386 



Transactions of the Society. 



Fig. 78. 



polyphase front <£ 3 which stands at an angle a little less than 

 45° to the plane wave-fronts, has according to the diagram an 

 aperture value not exceeding 86 ^ 00 in., and this value, if allowance 

 be made for the want of unison in its phases, would have to be 

 reduced to little more than one-half this figure.* Thus the light 



diffracted along this axis from this aper- 

 ture does not exceed in intensity what would 

 be carried by an undiffracted beam through 

 an aperture having a diameter of y^sV oo ^ n - 

 It is worth while to make a small 

 digression at this point in order to observe 

 that we could not increase the intensity 

 of the light diffracted along this axis by 

 lengthening the vertical diameter of the aperture. We should 

 thereby increase the number of phases on the polyphase front 

 and the area of the front itself in the same proportion ; but as we 

 should reduce its aperture value at least in the same ratio there 

 could be no resulting increase in the intensity of the radiation 

 along this particular axis. In like manner, if we reduced the dia- 

 meter of the aperture we should not necessarily thereby diminish 

 the amount of the light diffracted along the axis in question. We 

 should diminish the number of phases, but as these cancel one 

 another in pairs the removal of every successive complete set of 

 phases from the radiant surface will cause no change in the illumi- 

 nation at the focal point. This illumination 

 can only be affected to the extent to which 

 it may be increased or diminished by the 

 removal of a half-set, quarter-set, three- 

 quarter set or other incomplete set of phases, 

 and the change will be greatest when ex- 

 actly one half-set of phases is removed. 

 Then the light will fall from maximum to 

 zero, or rise from zero to maximum, or pass 

 from an intermediate degree of intensity 

 to its complementary degree of intensity, as the case may be. 

 But however the aperture value of the aperture may vary it 

 can only vary between the limits of equivalence to one half- 

 set of phases and zero. This fact affords us a simple rule for 

 determining the maximum amount of light that can be radiated 

 by diffraction along any particular axis. Suppose that we cut 

 down the aperture as shown in fig. 79, until the polyphase front 

 <j> n crossing the plane wave-front at an angle 6 n extends, as shown, 

 exactly from wave-front 10 to wave-front 12. Then the polyphase 

 front will contain one half-set of phases and therefore have a 



'« 



Fig. 79. 



* The fraction is exactly 



