366 Mr. R. Campbell on the Uniformity 



which it would give us to see such a number in the tables. Why 

 is this ? Simply because we started with the hypothesis that we 

 knew nothing about laws regulating the phsenomena and causing 

 either uniformity or variety. Now this hypothesis was morally 

 incorrect in this respect. For we knew this at starting, that 

 such laws may exist ; and if the degree of uniformity or the 

 reverse in the real tables present a striking contrast to that which 

 we should expect from the result of our hypothesis, we may 

 fairly be led to the conclusion that such laws do exist, and that 

 our tables justify us in looking for causes to explain their re- 

 markable features. 



For example, take tt = 5, 6 = 242, and suppose n large in com- 

 parison. (These are the figures referred to in Mr. Buckle's in- 

 troduction as those representing the suicides in our metropolis 

 for the five years 1846-50 inclusive; the numbers being in 

 1846, 266; 1847, 256; 1848, 247; 1849, 213; and in 1850, 

 229, as quoted from the 'Assurance Magazine.'') 



Our formulae will then become — 



_ 5 X 242-242+ 1 _ 969 

 ^^~ 4x242 "~968' 



969 X 970 



968 X 964' 



969 X 970 X 971 

 968 X 964 X 960' 



and so on. 



4-243 

 968 



_ 972 

 "■ 968' 

 ^ 972 X 976 



"^ 968x967' 



973 X 976 X 980 , 



"^= 968x967x966''^^^'°"°- 



Working out the results, we shall find the probability of the 

 number 242 occurring in a given year to that of 241, 240, &c. 

 occurring, in the following ratios : — 



242 

 241 

 240 



238 

 237 

 236 

 235 

 234 

 233 

 232 



•001 '•9989 

 •007i-992S 

 •019-9816 



•03G|-9654 



•059-9«5' 

 •088''9i93, 



•123 •8901 



•166 

 •218 



•278 . 



I-782 



231 11' 

 2301 !• 

 2291' 



2281' 



227:1' 



2261' 

 225 '2' 

 22412 

 223:2 

 2222' 



348^7419 



430i'6995 



524 •6560 



634 

 761 

 909 



•6119 

 •5677 



•5239 



080!-'4808 



278i-«89| 



510-3984J 



780'3596! 



221 



220 

 219 

 218 

 217 

 216 

 215 

 214 

 213 

 212 



■096h3229 



'468^2S84 

 •905[-256l! 



•422|'226i 

 •036I-I986' 



•768^1734; 



■fi4] •15061 



•693 '301, 



•958j-"i6 

 ■49 1-0953' 



21112' 

 210[14' 

 209|l7' 

 208 20' 

 207 25' 

 206;30' 

 205 37- 

 204|45' 

 203156' 

 202170- 



■0809l;i92 843^2+ "oo'-o 

 ■0682iil82 14060+ •00007 

 ■0572! 1721649500+ 



•0478 

 •0396 

 •0327 

 •0-268 

 •0218 

 •0177 

 •0142 



162 51170000+ 

 152'7fJ00000000 + 

 142 2445000000000 + 

 I &c. &c. 



