Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/174

 the ground, as well in the one shot as in the other: for thus you may see exactly how much one shaft flew farther than the other.

In my thoughts this experiment is very proper: and I do not doubt but that the flight, that is, the space between the shaft and the place where the chariot was at the shafts fall, will be less by much when one shooteth towards the chariots course, than when one shooteth the contrary way. For an example, let the flight of it self be three hundred yards, and the course of the chariot in the time whilst the shaft stayeth in the air, an hundred yards, therefore shooting towards the course, of the three hundred yards of the flight, the chariot will have gone one hundred; so then at the shafts coming to the ground, the space between it and the chariot, shall be but two hundred yards onely; but on the contrary, in the other shoot, the chariot running contrary to the shaft, when the shaft shall have passed its three hundred yards, and the chariot its other hundred the contrary way, the distance interposing shall be found to be four hundred yards.

Is there any way to shoot so that these flights may be equal?

I know no other way, unless by making the chariot to stand still.

This we know; but I mean when the chariot runneth in full carreer.

In that case you are to draw the Bow higher in shooting forwards, and to slack it in shooting the contrary way.

Then you see that there is one way more. But how much is the bow to be drawn, and how much slackened?

In our case, where we have supposed that the bow carried three hundred yards, it would be requisite to draw it so, as that it might carry four hundred, and in the other to slacken it so, as that it might carry no more than two hundred. For so each of the flights would be but three hundred in relation to the chariot, the which, with its course of an hundred yards which it substracts from the shoot of four hundred, and addeth to that of two hundred, would reduce them both to three hundred.

But what effect hath the greater or less intensness of the bow upon the shaft?

The stiffer bow carrieth it with greater velocity, and the weaker with less; and the same shaft flieth so much farther at one time than another, with how much greater velocity it goeth out of the tiller at one time, than another.

So that to make the shaft shot either way, to flie at equal distance from the running chariot, it is requisite, that if in the first shoot of the precedent example, it goeth out of the tiller with v. g. four degrees of velocity, that then in the other shoot it de-