WALL STRUCTURE IN THICK CELL WALLS 



123 



MmOM'm' is now hollow instead of solid, and it is no longer evident 

 that the centre point of each arc will have the highest intensity. On the 

 contrary, it can be shown that the intensity is now highest at the ends of 

 the arcs; this maybe seen quite simply in the following way. In Fig. 43(a) 

 let S be the spiral angle (cp. Fig. 43(Z))), (f> the angular distance of the 

 pole at P from the spiral axis Aa, d the angle between the great circles 

 MPm and APa and PN the perpendicular from P to the spiral axis. 



(a) 

 Fig. 43. For explanation, see text. 



Then since the great circle LI is a line of equal pole density, the density 

 at P on the surface of the sphere is inversely proportional to PN and 

 sin d, i.e. 



DpQcl /(sin <j) sin d), 



but sin 6= ■\/{\~cos'^ ^/sin^ (f), 



therefore 



i)pOcl/v'(sin2<^-cos2 5). 



The corresponding intensity in the photograph Ip, is proportional to 

 Dpy but <f> must be converted into a vector measurable on the photo- 

 graph. This can be done by substituting 



cos ^=cos d cos ip. 

 Hence 



IpOz l/v^(l— cos^ B cos^ ^— cos^ S). 



Ip is therefore a maximum at the points 



^==cos~^ (sin 6'/cos 0), 180— cos -^ (sin ^S/cos &), . .(1) 



