248 HENSLOW'S VIEWS. [BOOK i. 



Professor Henslow, in observations printed for private circu- 

 lation ; and I am happy to be able, by the permission of their 

 author, to lay them in this place before the public. 



" The scales on a cone of the Spruce Fir (Abies excelsd) are 

 placed spirally round the axis, at equal intervals ; and after 

 eight coils of the spiral, the twenty-second scale ranges verti- 

 cally over the first. If this arrangement be referred to a 

 cylinder, and then projected on a plane cutting its axis at 

 right angles, the angular distance (Divergence) between two 

 contiguous scales, seen from the centre, is VT of the circum- 

 ference. Hence the divergence of the generating or primary 

 spiral -/Y. The various peculiarities of the secondary spirals 

 which result from the above arrangement, may be seen by 

 inspecting^. 54. 



A. If any figure in this circle represent the divergence of 

 a spiral, the same will also represent the number of coils 

 which that spiral must make before the twenty-second scale 

 upon it comes vertically over the first. 



B. The figures in this circle (corresponding to the several 

 divergencies in A.) show the number of similar and parallel 

 spirals which must be coiled round the cylinder, in order 

 that every scale may range upon them. 



The same figures also indicate the height of each spiral 

 viz.: either the comparative lengths of the vertical lines 

 between scales 1. and 22. or the distance between two hori- 

 zontal circles through scales 1. and 2,; and, lastly, 



These figures are the common differences in the different 

 arithmetic series apparent on the consecutive scales of each 

 spiral. 



C is the arrangement of the first twenty-one scales on the 

 generating spiral. 



D shows the number on the scales which begin a second 

 series of each kind of spiral, i. e. the numbers on their twenty- 

 second scales. 



N.B. The number on the scale which begins a fresh series 

 of any spiral is found by the formula (a + 21 B) where (a) = 

 the number on the scale beginning a former series of the 

 spiral, and B the common difference of the numbers on two 

 contiguous scales. 



