Macedonian Cubit?

[Archimedes]

During some research into the length of the sarissa, I came across allusions to a "Macedonian cubit" that was three-quarters the length of the standard cubit. This was predicated upon a "bematists' stade" that was three-quarters the length of the standard stade.

Unfortunately, no specific ancient authorities were cited as the source for the shorter bematists' stade. Does anyone here know anything about it?

[amyntoros]

I've always had the understanding that the Macedonian stade was shorter, but I've no idea if any source specifically claims that it was so. I know that W.W. Tarn said so, and refers to it in his Alexander the Great Volume II, Sources and Studies, where he also wrote about the short cubit.

Appendix 2. The Short Macedonian Cubit

In Hellenistic Military and Naval Developments, 1930, p. 15, I gave reasons for supposing that, just as there was a short Macedonian stade (the bematists' stade), so certain measurements which we posses seemed imperatively to demand a short Macedonian cubit, otherwise they made no sense. I should have known that there was proof of such a cubit; I now give the proof.

Arrian (v,4,4) says that Indians were the tallest race in Asia, most of them being 5 cubits tall, or a little less; the exact source cannot be indicated, but his account of India is from 'those with Alexander and Megasthenes', i.e. from good sources (v,5,1). In v, 19,1 Alexander marvels at Porus’ height, he being over 5 cubits; the source here is Ptolemy or Aristobulus. This is given also by Diodorus (xvii, 88, 4), who says Porus was five cubits in height; he does not use Ptolemy, but his basis for book xvii was Aristobulus. It is obvious that these statements cannot refer to the Greek (Attic) cubit of 18-1/4 in.; “most” Indians were not 7 ft. 7 in. high, neither was Porus, who is represented as a very strong man and a great fighter. We get the proof, as regards Porus, in Plutarch (Alex lx), who, from some different source, calls him 4 cubits (Greek cubits here) and a span, 6 ft. 8-1/2 in. Now on Greeks, a Mediterranean people and therefore not tall, men of 6 ft., if met with in any quantity, would produce a very different impression from that which they would produce on tall races like the British among whom 6 ft. is common enough and everyone knows individuals of from 6 ft. 3 in. to 6 ft. 5 in.; so five cubits for ‘most’ Indians ought to mean about 6 ft., and Porus would be something over this; 6 ft. 8-1/4 in. is doubtless exaggerated, for Arrian only says ????? We can, however, go a little further here. Diodorus makes Porus 5 cubits, and a fine figure of a man (Diod. xvii, 88, 4); he also makes another Indian king, Sopelthes, a fine figure of a man, conspicuous among his people for his beauty and in height exceeding 4 cubits (xvii, 91, 7), i.e. Greek cubits; that is, he was over 6 ft, 1 in. Five Macedonian cubits were therefore roughly the equivalent of four Greek cubits of 6 ft. 1 in., which would make the Macedonian cubit about 14 inches long. But this equation of the two cubits is only a rough one; and as, roughly speaking, the bematist’s stade was three quarters of the Attic stade, and as other Macedonian measures ought to correspond, 14 in. may be a little long for the Macedonian cubit; 13-1/2 in. would be nearer the mark; probably it is safest to say it was somewhere from 13 in. to 14 in., that being as near as one can get.

This settles the question of the length of spears of Alexander’s phalanx, as well as the length of the rams used by Demetrius the Besieger and probably other measurements. Because the contemporary Theophrastus gave the length of the longest spears used by Alexander’s phalanx as 12 cubits, a common assumption has been that they were some 18 ft. long, which makes nonsense of Alexander’s tactics; his phalanx was a very different body from the later Macedonian phalanx with 21 ft. spears described by Polybius. It can now be seen that the longest spears used by Alexander’s men were from 13 to 14 ft.; this, of course, has been asserted before, but is now proved.

It is a perpetual trouble to the modern writer on Alexander that he often has no chance of knowing whether the stade of his sources means, in any particular place, the Attic or the Macedonian (bematist’s) stade. Henceforth he will have the same trouble over the cubit. It follows, too, that there must have been a short Macedonian foot corresponding to the short cubit. I do not recall meeting with it, but that may only mean that I have been reading with my eyes shut.

Personally, I think there are several problems with his argument about the cubit measurement, but I’ll wait and see if anyone else has similar thoughts.

Best regards,

[Archimedes]

I have photocopies of both of Tarn's quotes. Like you, I have problems with his argument, and I wonder why he didn't just cite a source for a "bematists' stade" that was three-quarters the standard stade. Even given a shorter stade employed by bematists for whatever reason, it doesn't necessarily follow that there would have to be cubits, feet, and whatnot similarly scaled down to three-quarters of the standard units.

[Archimedes]

According to this Wiki article, it would appear that Alexander's bematists used the standard Attic stade, not some shorter stade:

http://en.wikipedia.org/wiki/Bematist

[amyntoros]

According to this Wiki article, it would appear that Alexander's bematists used the standard Attic stade, not some shorter stade:

Very interesting. Could you tell me what exactly Tarn says about this? I was under the impression that he used the distances given by Alexander's Macedonians to come to the conclusion that the Macedonian stade was shorter, although I'm not sure where I might have read this or if I'm even correct. I don't have his books (except for Vol. 1 of his biography) but I believe I might be able to find the information online if I had the exact references. And, like you, I don't know of any ancient source that specifically states the stade was shorter. Must confess I'd never given this much thought before, but you have now piqued my curiosity.

Best regards,

[Archimedes]

Here's the other Tarn quote from his Hellenistic Military & Naval Developments:

"...and as the Macedonian stade--the stade of the bematists--was roughtly only three-quarters of the Attic stade, and as the different stades in use in the Greek world were all based upon different lengths of the foot measure, there must have been a short foot in Macedonia to correspond to the bematists' stade and presumably therefore a shorter cubit also." p.16.

Again, he asserts the existence of a shorter "bematists' stade" without citing any ancient authority or tangible metrological evidence.

[Taphoi]

Well, one problem with Tarn is that he implicitly assumes that Alexander's technical staff would have used the Macedonian cubit and stade in preference to the Attic, if such measurements existed.

In fact there are reasons to suppose the opposite. Eumenes, Alexander's Secretary, was a Cardian, a colony that I believe was refounded by Athens. Furthermore, the bematist Diognetus seems to have come from Erythrae in Ionia, which had formerly been part of the Athenian Empire. The Ephemerides may well have incorporated the Stathmoi (bematists' measurements of marches). The Ephemerides seem to have used Attic day counting (at least it seems to be the antique Attic system that is used by Plutarch in his main citation from the Ephemerides, which he says is almost word for word). Many, if not most, of Alexander's technical staff were Greeks rather than Macedonians, so why should they not have used Attic standards?

Best wishes,

Andrew

[amyntoros]

Hi Taphoi,

It makes sense to me also that the distances given (in Engels’ chart) are according to Attic standard. Which sends us right back to Archimedes’ original question – where IS there evidence of a shorter Macedonian, bematists’ stade? Bosworth in Alexander and the East: The Tragedy of Triumph debunks another suggestion that short stade measurements were used during the march through the Gedrosian desert. (Interesting that it is another Greek, Nearchus, who was thought to have given figures based on a shorter stade.)

Page 175

The stories certainly reflect the experiences of the march, the struggle against drifting sand, thirst, and sheer distance, but equally certainly they are embellished in the desire to make the best of the story – the besetting vice of war memoirs of every age. We may well believe that there were long overnight marches, but hardly of 50 or 70 miles, as Strabo suggests.(37) Otherwise how could a direct journey of 460 miles or so have taken 60 days of hard marching – as both Arrian and Strabo record?

(Note 37) Strabo 15.2.6 (722) attests marches of 200, 300, or even 600 stades. Arrian 6.24.5 also stresses the distance between water sources, but gives no figures. It is sheer desperation to assume (with Strasburger, Studien i. 459-62) that Nearchus was operating with a short stade (of 0.11 km.). It is unlikely that the bematists were working with strict accuracy in the Gedrosian wilderness; and most of the participants in the march had no way of measuring the distance they traversed. However, they would have been aware of the numerous digressions from the direct route (Arr. 6.25.2), which would have encouraged them to give the most exaggerated estimates. It would have felt like walking in circles – for ever.

Best regards,

[Taphoi]

Hi Amyntoros,

The case of Nearchus is interesting. He says he was born a Cretan, but he also lists himself among the Macedonians as a citizen of Amphipolis in his list of Trierarchs.

As for his stade, it comes from his Indian Ocean voyage. Brown calculates 9,150 stades from the Indica, whereas Nearchus himself gave the round figure of 10,000 stades. Brown gets 7,400 from Strabo for the same distance, which seems to be more correct in Attic stade terms. Brown attributes this to exaggeration by Nearchus due to the hardships of the voyage. I would suspect systematic error in the calculation of distances.

Nearchus was mainly moving in longitude. Many people will be aware that absolute calculation of longitude is almost impossible without very accurate timekeeping. Probably, therefore, Nearchus had to adopt an iterative technique. He needed to estimate his ship's speed then multiply it by the duration of each day's voyage. Ships used to use a system of throwing a wooden paddle over the side with a knotted rope attached. The knots would be at fixed intervals and the number of knots of rope drawn off a rotating drum by the dragging paddle in a fixed time gave the ship's speed. Nearchus may well have used something similarly primitive. But this system is subject to many potential systematic errors. Especially, a contrary ocean current would make the ship's speed look faster than it really was. There is in fact an eastwards ocean current in the northern Indian ocean, so Nearchus should be expected to have calculated a larger distance than he actually travelled, if he didn't correct for it.

Cordially,

Andrew

[smittysmitty]

The uncertainty that prevails over ancient measurements is apparently not new, proving to be just as misunderstood during the Roman period as is today. Attempts to convert the Greek stadia to the Roman mile vary according to who you read.

I believe moderns have attempted to measure the dimensions of various Classical period structures, such as racecourses(Hippodrome), the Parthenon among other buildings, concluding that mathematically they all correspond to Attic metrology. Further more, studies on Hellenistic period buildings apparently did not match up to those from the earlier period. I’m not sure if I understand the science behind such conclusions but this I am led to believe is one of the reasons for believing in a shorter Macedonian cubit.

In addition, a stone relief found on Samos depicting various measurements such as the cubit, span, rule, etc was found recently and gives further support to the notion of a shorter cubit. The stone is of unknown date and provenance which may present a problem. The particular paper I was reading also suggested that a Roman rule was found depicting Roman measurements on one side and Illyrian/Macedonian measurements on the other.

I have to admit, attempting to get a grasp of what has been written on ancient measurements is made particularly difficult given some modern writers use of metrics, whilst others use imperial measurements. A major headache as far a I'm concerned.

I guess what Tarn is asking is what do five cubits amount to? Given that the figures he's suggesting, it does seem rather unlikely that the majority of Indians would be over seven feet tall.

cheers!

[Archimedes]

Interesting material on the stade:

http://mathdl.maa.org/convergence/1/?pa ... odyId=1079

smitty, I think the recent discovery of which you speak is from Salamis, not Samos. I'm going to try to lay hands on the article, and if I do, I'll report back.

[smittysmitty]

I apologise for the misinformation. You are correct in saying Salamis.



Cheers!