f>7

the extrados V K, = II. Then R = AC -f 2V '^ * AC =

' Ob'

r 4- ~ 2 ” - — r 4- %i see. 3 ®. At the vertex R = AC -j-

' COS? <P

2VA — r + c 2n. When C = 0, then R is infinite.The evolute has no dependence on the magnitude ofthe radius AC.

Fig. 14 . Ellipse .

Put the semi-transverse CB — a — 50.the semi-conjugate AC — b — 25.the height of the key AV == FG = LY— n = 5.the absciss to the extrados VD = m = 70-

GH = HI = u and \/ AA- + 1 = v •

Then i?— 1 + - ^ - n ^ v = -A- a cubic equation

from which v may be found when a, b, m, and n aregiven, in this example falling under the irreduciblecase. See Barlow’s New Math . Tables.

v = 6.3369- GH = HI = u = —— v/V—1

a

— •</mn—bn-t- = 15.65, DK = -g Aj — l

= 2 u ~ - 80.661.

* bnv

Also put the angle the intrados makes, with its or-dinate FE, which is equal the angle the extradosmakes with its ordinate DK = <p.

Then Tang. z. = ~ a v'v 1 — ! = 3.12875, which

found in a table of Nat. Tang, gives the angle AFE= GFH = VKL = LYK = 72°.17 / .

GH = HI = n Tang. <p = 15.65.

HF = n secant. <p = = 16.43.