282 Miss Sarah Marks on the 
of the limb on the point A, and open or close the rule till the 
bevel of the undivided limb is on the point B. Now press 
the plain rule down so that the needle-points enter the paper, 
and keep it in position. Slide the hinged rule up till the line 
numbered 6 on the line of reference is coincident with the line 
on the plain rule, and mark the point where the bevel of the 
undivided limb meets the line AB. Continue to move the 
hinged rule up one division at a time till the whole line is 
divided. It is evident that the ordinary method has been 
used ; for the divided limb forms a line at some angle to AB, 
and is divided into seven equal parts, and against the undivided 
limb I can draw parallel lines through the points of section 
of the divided limb cutting AB in points equidistant from 
one another. 
This is the first method of using the instrument, and is 
useful in many ways :—to artists, for squaring out their can- 
vases when they wish to enlarge or diminish their drawings, 
although the second method would perhaps be best for this if 
a very large divider were used ; to decorators, who frequently 
find it necessary to divide lines into given numbers of equal 
parts in order to get patterns into a certain space; it would 
also be useful for finding the divisions on the scales of ther- 
mometers, as the distance between the freezing- and boiling- 
points is always an unknown length. 
The second method of using the instrument is this :—Let 
ABCD be an area to be divided into any number of parts, say 
five, by equidistant lines parallel to AD or BC. Produce AD 
both ways: place the bevelled edge of the undivided limb 
along BC, open or close the rule till the end of one of the 
lines marked 5 on the bevel of the divided limb is on the line 
AD. Slide the plain rule up, taking care that it is held high 
enough for its points not to tear the paper, till its line coin- 
cides with the 5-line, and press the points firmly into the 
paper. Now slide the hinged rule up till the division marked 
4 coincides with the line on the plain rule, and draw a line 
along the undivided limb cutting AB and CD. Bring each 
of the other three divisions against the line on the plain rule, 
and draw lines as before. These are the lines required. 
It is evident that, since the angle ABC may be any angle, 
it may be a right angle, so that lines can be drawn perpendi- 
cular to AB, dividing it into any given number of equal parts. 
This method is used in finding the mean pressure in gas- and 
steam-engines by means of an indicator-diagram. 
Let A BC D (fig. 3) be an indicator -diagram, H F the atmo- 
spheric line; GH, HC, tangents at the extremities of the 
diagram perpendicular to HI’. To find the length of the line 
