the balance, such as the rising and sinking of mountains.[16]

Most of Al-Khazini’s treatise, however, deals with hydrostatics, most particularly the determination of specific gravities. Al-Khazini goes to great length in describing the equipment necessary to obtain accurate results.   ‘The balance of wisdom,’ he says:

‘Is something worked out by human intellect, and perfected by examination and trial... Among its advantages:

1) Accuracy in weighing, this balance showing variations to the extent of a mithqal...

2) It distinguishes pure metal from its counterfeit, each being recognised by itself, without any refining;

3) That it leads to a knowledge of the constituents of a metallic body composed of any two metals, without separation of one from the other, either by melting, or refining, or change of form, and that in the shortest time and with the least trouble....’[17]

Al-Khazini uses this balance for varied purposes, from ordinary weighing, to taking specific gravities, examining the composition of alloys, changing dirhems to dinars, and many other operations.[18] Al-Khazini’s scrupulousness in the preparation of his equipment and materials, and in carrying out varied applications of his balance, make his work one of the best examples ‘of rigorous attention to scientific accuracy,' Hill observes.[19] His balance could perform the most accurate measurements, of up to 1 in 60,000.[20] Expressed in other terms, the balance was accurate to 0.06 gm on a load of 2.2 kg.[21] Such accuracy owes to the length of the beam, the special method of suspension, the extreme closeness of the centre of gravity and the axis of oscillation, and of course to the minutely precise construction of the instrument.[22] Expressed in modern terms, and compared with modern values, some of al-Khazini’s results show remarkable accuracy:

Substance                    Specific gravities                     Modern Value

                                    (Al-Khazini)

Gold:                           19.05 (cast)                              19.26-19.3

Mercury:                      13.56                                       13.56

Lead:                           11.32                                       11.39-11.445

Silver:                          10.30                                       10.43-10.47

Copper:                         8.66 (cast)                                8.67-8.73

Brass:                           8.57                                         8.45-8.60

Iron:                             7.74 (forged)                           7.60-7.79

Tin:                              7.32                                         7.29

Emerald:                      2.75                                         2.68-2.77

Pitch:                           1.04 (white)                             1.07

Sweet Water :                1.00                                         1.00 

Boiling Water :              0.958                                       0.960

Olive Oil:                     0.920                                       0.918-0.919

Blood of a man in Good health:                1.033                                       1.053[23]

This tabulation of specific gravities, Hill points out, was conceived much earlier by the Muslims than by the Europeans. Serious attention was first paid to the subject in Europe during the 17^th century, culminating in the work of Robert Boyle (d. 1691).[24] He determined the specific gravity of mercury, for instance, by two different methods, giving values of 13.76 and 13.357.[25] Both of these are less exact than the value recorded by al-Khazini, most of whose results, as can be seen, were fairly accurate.[26]

Al-Khazini’s work went beyond mere measurements, and as Winter points out, it captures the comprehensive nature of Muslim study of the balance. The following quotations say much about this:

‘This just balance is founded upon geometrical demonstrations, and deduced from physical causes, in two points of view:

1. It implies centres of gravity, which constitute the most elevated and noble departments of the exact sciences, namely, the knowledge that the weights of heavy bodies vary according to difference of distance from a point in common-the foundation of the steelyard.

2. As it implies a knowledge that the weights of heavy bodies vary according to difference in rarity or density of the liquids in which the body weighed is immersed-the foundation of the balance of wisdom.

To these two principles the ancients (the Greeks) directed attention in a vague way, after their manner, which was to bring out things abstruse, and to declare dark things, in relation to the great philosophies and the precious sciences. We have, therefore, seen fit to bring together, on this subject, whatever useful suggestions their works and the works of later philosophers, have afforded us, in connection with those discoveries which our own meditation, with the help of God and His aid, has yielded.’[27]

And:

‘Novelties and elegant contrivances in the way of balances, such as: the balance for weighing dirhems and dinars without resort to counterpoises; the balance for levelling the earth to the plane of the horizon; the balance known as the even balance’, which weighs from a grain to a thousand dirhems or dinars by means of three pomegranate counterpoises; and the hour balance, which makes known the passing hours, whether of the night or the day, and their fractions in minutes and seconds, and the exact correspondence therewith of the ascendant star, in degrees and fractions to a degree.’[28]

Hour balances consisted essentially of a long lever, one arm of which carried a vessel of water emptying in twenty four hours. The other arm had a sliding weight acting as a counterpoise and moving over the calibrations on the arm.[29] It was usual to calibrate the right hand arm by silver encased at appropriate distances along it, and the divisions were in units corresponding to the particular functions of the balance, such as units of time, values of specific gravities, etc.[30] The Muslims, as Winter also points out, were thoroughly familiar with the application in surveying and building of the parallelism of a balance beam with the plane of the horizon when the beam is evenly loaded.[31]