Curves formed by Cephalopods and other Mollusks. 249 



which results may be checked, or the angle ascertained on 

 small fragments of the shell ; and since the outer and inner 

 curves have the same angle, observations on either will suffice. 

 Thus e* cot a is given by any of the following ratios : — 



AO AE EO EK 



OC J GC ? OG' MG ; 



EK 



so e 2ncota is gven by -^^, a value chiefly useful for fragments ; 



TV , XJ-lN 



-, -cots , 



and e 2 bv 



AC AE EG 

 BD ? HD 5 



MG 

 FH' or FL " 



The first of these series gives the best result on unornamented 

 shells, and the second on ornamented. To facilitate the ob- 

 taining the angle from the observed ratios, the following Table 



of solutions of the equation cot « = —^ — has been prepared, 



77 



which may at once be applied to the others by squaring or 

 extracting the root : — 



Table of Solutions of cota= — — 



77 



E. 



a. 



E. 



a. 



E, 

 1-51 



a. 



82 32 



E. 



a. 



101 



o , 

 89 49 ! 



1-26 



8o 48 



1-76 



79 48 



102 



89 38 



127 



85 39 



1-52 



82 24 



1 77 



79 42 



103 



89 28 



1-28 



85 30 



1-53 



82 17 



1-78 



79 36 



104 



89 17 



1-29 



85 22 



1 54 



82 10 



1-79 



79 30 



105 



89 7 



1-30 



85 14 



1 55 



82 3 



1-80 



79 24 



106 



88 56 



1-31 



85 5 



1 56 



81 57 



1 81 



79 18 



107 



88 46 



1-32 



84 57 



1-57 



8] 50 



1-82 



79 12 



1 ; 08 



88 36 



1 33 



84 49 



1-58 



81 43 



1-83 



79 7 



1 09 



88 26 ! 



1-34 



84 41 



1*59 



81 36 



1-84 



79 1 



110 



88 16 



1-35 



84 33 



1-60 



81 29 



1 85 



78 55 



111 



88 6 



1-36 



84 25 



1-61 



81 23 



1-86 



78 49 



112 



87 56 



137 



84 17 



162 



81 16 



1-87 



78 44 



113 



87 46 



1-38 



84 9 



163 



81 10 



, 1-88 



78 38 



114 



87 37 



1-39 



84 1 



1-64 



81 3 



1-89 



78 33 



1 15 



87 27 



1-40 



83 53 



1-65 



80 57 



190 



78 27 



116 



87 18 



1 41 



83 45 



1-66 



80 50 



1-91 



78 22 



117 



87 8 



1-42 



83 38 



1-67 



80 44 



1-92 



78 16 



118 



86 59 



1-43 



83 30 



1-68 



80 37 



1-93 



78 11 



119 



86 50 



1-44 



83 23 



1-69 



80 31 



1-94 



78 5 



1-20 



86 41 



1-45 



83 15 



1-70 



80 25 



1-95 



78 



121 



86 32 



1 46 



83 8 



171 



80 18 



1-96 



77 54 



122 



86 23 



1-47 



83 



172 



80 12 



1-97 



77 49 



1-23 



86 14 



1 48 



82 53 



173 



80 6 



1-98 



77 44 



1-24 



86 5 



1 49 



82 46 



174 



80 



1 99 



77 39 



1 25 



85 56 



1-50 



82 39 



1-75 



| 79 54 



2 



77 33 



When the ratio is > 2, we generally have to deal with evolute 



