F r a n k fo r t -M u n ic h p la n e in th is a p p a r a tu s , i t w a s fo u n d b y e x p e r im e n t th a t th e a n g le fo rm e d b y th e
b a s i-n a sa l l in e w ith th e h o r iz o n ta l p la n e r a n g e d from a« 0 to 340; b y t a k in g th e m e an , th e a n g le w a s
fo u n d t o b e o n e o f a b o u t a7°.
In th e t a b le su b jo in ed is g iv e n a r e c o rd o f t h e v a r io u s o b s e r v a t io n s t a k e n , f r om w h ic h i t a p p e a r s th a t
th e la r g e s t a n g le s fo rm e d b y th e b a s i-n a s a l lin e a n d th e h o r iz o n ta l a r e u s u a l ly m e t w ith in s k u lls in
w h ich th e v e r t ic a l h e ig h t o f th e o r b it is g r e a t , w h ils t th e sm a lle r a n g le s a r e c o r r e la te d w ith n a rrow e r
o r b i t s ; s o to o , a w id e a n g le is g e n e r a l ly a s so c ia te d w i th an o r b ita l in d e x o f h ig h n um e r ica l v a lu e ,
a n a r row e r a n g le b e in g m o r e f r e q u e n t ly c o r r e la te d w ith a lo w in d e x .
TABLE XXIV showing the Correlation of the various Measures of the Orbit and the Orbital Index with the
A ngle formed by the Basi-nasal and the Horizontal, when the Skull is Oriented in the Frankfort-
Munich Plane.
N um ber. L o ca lity. O rbital
w id th .
O rbital
height.
D istance from
low er m argin o f
o rb it to thread.
A ngle fo rm ed
by basi-nasal
lin e w ith horizo
n ta l o fF .-M .
p la n e.
O rbital
in d ex.
1 European 89} 87 35 mm. 81.5° 94
II „ 86 32 29 80 88
HI „ 87 82 26 28-5 86
TV „ 87} 88} 29 28 89
V 88 38 27 80 86 1
VI „ 89 32 28 25 82
v n 84} 35 80 83 100
vm 86 83 25} 25 91
IX „ 89 87 84} 24 94 i
X „ 86 83 29 29 91
XI „ 86 80} 28 24 88
XII „ 88 82 25 25 84
XIII „ 87 81 27} 27 83
XIV „ 87 86 27} 25 97
XV „ 89 34 38 29 87
XVI „ 89 88 29} SO 84
x v n 40 86 80 26 90
x vm Egyptian 86 86 29 84 100
XIX „ 84 82 27 basion broken 94
XX „ 88 85 28 28 92
XXI 86 35 27 28 97
XXII 36 35 28 basion broken 97
XXIII „ 85 34 27 27 97
xxrv „ 89 80 27 28 76
XXV „ 87 28 26 26 . 75
XXVI „ 89 28 21} 25 71
xxvn (N. American)
t Indian J 39} 83 25 26 84
XXVIII Tasmanian 39 30 25} 28 76
XXIX ? 88 27} 25 26 71
XXX N. Guinea 85 84} 25 27 97
XXXI 1 89 87 80 27-5 94
XXXII Unknown 42 38 29} 26 90
xxxm „ 87 87 27 27 100
XXXIV „ 84 86 29} 29 105 I
XXXV „ 88 89 80} 28 102
XXXVI „ 88 83 22 25.5 89
XXXVII • „ 38 27 21} 22 71
XXXVIII Australian 84} 80 26} 25 88
N O T E I .
O n th e R e la tio n between th e C u r v e o f P r o b a b ility a s p r e s e n te d in th e f o rm o f a tru e C u rv e a n d
in B lo c k fo rm . (S e e p . 6 7 .)
F ig. 16.
F ig . 18.
A c om p a r is o n o f th e f ig u r e s h e r e g iv e n fo r th e fo rm o f th e p e r fe c t c u r v e w ill m a k e a p p a r e n t th e
fa c t th a t v a r io u s d iffe r e n c e s e x i s t . T h e th r e e f ig u r e s g iv e n in b lo c k fo rm a r e a l l d e r iv ed from th e o n e
t ru e c u r v e , an d th e d iffe r e n c e s w h ic h e x i s t a r e d u e to th e p o s i t io n o f th e m e an r e la t iv e t o th e m a in lin es
o n th e s q u a r e d p a p e r u sed . T h e f ir s t tw o g iv e s ym m e t r ic a l r e su lts , th e m e an b e in g on o n e o f t h e m a in
lin e s o f t h e p a p e r o r e x a c t l y h a l f w a y b e tw e en th em . T h e th i rd fig u r e h a s t ra c e s o f a s ym m e t r y d u e t o
th e fa c t t h a t th e m e an d o e s n o t fa ll in e ith e r o f th e tw o p o s i t io n s n e c e s s a r y fo r a s ym m e t r ic a l r e su lt .
A n e x p e r im e n t u p o n s q u a re d p a p e r w ill e n a b le th e r e a d e r t o a p p r e c ia t e th is e x p la n a t io n .
A s th e p r o b a b i l i t y o f t h e m e a n o f a n y o f o u r s er ie s fa llin g in o n e o f th e s e p o s i t io n s is v e r y sm a ll,
v e r y f ew o f t h e P r o b a b i l i t y C u r v e s g iv e n in th i s b o o k a r e s ym m e t r ic a l.
A p a r t from th e s e d iffe r e n c e s in th e b lo c k fo rm c u r v e s its e lf, a c u r v e o f th is s h a p e c a n n o t b e
a n e x a c t r ep r e se n ta t io n o f a t ru e c u r v e , b u t th e m a in p ro p e r tie s o f th e c u r v e r em a in v e r y a p p r o x im a t e ly
th e s am e . T h e m e a n is, o f co u r s e , s o a r r an g e d a s to b e th e s am e , a n d i t w ill b e fo u n d t h a t th e a r e a
an d th e a v e r a g e e r ro r in th e tw o c u r v e s a p p ro x im a t e v e r y c lo s e ly , a d iffe r e n c e a s la r g e a s o n e p e r cent,
b e in g v e r y ra re .
N O T E I I .
T h e S ta n d a r d C u r v e o f P r o b a b ility . (S e e p . 70.)
T h e r e is n o a p r io r i re a so n fo r t a k in g a n y p a r t ic u la r fo rm o f th e C u r v e o f P r o b a b i l i t y a s th e
s ta n d a rd fo rm , an d d iffe r e n t w r ite r s h a v e u s ed d iffe r e n t fo rm s .
O n e m a y b e d e r iv ed fr om Q u e t e le t ’s fig u r e s b a s e d o n th e e x p a n s io n o f ( 1 + * ) 999. W e h a v e
u s ed th is a lr e a d y in o n e in s tan c e , a n d i t h a s th e a d v a n ta g e o f b e in g th e o n e u s ed b y o th e r w r ite r s
o n th is su b je c t . S om e w r ite r s u n fo r tu n a te ly d o n o t s ta te w h a t t h e y r e g a rd a s th e s ta n d a rd fo rm . In
n e a r ly a l l c a se s th e s c a le o f r e la t io n b e tw e e n th e a b s c is s a e a n d th e o rd in a te s is d e te rm in e d fo r r ea so n s