37© Mr. Playfair’s Account of a 
quadrant in which columns occur of two different rocks ; and 
a rectangular cell is assigned to each column in the five rings 
to which the table refers. The letters Q and M denote 
quartz and mica; and where one letter only occurs, the column 
is entirely of the rock which it denotes. In the cells where 
both letters occur, the column consists of both rocks in the 
proportion expressed by the fraction prefixed to each letter. 
Thus in the seventh ring, the first quadrilateral is T 7 - quartz 
and JL mica ; the second, T 8 - quartz and mica ; the third, 
T 9 _ quartz and mica ; the remaining nine being entirely 
quartz. 
Now to apply the tables thus constructed to the computation 
of the attraction of any of the quarter cylinders, it must be 
observed, that sin. E is to be found for any column in the way 
already explained, and is then to be multiplied by bd, b being 
__ £££2 and d — T so that b d = = — , and therefore 
3 \z 3x12 9 
the coefficient of Q or M is ~ x sin. E. 
When the whole ring is of the same rock, the coefficient of 
sin. E computed for a single column is to be multiplied by 12, 
so that the whole attraction of the ring = ^ x 12 = ^22 ~ 
666.66, as before determined. 
In the mixed columns the sine of E is to be multiplied both 
into b d, and into the fraction prefixed to O for the quartz, and 
to M for the mica ; or if we would include the whole ring, as 
E is the same for all the columns contained in it, we must 
multiply b d by the numbers denoting the proportion of 
quartz or of mica in the whole of that ring. Thus in ring 5,. 
the first in the preceding table, the whole quartz = 11.4, the 
