128 DESCRIPTIVE BOTANY. PART I. 



1> 9> 17, &c. on one of these spirals; then counting 

 the number (viz. five) which lie parallel with I, 6, 11, 

 &c., and which run in a contrary direction, we can 

 also fix those numbers, upon that spiral : and it is easy 

 to see that, as these two sets of spirals intersect one 

 another, we may fix numbers to every other spiral 

 parallel to each of them, that is, to every scale ; and 

 thus the position of the generating spiral becomes ap- 

 parent, by observing the scales on which the numbers 

 1, 2, 3, &c. occur, in succession. We may easily count 

 the number of parallel spirals of the same class, even in 

 a mere segment of a cone, by observing the intersections 

 which they make with a circle drawn round it ; and, where 

 the cone is complete, they may be counted, by observing 

 how many lie between the coil which completes a length, 

 in one of them. Thus the spiral 1, 6, 11, 16 . . . 38, 

 46, 51, 56, has four others lying parallel to it, and 

 between two of its successive coils ; there are, therefore, 

 five such spirals in all, and, consequently, the common 

 differences on them are five. Looking to the truncated 

 edge, we might ascertain the same fact, by observing 

 that five such spirals meet it in the scales 59, 6l, 58, 

 &c. Also eight parallel spirals meet it in the scales 

 54, 59, 56, 6l, 58, &c. ' But even without numbering 

 many of the scales, we may ascertain, first the deno- 

 minator, and then the numerator, of the fraction which 

 expresses the divergence. We need only place the num- 

 bers 1, Q, 17 in one direction, and then pass from 17 to 

 22 in another direction, and we arrive at the scale 

 placed vertically over number 1 ; and thus we know that 

 21 is the denominator of the fraction. To find the nu- 

 merator, we must fix the scales 2 and 23 the latter 

 ranging vertically over the former ; and then fixing all 

 the scales that lie between the verticals (1, 22,) and (2, 

 23), which we shall find to be 9, 17, 4, 12, 20, 7, 

 15 through each of which other verticals may be 

 drawn we obtain the angular distance between 

 any two vertical lines, viz. $ of a circle : and this 

 gives the number 8, for the required numerator. This 



