Editor ial 277 



For exauiple, in tlio casc ol'ii iiunual ourve |'l^ — ^|J■2,^la- I-^m/i '^"^1 ^"3 = 0) tliorcforo 

 IVoluM,. om.r „t>,= -ü7449 V^^Z^M^l^''^. 67449 V^„3, 



and a ciirvo slioukl not by tliis critei-ion alono be assiinied not to lio miriiKil iink'.s.s tlio obsoi-vod 

 ^3 is at least two or three time» as largo as 



■G7449 ./-<r^ 



(iii) Put y = 4. 



Probable error ui>, = -07449 J IHZJ^tz^^lH+l^IHtl ^ 



For tlie normal cnrve since /i3 = 0, tliis reduces to 



•67449 ./^^^'= -67449 J^ c\ 



V «l V Hl 



tlie fornier valuo being exactly the saiue expression as holds for uioments about a fixed point. 

 Pui.iiu.EM VIII. To find thc corrdation in crrurs in (wo inuments both measured from 



the mean. 



As iii the last problem : 



hfi^ =fili\ —q?i/ifi'ii-i +terwM in /(, 



fi/j,^. = fifi'.y - </&lt^\' _ 1 + terms in /(. 

 Hence : 



hfiq ßfi,. = bfiq Sfi'ij' + qq' {S/t)- fi\ _ , fi\. _ , - fy' S/i Sjx\ii\' - 1 — '/ Sh S/j'^./i'^, j + terms in h. 

 Thiia : 



+ terms in h. 

 üsing (v) and (vi) \ve find : 



^_ ^ y-\ + q'-y-',,li',,+ qq'c''l^\ - 1 m'h' - 1 - y V'(f + 1 /^' - 1 - y^'a - 1 /^ V + 1 + terms i n h 

 Putting Ä = 0, iji/ = fii, we find: 



m 

 niustrations. 



(i) Suppose 5' = 2, q' — Z, then remembering ;i, =0, 



(ii) Suppose 5 = 2, (/' = 4, 



F8 -f^2M4- W 

 fT (T T = . 



(iii) Suppose 5' = 3, j' = 4, 



M- - M.i ('4 + l-M2'V:i - -^MjA*:) " ^»^2^ 6 

 o" (T y ^ ^ 



Ms Mt l'ifi Dl 



_ Mr - 5/^3^4 + ^ ^f^gVa ~ 3f*2A '5 



. (viii). 



