BS Fs Scientific Proceedings, Royal Dublin Society. 
Here draw OP (fig. 7) to represent the apparent co-dip in the 
given direction ; draw PM in the direction of strike of the bed, 
and OM perpendicular to it; then OM represents the true co-dip 
of the bed. 
(x11). Given the apparent dip of a bed in each of two given 
directions, e.g. on two vertical walls of a quarry, to 
find the true dip. 
Draw OP and OQ to represent the two apparent co-dips; then 
draw PQ and OM perpendicular to it (fig. 4 or 5) ; OM represents 
the true co-dip of the bed. 
In these last three questions we have used co-dips, and there- 
fore the cotangent-scale of the protractor. It is easy to devise 
solutions involving only dips and the tangent-scale, but they are 
not quite so readily practised. ‘Thus, for question (x11), draw OX 
and OY to represent the two apparent dips, and XP and YP per- 
pendicular to them, meeting in P; then OP represents the true 
dip (fig. 2). 
We pass on to a class of questions in which our second instru- 
ment is employed in conjunction with the protractor. The truth 
of the following solutions can be verified by simple diagrams. In 
actual practice the results are read off from the instruments them- 
selves without the intervention of any diagram. 
‘(xim1). Given the thickness of a bed or group of beds, to find 
the width of its outcrop, or vice versa. 
Here we suppose the angle at which the beds meet the surface 
of the ground to be known. For inclined strata on level ground 
it is the angle of dip; for horizontal strata on sloping ground the 
angle of slope; in any other case it is found as in (1v). The ratio 
of width of outcrop to thickness is the cosecant of this angle. To 
find it graphically we place the zero-point of the scale of equal 
parts on the centre of graduation of the protractor (fig. 1), and 
bring the edge of the simple scale to the proper angle as marked on 
the cotangent-scale of the protractor; then take the reading on the 
simple scale where its edge meets that of the protractor. We 
multiply or divide by this number according as the former or 
latter of the proposed questions is to be dealt with. 
