Hi John, At last signs of the truth...
> Theoretically it's correct that the projection of a circular > disc on to a flat surface parallel to the disc will be a circle. > Unfortunately the sun's apparent size results in the disc becoming > very blurred when you get a couple of hours off of local noon. The theory suggesting that a circular disc casts a circular shadow depends on the sun being a point source of light which is isn't! If the model on which the theory is based is refined to take the angular diameter of the sun into account, you find that the shadow is generally degraded into an approximate ellipse whose major axis is less than the diameter of the disc and whose minor axis is smaller still. The actual shape at a given time can be determined by noting the shape that the image of the sun that would form if the sun were projected through a pin-hole at the centre of the nodus (this image really is a true ellipse). You then draw the circular shadow that the simple theory suggests and at each point on the rim you draw this ellipse, being careful to preserve its orientation. You then get two envelopes, the inner of which is a fair approximation to the true shape of the shadow. The inverse of this effect occurs with an aperture nodus. The anti-shadow of a circular hole likewise distorts into an approximate ellipse but its major axis coincides with the minor axis of the shadow of the surrounding disc and vice versa. Of course the anti-shadow is bigger than the original hole. You have to use the outer envelope. Unless a nodus designer understands all this, it is ever so easy for the anti-shadow from the hole to exceed the size of the shadow of the surrounding disc. The result is indeed pretty useless! Frank King Cambridge University England -
