2Z6

Of Winds and Sounds.

HARMONICALPROPORTIONisthatwhick

is between those Numbers which afligst *

I.coL>b-

Weight, as F, according to its Length, and draWfl °of its right lin’d Position A B, into an oblique P 0 * 1 '^A D B,* by another Weight, as E. The formerbe call’d the Tending Force , and the latter the Inft*Force. t [,e

2. Now since the Tending Force F acts uponString in the Direction D B, it may be represents sthe Line C D, which Line or Force may be rewinto two others, viz. CB and C D ; of whichformer draws the String horizontally from D to Jjthe other acts in drawing the String directly Up^.a,from D to C. Therefore the Part of the Force ' r, . (0acts in drawing the String perpendicularly upwards j? qthe whole Force as C D to D B; or, by supposing ^to be indefinitely small, as CD to CB; becaui® ^that Cafe DB — CB nearly. But the Force tV ^acts in drawing the String upwards is equal to r g,flecting Force, because they balance each other. *■ ffore the Inflecting Force E is to the Tending F° s

^ ^ FXCD n

as CD to CB, or ——-— — D.

B C

3. Therefore, putting C D — S, and 2 C By^ ^

the Length of the String, we shall have "T"”'

hence it follows, that if F and L are given, u |nif the Tending Force and Length of the String te ^the fame, the Inflecting Force E will be always j;Line CDiS. This is confirmed by £xp er,! ”.For if AB be a Brass Wire 3 Feet long, st r< \ . if

over the Pulley at B by a Weight F = 3 Poun { e

then E be first £ an Ounce, it will draw the

through C D = | of an Inch ; if E be an Ounc

will draw it through C D = * of an Inch ; and p jj

4. The String being drawn into the Position

has an Endeavour to return, which is call’d ^ . £jpgtutive Force, and which re-acts against the >