310 
SOUTHERN CULTIVATOR. 
paste the edges down. It will then lie evenly. Now, 
take your strip of paper, and lay it on the paper you in- 
tend to work on, placing one pin hole where you mean to 
have the centre of your circle. Put a pin into that hole, 
and tap it sufficienlty to make it stick in the table. Then 
put the point of a pencil, well sharpened, through the 
other pin hole, and by means of the pencil carrying the 
paper around the pin, as a centre, describing the circle on 
the paper. Now, from the centre of the circle draw a 
line through the circumference, and another line across 
this, just where this cuts the circumference. These two 
lines must be drawn perpendicular to each other, and they 
will necessarily be so, if the last one drawn intersects the 
first just where the first crosses the circle, provided the 
last just touches the outside of the circle. This, however, 
must not be relied on as the means of making the lines 
perpendicular, for, though true in theory, it is almost im- 
D 
C 
{Fig. 3.) 
practicable. In Fig 3 may be seen this part of the work, 
with all the rest that is required to prepare the scale that 
is to be transferred to the instrument. This figure is not 
drawn on the same scale as Fig. 1 . For being designed 
to show that equal divisions on the tangent becomes un- 
equal on the arc, it was necessary to enlarge the scale. 
It will also be seen by means of this figure that the differ- 
ence between the first three or four divisions is scarcely 
perceptible. And I have found that, with a 9 inch index 
and inch divisions for 1 foot elevation or depression, 
that one might easily fall into the error that they would 
continue equal. But to proceed with the work, the line 
A B is to be divided into quarters of inches, laying off the 
divisions each way from the point of insertion with the 
line C D. Then, with much precision, draw lines from 
these several divisions on A B, to the centre of the circle. 
The points where these lines cut the circle, are to be 
transferred to the circle made on the scale-board, c, of the 
compass. The best way to do this, is to cut your paper 
from the board or table, and then, with a sharp pair of 
scissors, to cut exactly around on the line that forms the 
circle. The round edge, so obtained, is then to be laid up 
to the circle on the scale and the divisions are to be dotted 
off on the circle of the scale. But it is all-important that 
the starting place of this scale be right. This is easily 
found. Take your compass with its v/eight suspended as 
in Fig 1, and set its feet on a floor. Mark around its feet, 
on the floor, with a pencil. Without moving it, look at 
the circle on the scale, c, and just where the index is at , 
the circle make a fine pencil-mark. Now lift up your com- 
pass and place each foot of it on the floor, exactly where 
the other foot stood when you made the pencil-marks on 
the floor. Without moving the instrument, look again at 
the circle and index. If the floor should happen to level 
your index will be again at the same place on the circle, 
and this place will be your starting point in marking ofT 
your scale. If, however, (as in all probability will be the 
case) the floor is not level your index will point to some 
other place on the circle. Make a fine pencil mark here 
also, as in the other trial. Now find the middle point be- 
tween the two marks and dot it ; this will be your stajrt- 
ing place. Take the paper that you cut out, and place 
its round edge up to the arc of the circle on your scale- 
board, taking care to put the end of the line, that was 
drawn from your centre to 0 , exactly to the place that 
you have found for your starting place, and d®t off your 
divisions numbering them each way from the starting- 
point, which must be marked 0. The instrument is now- 
finished. 
When its feet are set down, if one is an inch higher 
than the other, the index will be at 1 , on the side of the 
higher foot, and will indicate a dilTerence of one inch in 
three feet, or four in twelve, or five in fifteen. If you want 
the divisions of your scale to be subdivided into halves 
and quarters, this must not be done by making equal sub- 
divisions on the scale itself ; but they must be made equal 
on the line A B, Fig. 3, and then treated like the other 
divisions. This will put them on the circle of Fig. 3; 
from which they may be transferred to the scale on the 
compass. 
I have given directions for making an instrument, the 
compass of which strides three feet. For this reason, I 
say make the length of the index, from the axis on which 
it turns to its point, 9 inches, and then divide your line, 
A B, into quarter's of inches. The principle on which this 
ts done is as simple as it is mathematically correct — the 
ratio of 9 inches (the radius of the circle in Fig. 3, and 
also the length of the index and radius of the circle on 
the scale-board) to 36 inches (the stride of the compass- 
or radius of such a circle as it would describe) is 4; and 
the ratio of of an inch to 1 inch is 4. The line B A, fig.. 
3, is a tangent of the circle in that figure; and a line 
drawn from one foot of the compass (when standing on 
the ground) perpendicular to the earth, is a tangent to the 
circle of which the compass describes an arc, when, with 
one foot stationary the other is raised or lowered, as is 
the case in the use of the instrument, at every inequality 
in the ground. Hence the divisions of these tangents 
must bear the same proportion to each other that the radii 
of the two circles (f. e., the length of the index and stride 
of the compass) bear to each other. In making an instru- 
ment of other dimensions than those of the one I have 
described, all the variation from any directions, for making 
the scale and index, is to take a different length for the 
index; or, should it be preferable to take the same as be- 
ing a convenient length, than the divisions of the line A B, 
Fig. 3, must be varied so as to agree with the difference 
of stride between the compass, or rafter level to be used,, 
and one of 3 feet stride. By this rule the divisions of the 
line A B for an instrument of 4 feet stride would be into 
3-16 of an inch each. It would be better, however, to re-- 
tain the divisions of the line into fourths, and to make the 
index correspond, by making it one-fourth of the stride 
(i. e . , for 4 feet make it 1 foot.) The index might be made 
even 6 inches, by making the divisions of line A B ig of 
an inch instead of a 3 ^ for an instrument of 4 feet, or 4S 
inches, 6 being 3 ^ of 48. 
Now, that part of the instrument which has no neces- 
sary connection with the compass as such, can be just as 
well attached to a rafter ; and whatever ration in inches 
exists between the stride of the rafter, and the length of 
the index from the point on which it is swung, (z. e., the 
