Royal Microscopical Society, 211 



horizontal row by full lines and tliose of the other by clotted 

 lines ; number them consecutively from the central point 0, and 

 project these data severally on to planes bounding the top and 

 bottom of the elevation required, Fig. 7, when by connecting the 

 points of the top with the corresponding points at the foot, we 

 arrive at the central positions of each vertical row along the whole 

 length, Fig. 7. 



As the transverse disposition involves a duplicate system, it 

 will be necessary to set out a diagram of each layer separately, 

 Figs. 5 and 6, by constructing the curve these transverse courses 

 assume from the inchnation to be given to the tube, which will be 

 determined by projecting them horizontally from Fig. 4, c and d, 

 and transferring the same, each on to a plane representing the top 

 of the tube at the angle induced by the stipulated inclination, as 

 shown on tlie right of Figs. 5 and 6, when the intersections of the 

 horizontal lines li'om each of these points, to 8 for the upper, and 

 1 to 7 for the lower row, with their coincident vertical hnes from 

 the ijlan, Fig. 4, will give their central positions taken at their 

 shoulders, forming the limits of the said curve assumed by the 

 horizontal layers ; then by striking radii from the centres e and / 

 in each individual instance, we obtain the axial angles of the pellets, 

 upon which the several outhnes for one-half of the elevation have 

 now to be individually projected, as shown on the left of Figs. 5 and G. 



On the careful execution of the foregoing preliminary operations, 

 as well as on the accurate projection of every individual pellet on 

 each axis, must depend the integrity of the finished work. It will 

 be seen that while the outlines of those of the central row are 

 circular, those of every row beyond depart by minute but definite 

 gradations from the outline of a circle to that of the forms inscribed 

 on the iilan, Fig. 4, and although those next adjacent to the central 

 row may pardonably be represented by circles also, it leaves no less 

 than seven different and distinct forms, each at a different angle, to 

 be individually projected for one-half the elevation, in the same 

 manner, though not necessarily with the same minutiae, as described 

 for the enlarged view, Figs. 1, 2, 3, 



The pellets of the three central rows having been described by 

 circles, those of the next adjacent have to be alternately depicted 

 by repeating the several radiating axes obtained on Figs. 5 and 6, 

 down the whole length of the tube; their points may be determined 

 by means of vertical lines from the plan, and then- shoulders being 

 at right angles with their radiating axes should be set off at the 

 several intersections of these axes, with the vertical lines first pro- 

 jected from the plan, when their diameters may be squared off from 

 the central line of pellets, by which means we obtain the points 

 which hmit the several outlines all down the tube ; the centres in 

 the one row, and the peripheries in the other, answering as data for 



