350 Proceedings of the Royal Physical Society. 



the manner already described in the previous cases, and are 

 thence projected on to the primitive by lines radial to o — 

 the proportional distances being taken from the fractional 

 scale described in paragraph 46. Positions so determined 

 are, as before, set off upon the corresponding quadrants on 

 the opposite side of the circle. 



60, We have next to determine the positions of the poles 

 in the prism zone {ah) which lies on the line ox. The 

 sphere of projection for this purpose is now supposed to be 

 turned round, and viewed from c. Quadrant v. is set apart 

 for that aspect of the sphere. A line is drawn from A in 

 that quadrant (see Fig. 3) to the point where oz cuts the 

 primitive — this point representing the extremity of the axis 

 h (which is taken as unity) between v. and vi. This repre- 

 sents the direction of the unit prism face m (110) as viewed 

 from c. A perpendicular is drawn to this line outward from 



0, the point where it cuts the primitive is marked m, and the 

 outward continuation of the line M. Parallels to ox, oz, are 

 drawn at any convenient distance outside of the primitive 

 from ox, oz, to meet M. Number these lines aM as 1, and 

 Mc as 2. Intercepts between a and 7ii are measured upon 



1, and those between m and h upon 2. When these are 

 determined, lines are drawn from the respective points to 

 the primitive radial to o, and then from these points on the 

 primitive they are projected on to ah by lines radial to where 

 oz cuts the primitive between vii. and viii., as shown by the 

 dotted lines on Fig. 3. These points, so determined, mark 

 the projection of the poles of the several prisms on the h 

 projection, and are to be set off on either side of o. 



61. Lastly, we require to determine the positions of the 

 poles on (he). For this purpose we must remember that we are 

 at liberty to conceive of the sphere of projection being turned 

 about so as to be viewed in any position, and we may thus 

 devote another quadrant to the projection of the poles as 

 viewed from a position different from either of the others. 

 Quadrant VI. is to be used for the projection of the zones in 

 that aspect. The inclination of the a axis in this case has 

 no effect upon the projection, beyond the foreshortening of 

 c. To determine the cardinal pole e, we have, therefore, first 



