T^] 



Introduction 



Ixxv 



multiply by plus aud minus abscissae increasing by units — the 'working unit.' 

 Thus an error made in an early moment may be carried on to the later moments. 

 To control the results Table L was calculated a number of years ago, and from it 

 the fourth moments for such frequencies as most usually occur can be read off at 

 sight, and the raw fourth moment column thus tested before proceeding further. 



(i) 



(ii) 



(iii) 



(iv) 



(V) 



(vi) 



(vdi) 



Head 

 Length 



Frequency 



Abscissa 



JV^i' 



Nv,^ 



^^3' 



^■^4' 



Table L 



171 



1 



-20 



- 20 



+ 400 



- 8,000 



+ 160,000 



160,000 



3 



1 



19 



19 



361 



6,859 1 130,321 ; 130,321 



S 



2 



18 



38 



648 



11,664 209,952 1 209,952 



k 







17 



— 







— — i — 



3 



3 



16 



48 



768 



12,288 196,608 , 196,608 



6 



3 



15 



45 



675 



10,125 1 151,875 151,875 



7 



5 



14 



70 



980 



13,720 ^ 192,080 ! 192,080 



8 



7 



13 



91 



1,183 



15,379 199,927 199,927 



9 



12 



12 



144 



1,728 



20,736 



248,832 



248,832 



180 



13 



11 



143 



1,573 



17,303 



190,333 



190,3.33 



1 



17 



10 



170 



1,700 



17,000 170,000 



170,000 



2 



28 



9 



252 



2,268 



20,412 



183,708 



183,708 



S 



24 



8 



192 



1,536 



12,288 



98,304 



98,304 



4 



43 



7 



301 



2,107 



14,749 



103,243 



103,243 1 



5 



53 



6 



318 



1,908 



11,448 



68,688 



68,688 



6 



57 



5 



285 



1,425 



7,125 



35,625 



35,625 



7 



55 



4 



220 



880 



3,520 



14,080 



14,080 



8 



68 



3 



204 



612 



1,836 ' 5,508 



5,508 



9 



83 



2 



166 



332 



664 1,328 



1,328 



190 

 1 



2 



85 



96 



102 



- 1 





 + 1 



- 85 



+ 85 

 + 102 



85 



+ 85 

 + 102 



85 

 102 







+ 102 



+ 102 



S 



79 



2 



158 



316 



632 



1,264 



1,264 



Jt 



83 



3 



249 



747 



2,241 



6,723 



6,723 



5 

 G 



7 



66 

 66 

 56 



4 

 5 

 6 



264 

 330 

 336 



1,056 

 1,650 

 2,016 



4,224 



8,250 



12,096 





16,896 



16,896 

 41,250 

 72,576 





42,250 





72,576 



8 



43 



7 



.301 



2,107 



14,749 



10.3,243 



103,243 i 



9 



35 



8 



280 



2,240 



17,920 



143,360 143,360 



200 



30 



9 



270 



2,430 



21,870 



196,830 ! 196,830 



1 



20 



10 



200 



2,000 



20,000 



200,000 200,000 



2 



24 



11 



264 



2,904 



31,944 



351,384 1 351,384 



S 



14 



12 



168 



2,016 



24,192 



290,304 , 290,304 



k 



13 



13 



169 



2,197 



28,561 



371,293 371,293 



5 



8 



14 



112 



1,568 



21,952 



307,328 , 307,328 



6 



3 



15 



45 



675 



10,125 



151,875 151,875 



7 



6 



16 



96 



1,536 



24,576 



.393,216 



393,216 



8 







17 



— 



— 



— 



— 



— 



9 



1 



18 



18 



324 



5,832 



104,976 



104,976 



210 



1 



+ 19 



+ 19 



+ 361 



+ 6,859 



+ 130,321 



130,321 



Totals 



1306 



— 



+ 



+ 



+ 



+ 



— 



hi 



