328 



SUMMARY AND CONCLUSIONS. 



GENERAL CRYSTALLOGRAPHIC CHARACTERS OF THE 

 HEMOGLOBIN CRYSTALS. 



The constant recurrence of certain angles in the hemoglobin crystals of 

 different species, even when the species are widely separated zoologically and 

 when their crystals belong to various systems: 



On examining the tabulations of the crystallographic characters given 

 at the end of Chapters IX to XVIII, and comparing the prism angles 

 there recorded, it will be noticed that the majority of these angles are 

 found to approximate to a few angles or to he in one of a few groups. The 

 most common angles are those lying near 88, 76, 66, and 60. On exam- 

 ining these angles more carefully they can be grouped a little more exactly. 

 A considerable number are exactly 60 and 90 (mainly of crystals of the 

 hexagonal and tetragonal systems), but leaving these out of account for 

 the moment, the rest (monoclinic and orthorhombic) may be arranged into 

 groups that approximate 88, 82, 73, 66, 61, 58, and 36 to 37. On aver- 

 aging these groups, and comparing the average axial ratios that may be 

 computed from them, they may all be reduced to a series of ratios; when 

 it may be seen that the ratios computed from these angles stand in a simple 

 relation to each other and form a series. From averaging of these angles 

 in the groups near 88, 76, 66, and 58, in each of which groups there are 

 many examples, a normal value for the ratio underlying the series which 

 may be taken as of unity for the angles near 88, the following average 

 values for these angles may be computed: 88 36', 75 56', 66 5', and 58 17'. 

 These stand in simple relation with each other as follows : Calling the ratio 

 from the angle 88 36' a ratio of 1:1, then the angle 75 56' gives the ratio 

 5:4; the angle 66 5' gives the ratio 3:2, and the angle 58 17' gives the 

 ratio 7:4. 



The series can readily be extended to include the other simple ratios, 

 and table 51 gives the ratios that have been computed on the basis of the 

 above mean angles, beginning with the angle 88 36' as having the ratio of 

 1:1. The figures from which the ratios are established are the cotangents 

 of the semi-angles of the prisms, which are also added to the table. All of 

 these ratios here tabulated, with the exception of those given in parentheses, 

 are ratios of the fifth complexity series of Victor Goldschmidt, as derived 

 by his Law of Complication: 



TABLE 51. Simple ratios and mean angles computed from 

 them for ratio of 1 : 1 =88 63'. 



