330 Proceedings of the Boyal Physical Society. 



side, and the various divisions of the metre scale on the 

 other, draw fine lines in carmine ink for the decimetre 

 divisions, in blue for the centimetres, and in Indian ink for 

 the millimetres, continuing these least subdivisions towards 

 the needle only as far as they remain clearly separate. From 

 this scale, which we shall use under the name of the decimal 

 SCALE, a line of any length likely to be needed can be divided 

 accurately into any required number of decimal parts to 

 three places — the unit being the distance across the scale 

 measured at right angles to the base line. 



22. Choosing from this scale a radius equal to five centi- 

 metres, we carefully draw in a circle of a decimetre in 

 diameter, across which are to be drawn two diameters at 

 right angles to each other, which divide the circle up into 

 four equal quadrants. These may be lettered with Eoman 

 numerals L, IL, IIL, IV., taking the first figure in the bottom left 

 hand quadrant, and the others in order counter-clockwise. 

 The circle in future will be referred to as the primitive, or 

 the circle of projection, because it represents on paper the 

 sphere of projection formerly used. Its centre is to be signed 

 0, which stands for origin. From o produce the cross 

 diameters beyond the circle, and conceive of these lines as 

 indicating simply directions. The right and left direction 

 will be referred to as ox, and the direction at right angles to 

 that as oz, in both cases regardless of the length of the lines 

 in question. (See Fig. 1.) 



23. Suppose now that we have an orthorhombic crystal to 

 project, and that we take Barytes as a fairly easy one to 

 deal with. The first point to notice in this is that the 

 crystal molecules in this species are arranged in such a 

 manner that the unit form of the resultant crystal builds a 

 solid in which the three axes are of markedly unequal 

 length. Let us assume for working purposes that the right 

 and left axis ox represents unity in the proportions of the 

 crystal as well as the radius of the circle of projection. If 

 we turn to ''Dana" we find that, relatively to this unit, the 

 front and back axis {a) is less than unity, and measures 

 •8452, while the vertical axis (c) is greater than unity, and 

 Pleasures 1'31359. We take the first three places of decimals 



