28 



Tkhi suctions of the Society. 



5. Efficiency factor. 



Condensation factor = r = !- > — --^ p) = s {nc + s). 



P P 



The following diagram (fig. 24) will aid 



the determination of this coefficient. 

 Here D x . . D 2 = A. measured on the 

 edge of the beam AAi/. D n is the 

 middle point of the segment, and 

 D n . . rji is the axis passing through 

 the points D« and rj l . Therefore, 

 c x . . £., is the projection along 

 this axis of D 1 . . 1) 2 = cos a X. In 



D 2 . 



take 



such that D., 



= J) 1 . . D 2 . Then D x . . £ 3 will be 



a monophasal surface, since every 

 point in this surface is distant from 

 the corresponding point in D l . . D 2 

 by a length, measured along the axis 

 D n . . •>?!, equal to the distance be- 

 tween that corresponding point and D. 

 Therefore, every point in D : . . t 3 

 is isophasal with D 1 . Moreover, e 1 . .c 4 , 

 drawn parallel to Dj . . t 3 , is also a 

 plane wave-front. It follows that 

 e l . . e 2 represents a polyphasal sur- 

 face, and that the phase range in 



c i • • e 2 = (1 — sm a ) - ^i anc l accord- 

 ing to the well known expression for the efficiency of a polyphasal 

 radiant surface — 



(5) 



_ 2 sin {(1 — sin a) ir] _ sin {(1 — sin a) tt} 

 (1 — sin a) 2 ir (1 — sin a) -k 



= sm { — = — 7rl 



IN ( (N - j 



(N - n) 7T 



We have so far brought into the reckoning the phase changes due to 

 the finite length of the small surface 8 S, but not those due to its finite 

 breadth. It is, however, obvious that the breadth of 8 S will not be 

 uniform, and not sensibly uniform, as we pass upward from the normal 

 point towards the aperture A . . A, except, perhaps, in the case of an 

 extremely short beam. In any ordinary case it will vary, and will vary 

 very nearly in the proportion of the length of D (= n c p). We may 

 therefore say, without sensible error, that the angle subtended at the 

 point ■)] 1 by the radiant wedge is for practical purposes invariable. Let 

 this angle =2/3. Then from a horizontal line, equal to the breadth of 

 ■8 S, through the point D„, the extreme difference of optical paths to -q^ 

 will be (sec /? — 1) n c p, and the corresponding phase range (sec (3—1) 



n £ 2 ir. Let this angle be written n 0, and we shall obtain for the 

 whole impulse emitted from 8 S when resolved along the Dn . . rj x axis. 



