118 Professor Airy on the 



This indicates a series of dark circles, whose diameters are the same as 

 those of the circles seen with either of the plates singly. 



2. The expression also vanishes when 



™-(v-x)=o. 



or when 



ttB . 



~Y = X> = *■ + X> = 2 7T + x , &c. 



Now when 2</> increases from to 90°, from 90° to 180°, &c. x a ^ so ™" 

 creases from to 90°, from 90° to 180°, &c. : consequently x will never 

 differ much from 2 (p. So that the expression vanishes when 



— — = 2 0, = 7T + 2(p, = 2tt + 2(f), &c. nearly. 



In the curve defined by this equation, it is plain that 9 increases con- 

 tinually as <p increases, and consequently increases continually as <p in- 

 creases. The curve therefore is a spiral in such a position that if we look 

 at a point above the center, and follow the curve towards the right-hand, 

 the radius vector continually increases. 



3. Now if we increase <p by 90°, or 180°, or 270°, we get the same 

 values for x> increased by ir, or 2tt, or 3ir. Consequently the values of 



the radius vector, at a point of the dark line, are found by making ^— 



in the first of these to -k + x, 2 -k + x, 3 t + x> &c. 

 in the second to 2 ir + x> 3-n- + x, 4 -w + x> & c - 



in the third to 3 ■*■ + x> 4 vr + x> 5 -n- + x, &c. 



These are evidently the same series of values as that found with the origi- 

 nal value of <p. That is, if we draw four radii vectores of equal length at 

 angles of 90°, and if one of these terminate in a point of the dark curve, 



