( 34 * ) 
following Propofition I fhew the Fornix or Arch whiclr 
fupports its own Weight to be the fame with the Catena,- 
ria. In the two next Proportions I fhevv how to find the 
Figures of pfliable Surfaces which are charged with the 
Weight of a Fluid- In the 2 id and 23 d Proportions I 
treat of the Motion of a Mufical String, and give the 
Solution of this Problem: To find the Number of Vibrati- 
ons that a String will make in a certain time, having gi- 
ven its Length, its Weight, and the Weight that flretch- 
esit. This Problem I take to be entirely new, and in the 
Solution of it (in the laft part of Prop 23.) there is a re- 
markable fnftance of theUlefulnefsof the Method of firft 
and laft Ratio s. The 24^ Proportion gives the Inven- 
tion of the Center of Ofcillation of all Bodies ; and in 
the 2 $th Propofition I have given the Tnvefligation of the 
Center of Percuflion. It is known that this Problem is 
folved by the fame Calculus as the foregoing ; wherefore 
it is generally thought that thefe two Centers are the fame. 
But that is a Miftake^ becaufe the Center of Ofcillation 
can be but one Point; but the Center of Percuflion may 
be any wherein a certain Line, which this Propofition 
fhews how to find. There is an Error in this Propofiti- 
on, which I was not fenfible of till after the Book was 
publiflvd, wherefore I take this Opportunity of corre&ing 
of it. It does not afled: the Reafoning by which I find 
the Diftance of the Center of Percuflion from the Axis of 
Rotation, but it is this* that I fuppofed the Center of 
Percuflion to be in the Plane pa fling thro’ the Center of 
Gravity, and perpendicular to the Axis of Rotation .• 
which is a Miflake. It is corrected by the following 
Propofition. 
