Beatrice M. Cave and Karl Pearson 
343 
extetit spurious. For if /j, I^, ... 1^ be the individual indices and 1^ the synthetic 
index, then = yV (-^i + -^2 + ••• +-^1") ^"^^ ^'^y individual index Iq, if there be no 
correlation between such individual indices, would give 
and accordinolv 
1 s (I, - 1) {I, - 1,) = s [I, - i,y 
10^'^.' 
1 
•'s 
■s/a\ + (t\ + ...+a\ 
J-i -'2 •'10 
TABLE I. 
Professor Mortara's Table of Index Values of Italy. 
Numerical Index (Mean 1901— 1905) = 100. 
Year 
Eailways 
Shipping 
Revenue 
International 
Commerce 
a c 
A a 
"y* ^ 
6 — 
Cu <1J 
H 
-r. 
SavinRR 
Banks 
Coal 
0 
cj 
0 
H 
Synthetical 
Index or 
Arithmetic 
Mean Index 
188.5 
61 
63 
78 
72 
38 
82 
47 
53 
82 
98 
67-4 
1886 
62 
63 
79 
74 
40 
87 
53 
52 
86 
94 
69-0 
1887 
68 
73 
82 
78 
42 
94 
55 
64 
88 
91 
73-5 
1888 
70 
71 
83 
62 
43 
98 
57 
69 
86 
81 
72-0 
1889 
71 
77 
85 
70 
45 
99 
58 
71 
86 
78 
74-0 
1890 
72 
78 
66 
66 
46 
97 
59 
78 
87 
81 
75-0 
1891 
72 
72 
85 
60 
48 
96 
60 
70 
88 
80 
73-1 
1892 
71 
75 
86 
64 
51 
96 
64 
69 
89 
80 
74-5 
189.3 
70 
70 
85 
64 
55 
95 
65 
66 
90 
73 
73-3 
1894 
72 
72 
86 
63 
57 
93 
65 
84 
89 
71 
75-2 
1895 
73 
76 
89 
66 
60 
92 
68 
77 
88 
70 
75-9 
1896 
75 
77 
90 
67 
64 
94 
70 
73 
88 
73 
77-1 
1897 
78 
80 
90 
68 
68 
96 
73 
76 
87 
75 
79-1 
1898 
81 
84 
91 
78 
73 
96 
75 
79 
89 
78 
82-4 
1899 
86 
88 
93 
88 
75 
96 
79 
87 
91 
82 
86-5 
1900 
89 
89 
94 
91 
78 
96 
83 
88 
92 
82 
88-2 
1901 
90 
91 
96 
92 
85 
96 
87 
86 
95 
92 
91-0 
1902 
96 
99 
98 
95 
93 
97 
92 
96 
97 
94 
95-7 
1903 
101 
103 
99 
99 
103 
99 
99 
99 
99 
102 
100-3 
1904 
105 
102 
101 
103 
111 
101 
107 
105 
102 
103 
104-0 
190.5 
108 
105 
105 
111 
108 
107 
115 
114 
106 
109 
108-8 
1906 
119 
123 
108 
132 
107 
115 
127 
137 
109 
118 
119-5 
1907 
126 
125 
108 
144 
114 
120 
144 
148 
115 
125 
126-9 
1908 
134 
129 
113 
1.39 
122 
120 
155 
1.50 
124 
132 
131-8 
1909 
139 
140 
121 
149 
132 
123 
168 
165 
131 
140 
140-8 
1910 
146 
146 
129 
159 
140 
130 
180 
166 
138 
147 
148-1 
1911 
155 
156 
135 
167 
149 
136 
187 
171 
144 
153 
155-3 
1912 
165 
169 
138 
179 
158 
141 
192 
179 
151 
160 
163-2 
Mean 
94-8 
116-3 
97-6 
96-4 
82-3 
103-3 
95-9 
99-0 
I 
100-6 
1 
98-6 
96-5 
44—2 
