From these considerations it follows that before the Greeks came into contact with either Phoenicians or Lydians they had a weight standard of their own, the Talanton of the Homeric Poems, based on the cow, which was as yet only employed for the weighing of gold.
This standard we have found to be identical with one of the two chief standards employed in historical times for silver, and which from first to last was the only standard employed for gold in all parts of Hellas Proper.
As we have seen that gold was to silver in that region as 15:1, there was not much difficulty in regarding fifteen weights or staters of silver as equivalent to one of gold of like weight. Hence there was not the same need in Greece to devise a separate silver standard as there was in Asia, where the relation of the precious metals stood as 13·3:1, a fact which made simple exchange very difficult. On the other hand we have seen that for the Aeginetans and Greeks, who used the so-called Aeginetic standard, the decimal system, the simplest and most primitive method of reckoning, had a powerful attraction.
Primitive peoples perform all their calculations by means of counters, using for such purposes their fingers and toes or seeds or pebbles.
Nature herself has supplied man with the simplest and most convenient of counters in his ten fingers. Hence naturally arises a preference amongst primitive peoples for counting by tens, and this method, although it has at times been supplanted partially (seldom altogether) by the duodecimal and sexagesimal systems, which are superior by possessing a greater number of submultiples than the decimal (e.g. 12 = 6 × 2, 4 × 3, whilst 10 = 5 × 2 only), was adhered to by the Egyptians all through their history down to the latest Pharaohs. It may then perhaps be argued that it was through Egyptian influence with Greece that a large part of Greece adopted for their silver a standard based on the decimal system, especially as certain traces of Egyptian influence in very early times have been discovered of late. But as I have already pointed out above when discussing the theory of an Egyptian origin for the Aeginetan standard, because standards of like weight are found in two different regions, it by no means follows that one has borrowed from the other. If we can point out that in both Egypt and Greece there was a standard for gold almost identical in weight, it is at once apparent that there was no need for the Greeks to borrow from the Egyptians the idea of making ten silver ingots or wedges equal to one gold; especially as the decimal idea was next to that of five the simplest and most rudimentary form of calculation known to mankind. It is certainly preposterous to suppose that the Greeks were too barbarous at the time when they had attained a knowledge of silver to devise such a simple process as that of taking the fifteen ingots of silver, which from the natural laws of supply and demand they regarded as the equivalent of one gold ingot of like weight, and redividing them into ten new ingots of silver. This surely will not seem an incredible feat for the early Hellenes to perform when we recall to mind the extraordinary skill in arithmetic which is found among some barbarous peoples. “In West Africa a lively and continual habit of bargaining has developed a great power of arithmetic, and little children already do feats of computation with their heaps of cowries[289].” To imagine that the Greeks could not perform so simple a feat as that which I propose is to assume that they were in a far lower condition of culture and intelligence than the negroes of West Africa, rather resembling the lowest known tribes of men, such as the aborigines of Australia and the savages of the South American forests. To make such an assumption respecting a race which has shewn such an unrivalled potentiality of progress and development as the Greeks is absurd.
At this point it will be convenient to take a general survey of our results so far. We found in the Homeric Poems a twofold system of currency, the gold Talanton, and the cow or ox, the latter alone being employed to express values: we next found that the Talanton was the equivalent of the cow, the metallic unit being clearly the later in origin, and being based on or equated to the older unit of barter. Through the sacerdotal tradition of Delos we were enabled to fix the value of the Homeric Talanton at 2 gold Attic drachms, or a Daric (135-130 grains Troy). Next came the standards used in historical Greece. (1) The Euboic (135 grains Troy) used for silver in the great Euboic towns, in Corinth, in Athens from the time of Solon, and as a matter of course in the Chalcidian and Corinthian colonies, and employed as the sole unit for gold in all parts of Greece Proper at all periods; (2) the Aeginetic (200-195 grains) employed in Peloponnesus, in Boeotia and Central Greece. We learned that the Euboic standard coincided with the Homeric Talanton, thus finding the Greeks of historical times using the same standard universally for gold which they had employed long before the introduction of the art of coining from Asia, and partly using this same standard for silver, whilst in other states they employed a standard for the latter metal, which was based on the gold unit, simply dividing the amount of silver equivalent to it into ten parts instead of fifteen.
We then put the question, “Is it rational to suppose that the Greeks borrowed in the 7th century B.C. along with the art of coining from Asia a standard which they themselves already long since possessed?”
At the time when I first put this view forward, I was unable to offer any concrete proof of the existence of such a standard on Greek soil before the introduction of coined money, although the literary evidence was of the strongest kind. Since then I have been enabled to obtain some data of considerable importance. I have already ([Chap. II.]) described the rings and spirals of gold and silver found at Mycenae, and shewn that they were not improbably made on a standard of 135 grs. We have thus found some definite evidence of the existence of a gold and possibly a silver standard, corresponding to the standard used for both metals in after ages under the name of the Euboic or Attic. It may of course be argued that though found on Greek soil, they are not really Greek in origin. For instance there may be certain indications of Egyptian art and influence in these pre-historic remains, such as the frieze discovered in the Palace at Tiryns of alabaster inlaid with blue glass which according to Lepsius and Helbig[290] is the mock lapis lazuli which the Egyptians were so fond of making in imitation of the rare and costly real stone which had to be brought from Tartary. Granting then for the sake of argument that the Homeric Talent was a standard introduced into Greece from Egypt at a very early period, it by no means follows that this standard has had a scientific origin. The Greeks it will be noticed found it necessary in taking over this standard to equate it to their primitive barter system. If then the process of human development is such that the Greeks, who above all people shewed the most extraordinary power of acquiring civilization, found it necessary even when presented with a ready made standard for metallic currency, to bring it into harmony with their immemorial system of appraising values by means of the cow, there is certainly a strong presumption that the people from whom they derived that metallic standard had not themselves obtained it by any mathematical process.
We can hardly doubt that mankind first obtained empirically the art of weighing, and that it was only at a later period that mathematics were called in to fix scientifically the standards obtained by the older and cruder method. Such is the function of mathematics still. Thus Professor Cayley observed (in his address at Stockport), “I said I would speak to you not of the utility of mathematics in any of the questions of common life or of physical science, but rather of the obligations of mathematics to these different subjects. The consideration which thus presents itself is in a great measure that of the history of the development of the different branches of mathematical science in connection with the older physical sciences, Astronomy and Mechanics. The mathematical theory is in the first instance suggested by some question of common life or of physical science, is pursued and studied quite independently thereof, and perhaps after a long interval comes in contact with it or with quite a different question[291].”
If such then is the part played by mathematics in an age when even the mathematician has come to the aid of the hangman, and the wretch meets a well-deserved doom in strict accordance with a mathematical formula, a fortiori must empirical discovery have preceded mathematical theory in the second millennium before the Christian era. Just as countless malefactors were successfully executed by empirical Jack Ketches before ever the mathematician turned executioner, so we may be certain that untold sums of gold had been weighed by means of natural seeds and according to a standard empirically obtained before ever the sages of Thebes or Chaldaea had dreamed of applying to metrology the results of their first gropings in Geometry or Astronomy.