*Some other curious properties of the Italic and Babylonian hours.* I will adopt here the Frank’s notation : F=French or modern hours; I=Italic; B=Babylonian.
Moreover T=Temporary and D = duration of the clear day (from dawn to sunset). The simple following formulae are valid: I=F+(24-D)/2 (1) B=F-(24-D)/2 (2) T=6+12(F-12)/D (3) I+B = 2F (as usual) I-B = 24-D= duration of the night (1) and (2) suggest one method to draw the daily lines (hyperboles) corresponding to the days whose length is equal to an integer of hours =D. If the duration D is an odd number it is necessary to have the hour lines with modern hour every half an hour. If we take , for instance, D=14 they become I=F+5 and B=F-5: the hour lines with modern hours F, Italic I and Babylonian B meet in a point that belongs also to the daily line corresponding to the day whose length is 14 hours. If we connect all the points that we obtain changing the value of F we have daily line. For instance F = 7; I=12; B=2 or F=16; I=21; B=11 For instance: with D=9 we have I=F+7.5 and B=F-7.5 ---------------------- In the points of the daily lines corresponding to a duration D=6, 12, 18 we find four hour lines with an integer number of hours : with modern, Italic, Babylonian and Temporary hours. (see formula n. 3) For D=18 it is necessary to consider only the values of F multiple of 3. For D=6 we have T=2F-18 and, for example, the lines with F=10, I=19, B=1, T=2 pass all through the same point. For D=18 we have T=2F/3-2 and, for example, the lines with F=15, I=18, B=12, T=8 pass all through the same point. This is a simple ( J ) method to draw the Temporary hour lines. Best wishes Gianni Ferrari
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