* 
404 Description and Use of 
Proceed as above, and press down the points in the 4th 
grand division, and C will fall against the 5th point, from 
which draw a line to B. Then make CD equal to Al, and 
draw DE parallel to CB, and BE will be the length of 
eight divisions on the line AB, to which apply the instru- 
ment and finish the division. 
When the division can be made with one remove of the 
instrument, it may be easily done by trial without drawing 
an additional line. - 
To divide any line AB into a given number of equal 
parts, each greater than 1, but less than 2, of the greatest 
divisions that can be made by the instrument. 
Rule. 
1. Draw AC (fig. 2.) making any angle with AB. 
2. With the instrument drawn to its greatest extent, 
make the required number of divisions along AC, the last 
point being at C. 
3. Join CB, and parallel thereto draw lines from all the 
points to AB; or, without drawing the lines, make marks 
in AB, which will then be divided as required. 
Let the greatest division that can be made by the instru- 
ment be called D. 
Then, to divide AB into any number of equal parts, each 
greater than 2 D, but less than 3 D, : 
Rule.—Mark AC with twice the required number of 
divisions, each equal to D, and having joined CB, draw 
parallels from every 2d point in AC to AB, or make marks 
therein. 
If the divisions to be made on AB are greater than 3 D, 
but less than 4 D, 
Mark AC with three times the required number of divi- 
sions, each equal to D, and draw parallels from every 3d 
point, &c. 
N.B. When the divisions on AC are nearly equal to 
those on AB, the angle at A may be small ; but it will be 
best to make it larger as the difference is greater. 
The length of a line being given in inches, to divide it 
into a given number of equal parts by the lines of t and 3 
inches on the scale. 
Rule. 
Multiply the number of inches by 2 or 4, to bring them 
into half or quarter inches. Then say, 
As the number of parts given: to the number of parts 
in the sectograph: so is the length of the line giyen to the 
Jength of one extent of the sectograph. Take 
