135 
ment. It is the object of the observer to detect and represent 
that order by some arithmetical symbol. This may be done by 
attending closely to the fol- 
lowing directions: — Obs. 1. 
Fix upon any scale as No. 1, 
and mark the scale which 
lies in as nearly a vertical 
line over it as possible, viz., 
numbered at 22. Obs. 2. 
Note the scales which are 
below , nearest £o,and overlap 
that scale (No. 22). Obs. 3. 
Run the eye along the two 
most elevated spirals, one to 
the right hand, the other to 
theleft; and passing through 
these scales which overlap 
the scale numbered 22.* 
Obs. 4. Count the number 
of spirals (called secondary) 
which run round the cone 
parallel to these two spirals 
just observed ; there will be 
found to be eight such 
parallel spirals to the right, 
and thirteen to the left, in- 
clusive respectively of the 
two first noticed. 
17. From these obser- 
vations, a rule has been 
deduced for obtaining the 
fraction which represents 
the angular divergence of 
the so-called generating ” spiral which takes in every scale 
on the cone, in a manner similarly to those described above. 
Rule : The sum of the two numbers of parallel secondary 
spirals, viz. 13 + 8, or 21, forms the denominator, and the 
lowest, 8, supplies the numerator ; so that ^ t represents the 
angular divergence of the generating spiral. From this it is 
obvious that the scale immediately over No. 1 will be the 22nd, 
and this must commence a new cycle. 
# These spirals are shaded in the figure so as to render them more con- 
spicuous ; viz., the spiral 1, 9, 17, 25, &c., to the right ; and 1, 14, 27, 40, 
&c., to the left. I have said the most elevated spirals , because, had I chosen 
the spiral passing through the scales 1, 19, 37, 55, &c., or 1, 6, 11, 16, &c., 
the object of search would not have been obtained. 
