CONTROVERSIES AS TO HERON’S DATE 305 
the distance between Rome and Alexandria. 1 Unfortunately 
the text is in places corrupt and deficient, so that the method 
cannot be reconstructed in detail. But it involved the obser 
vation of the same lunar eclipse at Rome and Alexandria 
respectively and the drawing of the analemma for Rome. 
That is to say, the mathematical method which Ptolemy 
claims to have invented is spoken of by Heron as a thing 
generally known to experts and not more remarkable than 
other technical matters dealt with in the same book. Conse 
quently Heron must have been later than Ptolemy. (It is 
right to add that some hold that the chapter of the Dioptra 
in question is not germane to the subject of the treatise, and 
was probably not written by Heron but interpolated by some 
later editor; if this is so, the argument based upon it falls to 
the ground.) (2) The dioptra described in Heron’s work is a 
fine and accurate instrument, very much better than anything 
Ptolemy had at his disposal. If Ptolemy had been aware of 
its existence, it is highly unlikely that he would have taken 
the trouble to make his separate and imperfect ‘ parallactic ’ 
instrument, since it could easily have been giafted on to 
Heron’s dioptra. Not only, therefore, must Heron have been 
later than Ptolemy but, seeing that the technique of instru 
ment-making had made such strides in the interval, he must 
have been considerably later. (3) In his work -rrepl poncov 2 
Ptolemy, as we have seen, disputed the view of Aristotle that 
air has weight even when surrounded by air. Aristotle 
satisfied himself experimentally that a vessel full of air is 
heavier than the same vessel empty; Ptolemy, also by ex 
periment, convinced himself that the former is actually the 
lighter. Ptolemy then extended his argument to water, and 
held that water with water round it has no weight, and that 
the diver, however deep he dives, does not feel the weight of 
the water above him. Heron 3 asserts that water has no 
appreciable weight and has no appreciable power of com 
pressing the air in a vessel inverted and forced down into 
the water. In confirmation of this he cites the case of the 
diver, who is not prevented from breathing when far below 
1 Heron, Dioptra, c. 85 (vol. iii, pp. 302—6). 
2 Simplicius on De caelo, p. 710, 14, Heib. (Ptolemy, vol. ii, p. 263). 
3 Heron, Pneunwtica, i. Pref. (vol. i, p. 22. 14sq.). 
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