Now consider a propositional function **Fx** in which the variable argument x is itself a propositional function.

Corresponding to the argument log x it gives the values of log (I -**Fx** - 1) and log (1+x).

(ii.) Repeated divisions of (24) by x+x, r being replaced by rd I before each division, will give (I +xy 2 = I -25+3x2-4x3-F...+(- )r(r (I)xr + (-) r+l x r+1 1(r+ I) (I +5)- 1 + (1 + 5)-21, (I-**Fx**)-3=I - (3x-6x2 - IOx3+...+(-)rï¿½ 2l(r+I)(r+2)xr +(-) r+l x r+1 12 (r+I) (r+2) (' +x)-1+(r+I)(I - **Fx**) - 2 +(I +x)-3},&c.

Thus, if x = R cos 4), C =,r2R2J1(pR) pR and the illumination at distance r from the focal point is 4T2 r 21rRr1 **fX** (2 fKr) a J The ascending series for J 1 (z), used by Sir G.

The general results may be summarized as follows: if the width of the slit is equal to **fX**/4D (where X is the wave-length concerned, D the diameter of the collimator lens, and f its focal length) practically full resolving power is obtained and a further narrowing of the slit would lead to loss of light without corresponding gain.