an Instrument called The Sectograph. 405 
' Take this extent between the extreme points from the 
line of half or quarter inches (as the case may be), and this 
extent applied to the given line will divide it as required. 
Examples. 
1. Let it be required to divide a line of 5 inches long 
into 17 equal parts ? 
Here 5 x 2=10 half inches. Then 
As 17: 8::10:4°706 nearly. Take this number be- 
tween the extreme points of the sectograph from the line 
of half inches. Then apply it to the given line, and it 
will divide it as required. 
2. To divide a line of 64 inches long into 37 equal parts? 
Here 64 x 2=13 half inches. 
Then, as 37 :8::13: 2°811 nearly, to be taken from the 
Jine of half inches, as in the last example. 
3. To divide a line of 143 inches long into 23 equal 
parts? 
Here 142 x 4=59 quarter inches. Then 
As 23: 8:: 59: 20522 nearly, to be taken from the line 
of quarter inches. ; 
4. To divide a line of 25% inches long into 31 equal 
parts ? 
_ Here 252 x4=1034 quarter inches. Then 
‘As 31:8::103°5: 2671 nearly, to be taken from the 
line of quarter inches. 
5. To divide a line of 48°35 inches long into 100 equal 
parts ? 
Here 48°35 X4=193'2 quarter inches. Then 
As 100: 8 :: 193'4: 15°472 to be taken from the line of 
quarter inches. 
If the length of the line to be divided is not given in 
inches, it may easily be found by measuring, and then di- 
vided by this method, which in some cases will be found 
to be preferable to the other. 
Use of ihe Lines on the Scale. 
The several lines on the scale, which belong to the circle, 
are adapted to the radius of the instrument, which is the 
distance between the central point and one extreme point. 
1. Of the Line of Chords. 
To raise a perpendicular, or make an angle of 90 degrees. 
Rule.—¥ ix the middle point (fig. 3.) of the instrument in 
the point B, or that from which the perpendicular is to be 
.c8 drawn, 
. 
