Simpler Methods in Crystallogra])liy. 347 



tion. In the system just noticed, the vertical axis is taken 

 as being at right angles to both the others, while in the 

 Monosymmetric system, what is usually taken as the 

 vertical axis is inclined. But for a right understanding of 

 what is to follow here, the reader is asked to conceive of 

 there being two sets of axes present — one normal, and of the 

 same nature as in the Orthorhombic system ; and another, 

 in which the right and left axis 6 remains unchanged in 

 direction, while the vertical axis c is inclined, usually for- 

 ward at the top, and the back-and-front axis a, still at right 

 angles to the last-named, is inclined in front below the 

 horizontal front-and-back axis. The inclination of the plane 

 containing o&, and the inclined axis to the plane containing 

 o& and the vertical axis, varies, like the length of the axis, 

 with each species. It is usual to distinguish the angle which 

 these two planes form with each other by ^ — the angle being 

 measured from below, on the front side. Therefore the 

 angle which the inclined c axis makes with the vertical or 

 zc axis is equal to a right angle minus the angle denoted 

 by ft or, in other words, is the complement of that angle. 

 Furthermore, the inclined angles when projected from the 

 sphere on to the plane of projection are fore-shortened to fi 

 in a manner that will be more fully described further on. 



55. We may view the sphere of projection from any point 

 on its surface. We might, for example, suppose the eye to 

 be placed at a, and the poles to be projected on to the right 

 and left vertical plane, passing through the centre ; no 

 specially useful purpose would be gained by employing such 

 a projection. Or we might view it from above, and conceive, 

 as is usually done with the projections of all the systems 

 with rectangular axes, that the poles are all projected from 

 the under surface of the sphere on to the horizontal plane 

 passing through the centre. This is often done, and the c 

 projection, as it is termed, is often as useful in the present 

 case as it is in the others. Lastly, we might suppose the eye 

 to be placed at &, with a right and left, and c vertical ; in 

 which case the poles on the four quadrants at the back of the 

 sphere, as they would appear if viewed on its concave 

 surface, are supposed to be projected upon a plane contain- 



