340

Plate

XXXVIII.

fig. Z-

Of Light and Colours.

Pores of Air of different Thicknesses istthose Bodies; and according to the diffe-, rent

Squares to be in the Arithmetical Progression of theeven Numbers 2, 4, 6, 8, 10, 12.

13. All this follows from the Nature of the Circle;for let the Circle E F G be the Section of the Spherewhose Convexity is equal to that of the Double-Con-vex above-mentioned, and the Line A B a Section of theplane Surface of the Plano-Convex touching the otherin the Point D ; then supposing D r, D/, the Semi'diameters of two Rings, the Thickness of the Air be-tween the Glasies at those Rings will be r £ and fitwhich are equal to Os and D L, respectively. If there-fore, as usual, we put DG=«, D a—x, D b — %jac — (D e — ) y, and bd — (D/= ) Y ; then by theProperty of the Circle we have yy — ax — xx, an®YY — a~K — XX; and therefore y \: Y x :: ax —**

: sX — XX x : -—- X X. But when a or D j?a—x

very great with respect to x and X, or D a, D b, then

-—~ — x nearly ; consequently, in the present Cas 3

y^ : Y* :: x ; X ; or the Squares of the Semidiamet erSof the Rings Dr, D f, are as the Intervals e £, fd, ° {Thicknesses of the Plates of Air in those Places ; antherefore the Squares of the whole Diameters are in th sfame Ratio.

14. Sir Isaac measured the Diameter or the 5th dat^Circle (suppose 2 D/) and found it equal to 4 of asInch ; but then viewing it through a Glass \ of an Inchthick, and nearly in the Perpendicular, it must byfraction appear diminished nearly in the Proportion 0

—= 2 D/therea 1

79 8

7 ?

yg to 80; so that, As 78 : 80

Diameter between the Glasses. Whence D f ■

and in this Experiment D G = 182 Inches, vee h?, v .

D G '