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304 
HERON OF ALEXANDRIA 
Hipparchus. And first we will show how we can measure an 
interval of time by means of the regular efflux of water, 
a procedure which was explained by Heron the mechanician 
in his treatise on water-clocks.’ 
Theon of Alexandria has a passage to a similar effect. 1 He 
first says that the most ancient mathematicians contrived 
a vessel which would let water flow out uniformly through a 
small aperture at the bottom, and then adds at the end, almost 
in the same words as Proclus uses, that Heron showed how 
this is managed in the fiv*t book of his work on water- 
clocks. Theon’s account is from Pappus’s Commentary on 
the Syntaxis, and this is also Proclus’s source, as is shown by 
the fact that Proclus gives a drawing of the water-clock 
which appears to have been lost in Theon’s transcription from 
Pappus, but which Pappus must have reproduced from the 
work of Heron. Tittel infers that Heron must have ranked 
as one of the ‘ more ancient ’ writers as compared with 
Ptolemy. But this again does not seem to be a necessary 
inference. No doubt Heron’s work was a convenient place to 
refer to for a description of a water-clock, but it does not 
necessarily follow that Ptolemy was referring to Heron’s 
clock rather than some earlier form of the same instrument. 
An entirely different conclusion from that of Tittel is 
reached in the article c Ptolemaios and Heron ’ already alluded 
to. 2 The arguments are shortly these. (1) Ptolemy says in 
his Geography (c. 3) that his predecessors had only been able 
to measure the distance between two places (as an arc of a 
great circle on the earth’s circumference) in the case where 
the two places are on the same meridian. He claims that he 
himself invented a way of doing this even in the case where 
the two places are neither on the same meridian nor on the 
same parallel circle, provided that the heights of the pole at 
the two places respectively, and the angle between the great 
circle passing through both and the meridian circle through 
one of the places, are known. Now Heron in his Dioptra 
deals with the problem of measuring the distance between 
two places by means of the dioptra, and takes as an example 
1 Theon, Comm, on the Syntaxis, Basel, 1588, pp. 261 sq. (quoted in 
Proclus, Hypo typo sis, ed. Manitius, pp. 309-11). 
2 Hammer-Jensen, op. cit.