86 



r, —r]/'2. sin {y -f 45°) 

 is 51 inoiré-image of (wo ortliogonal imissoiis. 



The c'üiistaiil factor cosy — sin y oiil} alter.s llie iMagiiiliide. 

 Wlien 



.r sin y — y cox y z= .v 

 X cos y — y sin y z=: y 

 it follows, that 



y cos y — w sin y 

 cos 2 y 



sm y 

 cos 2 y 



iy cotg y — x) 



y sm y — w cos y sin y = — 



y = n = — ö~ ' ^y~''^ '^^^9 y) 



cos 2 y cos 2 y 



sin y 

 Omitting the constant factor — -^r- , that does no( alter the form, 



COsZy 



we find at last, that the moiré-image for obIi(|ue unissons proceeds 

 from that for orthogonal iniissons by the linear substitution 



.t-, = — X + y cotg y 

 Vi — y— ^ cotg y. 

 The form, thus chosen, gives rise to an easy construction, exe- 



cnted in fig. 7. The new ordi- 

 nate, f. i. is found by drawing 

 from a point P (.i', y) a straight 

 line, that builds an angle = y 

 with the ordinate of P. 



By this constructioji , the 

 double symmetry is lost; the 

 axes turn to each other over 

 an angle 90° — y. 



In fig. 7, a flattened oval is 

 obtained^); when the original 

 curve lies nearer to the centre 

 Fig, 7. and tuins its convex side to 



the axes, the hyperbola's ^) are built. 



1) See the experimental, curves in my first paper, fig, 4. 



') A mathematical explanation of interference-curves, wholly different from the 

 here given, is to be found in Mr. T. K. Ghinmayanandam : On Haidinger's Rings 

 in Mica. Proc. Royal Society. Vol, XGV, p. 176-1 89. 



The author maintains the pure hyperbola's and the ovals of Cassini, which, 

 however, build a rather rough approximation. 



