1882.J of platinum, by the late Prof. W. II. Miller. 237 



graduated circle a disc of brass having three slots, or one slot and 

 a three faced hole in it, in which the levelling screws of the vertical 

 goniometer would rest. The work was left in an incomplete state, 

 and only notes for the paper, the table of measurements and a 

 somewhat rough stereographic projection were found. I have 

 thrown these notes into a slightly more complete form and have 

 made an accurate stereographic projection (see Plate) on a larger 

 scale. In this projection the centre gives the zero of the horizontal 

 circle, and the distance of any point from the centre gives the 

 reading of this circle. The zero of the vertical circle is at the 

 top of the projection, and the readings of this circle proceed from 

 this point round to the left. Poles at a distance from the centre 

 exceeding 90° fall below the paper and would truly be situated 

 outside the primitive circle. By supposing the position of the 

 eye changed to the extremity of the diameter perpendicular to 

 the primitive above the paper, these poles will fall within the 

 primitive ; and their positions on this supposition are shown by 

 surrounding the pole by a circlet. It will be noticed that poles 43 

 and 145, 55 and 140, 57 and 139, and 67 and 135, are very nearly 

 above one another. They would be accurately superposed if the 

 plane of projection were a plane of symmetry with respect to these 

 poles. Prof. Miller has left no note of the way in which he ac- 

 tually made the observation ; but it is clear that he had con- 

 siderable confidence in the accuracy of the observations, and that 

 the two goniometers were well adjusted. His usual plan was to 

 bring the image of a bright signal (a minute triangle or line) 

 reflected from each face of a zone into coincidence with that of 

 a faintly illuminated vertical line as seen in a vertical blackened 

 mirror. The readings of the two circles for any face are those 

 given when the image of the bright signal was superposed on that 

 portion of the faint line which lay in the horizontal plane through 

 the bright signal. There are thirty-nine poles below the paper 

 none of which are parallel to those above. This would be manifest 

 at once during the observations, for such planes would be succes- 

 sively adjusted by rotating the vertical circle alone through 180°. 

 Testing the zonal relations by means of the stereographic pro- 

 jections I have only succeeded, with such trial as I have given it, 

 in finding about four or five poles to be common to any one zone. 

 Were the bead a simple or twin crystal belonging to the cubic 

 system (that accepted for platinum) it is almost certain that a 

 much larger number of planes would lie in zones. I give such 

 zones as I have observed by inclosing the numbers of the poles in 

 square brackets, and append a query (?) whenever the pole does not 

 accurately lie in, but is very near to, a zone ; [94, 90, 51, 52, 141], 

 [96, 07, 76, 75, 138, 88(?j], [52, 30, 22 (?), 26, 71, 123], [59, 

 30, 43, 73 (?)], [42, 30, 33, 54 (?)], [94, 75, 78(?), 124, 125], [140, 



