Water Weighing, pp. 424-25, Galileo on the Isochrony of the Pendulum, Isis, Vol.59, No.4, pp.414-426, The University of Chicago Press on behalf of TheHistory of Science Society
To time the descent of bodies along inclined planes Galileo uses the method of water weighing:
« For the measurement of time we employed a large vessel of water placed in an elevated position; to the bottom of this vessel was soldered a pipe of small diameter giving a thin jet of water, which we collected in a small glass during the time of each descent, whether for the whole length of the channel or for a part of its length; the water thus collected was weighed, after each descent, on a very accurate balance; the difference and ratios of these weights gave us the difference and ratios of the times, and this with such accuracy that although the operation was repeated many, many times, there was no appreciable discrepancy in the results. »
The accuracy he claims is rather high: "… the deviation between two observations never exceeded one-tenth of a pulse-beat. .." If Galileo is being truthful, water weighing certainly entitles him to claim that ". . . the spaces traversed (by the falling body) were to each other as the squares of the times. .. ." And if Galileo uses this same method to time the oscillations of the pendulum, he is equally entitled to claim that the periods are isochronous. Indeed, water weighing is the most convincing support for this thesis. Galileo does not say that he used water weighing in the case of the pendulum. It is, however, probable that he did. On the one hand, the pendula, in his words, are an example of freely falling bodies:
« It occurred to me therefore to repeat many times the fall through a small height in such a way that I might accumulate all those small intervals of time that elapse between the arrival of the heavy and light bodies respectively at their common terminus, so that this sum makes an interval of time which is not only observable, but easily observable . . . and besides this, I also wished to rid myself of the resistance which might arise from contact of the moving body with the aforesaid inclined plane. Accordingly I took two balls, one of lead and one of cork . . . and suspended them by means of two equal fine threads... »
On the other hand, the precision he claims for this method is sufficiently high for the task. In the case of a short pendulum he can time a small series of oscillations and obtain the period by dividing the mass of water by the number of oscillations. In this way he cannot be certain that each oscillation takes an equal time. However, in the case of a long pendulum the precision of the method allows him to time single oscillations. Hence, water weighing can show him directly that the pendulum is isochronous. Finally, water weighing is more reliable than any other current method of measuring short intervals of time. It is more reliable than the water clock or counting pulse beats. In water weighing, the quantity that is directly measured is mass, which changes of temperature do not affect.
La description de Galilée des experiences de chute des corps graves, utilisant comme instrument de mesure précise du temps le poids d'une certaine quantité d'eau.