# Reception of the New Physics

Chapitre 21, 1639-40, Reception of the New Physics, p.399-40

*You tell me you would like to know the device by which I was able to assure myself that the vertically falling body leaving from the rest passed 100 braccia of height in five seconds. Here two things are sought: the first is the time of descent through 100 braccia, and the second is to find what part that time is of 24 hours in the [del primo mobile]. As to the first operation, the descent of that ball that I make descend through a channel, arbitrarily sloped, will give us all the times - not only of 100 braccia, but of any other quantity of vertical fall – inasmuch as (as you yourself have demonstrated) the length of the said channel, or let us call it inclined plane, is a mean proportional between the vertical height of the said plane and the length of the whole vertical distance that would be passed in the same time by falling moveable. Thus for example, assuming that the said channel is 12 braccia long and its vertical height is one-half braccio, one braccio, or two, the distance passed in the vertical will be 288, 144, or 72 braccia, as is evident. It now remains that we find the amount of the time of descent through the channel. This we shall obtain from the marvellous property of the pendulum, which is that it makes all its vibrations, large or small, in equal times. This requires, once and for all, that two or three or four patient and curious friends, having noted a fixed star that stands against some fixed marker, taking a pendulum of any length, shall go counting its vibrations during the whole time of the return of the fixed star to the original point, and this will be the number of vibrations in 24 hours. From the number of these we can find the number of vibrations of any other pendulums, longer or shorter, at will, so that if for example those counted by us in 24 hours, were 234,567, then taking another shorter pendulum with which one [friend] counts 800 vibrations while another counts 150 of the longer pendulum, we already have, by the golden rule, the number of vibrations for the whole time of 24 hours; and if we want to know by these vibrations the time of descent through the channel, we can as easily find not only the minutes, seconds and sixtieths of seconds, but beyond that as we please. It is true that we can pass to a more exact measure by having observed the flow of water through a thin passage, for by collecting this and having weighed what passes in one minute, for example, then by weighing what passes in the time of descent through the channel we can find the most exact measure and quantity of this time, especially by making use of a balance so precise as to weigh one-sixtieth of a grain. So much for the device, which I think you will deem very exact, though if you then want to experiment whether what I wrote about 100 braccia in five seconds be true, and you should find it false, [remember that] to exhibit the extreme foolishness of him who wrote [Scheiner] and assigned the time of a cannonball from the lunar orb [to the earth], it mattered little whether the five seconds for 100 braccia was true or not.*

*Galileo at Work*, His scientific Biography, The University of Chicago Press

Une partie de la lettre de Galilée à Giovani Battista Baliani qui répond à la question comment mesurer avec précision le temps de la chute d’un corps (100 braccia en 5 secondes). (En anglais)

- *Opere de Galileo Galilei*, Vol XVIII, lettre 3897, de Galilée à Baliani, le 1 Août 1639