September 23, 1909J 



NA TURE 



Z^7 



Chinese Names of Colours. 



The correspondence on the above subject, started by Mr. 

 A. H. Crook in Nature of January ii, 1906 (p. 246), was 

 lately recalled to me when I heard, for the first time, the 

 phrase " hsiieh ch'ing " (Cantonese sut„ ts'eng) — snow- 

 blue — used in conversation. It was used in this case in 

 naming the colour of a flower, and struck me as particu- 

 larly appropriate ; the colour might well be described as 

 one of those termed " ch'ing " diluted to a pale shade 

 with white snow. 



It hardly seems likely that any natural colour of snow 

 itself should be tlie origin of the phrase, or how would 

 one account for " shui hung " — water-red? The latter 

 means pink, or, as one might say, a watery and " washed- 

 out " red. Natural water of a pink colour is scarcely 

 common. 



Independently of the foregoing, though perhaps bearing 

 on it, I should like to point out how the origin of some 

 Chinese phrases may well have been obscured ; this is by 

 the substitution of one character for another nearly like 

 it in sound, but not in sense. This may be illustrated 

 by a case ii» which the change appears to be now taking 

 place. 



" Wang'' pa' " — forget eight — is a term denoting a 

 person of infamous occupation, and also a kind of tortoise. 

 This looks already suiVicIentiy obscure, but is fully 

 accounted for to the satisfaction of dictionary-makers and 

 their kind. 



It happens, however, that illiterate persons frequently 

 wish to write this name. In many cases they may not 

 know the character for " forget," but they well know that 

 for *' king " (wang-), and the slight difference in sound is 

 easily overlooked. The practice is being copied among the 

 more literate, and it seems likely that in the end " wang" 

 pa' " — king eight — will entirely supplant the original (and 

 now less common) form, and when this process is com- 

 plete a sensible derivation will be impossible without refer- 

 ence to an older literature. 



The process is almost parallel to some changes of spell- 

 ing in English, but results in more complete obscurity. 



Alfred Tingle. 



Pei Vang Mint, Tientsin. 



Percentages in School Matks. 



Mr. Cunnincii.4m's inquiry (August 5) is aimed, appar- 

 ently, at obtaining a kind of index mark for each candi- 

 date in an examination containing several papers. In 

 getting a boy's percentage mark in any one paper there 

 is no trouble ; but the question is. By what law are per- 

 centages in different papers to be combined in order to 

 get an index mark? Percentages may be combined in an 

 infinite number of ways ; which is the way Mr. Cunning- 

 ham desires ? 



Consider three papers : — (i) looking at all the questions 

 in the three papers as a whole, if marks have been 

 assigned to each question with due relativity to, all the 

 other questions, (2) if the boys have each been properly 

 prepared for all these questions, and (3) if fair time 

 has been allowed for each of the papers, then each 

 boy's inde.x mark is clearly his total marks gained in the 

 three papers divided by the total maximum marks of the 

 three papers. The whole matter may be expressed more 

 easily thus : — Let a boy gain marks x, y, z in three 

 papers the maximum marks of which are a, h, c ; his 

 index mark may be expressed by px + qy + rz, and will 

 depend on the constants />, q, r. For example, if p=i/a, 

 (7 = 1/6, r=i/c-, the index mark is x/a + y/b + s/c (or this 

 divided by 3, the mean of the averages). Again, let 

 p = l/{la + mb + iic), (j = &c., r = &c., then the index mark 

 will be (!.v-fmy-t-n3)/(/a-f-m6-f-nc), which reduces to the 

 first example when l = in = n. In this case we have still 

 the ratios I : in : n in our power. For example, suppose 

 papers set in Latin, French, and Greek, and take Mr. 

 Cunningham's numbers for them respectively, namely, 37 

 out of 50, 50 out of 50, 71 out of 100, and suppose, on 

 comparing the papers, that Latin is reckoned half as hard 

 again as French, and Greek a quarter harder than Latin, 

 then their difficulties would be Latin, French, Greek as 



NO. 2082, VOL. 81] , 



12:8:15, and it would seem fair to take these values 

 for I : III : n. Thus the index mark for this boy would be 

 (12. 37-1-8. 5o-|-i5.7i)/(i2. 50-1-8.50-1-15. 100), or 1909/2500, or 

 0-7636 (per cent. 76'36). If, however, each one of the 

 questions has had marks assigned to it relatively fair 

 when compared with the marks of all the other questions 

 of the three papers, and if the time allowed for each 

 paper is proportionate to the work required by an average 

 boy to answer the paper, then would l = m = n=i, and the 

 inde.x mark would be 158/200 (or per cent. 7900). Thus, 

 Mr. Cunningham must settle for himself, in accordance 

 with the circumstances of each case, the values of the 

 ratios I : m : n. The above includes the cases of Mr. 

 \Mialley and Mr. .•\begg, and, I believe, will cover Mr. 

 Pickering's case too, but I have tried unsuccessfully to 

 understand his numerical table. 



.\ kindred question is sometimes asked. What is the 

 master-average of a set of averages? For example, thirty 

 schools send in candidates for a paper ; each school gets 

 its own average of the marks gained by its pupils in 

 the paper (this is the mark of value for the school) ; but 

 the examining body wants some information as to how 

 the paper has been done in general, for the sake of com- 

 parison with similar papers in other years, hence a master- 

 average, or some equivalent, has to be determined. 

 .Assuming all the candidates from the whole thirty schools 

 to be equally prepared for the paper, obviously the examin- 

 ing body will obtain its desired result by dividing the 

 total sum of all gained marks by 100 N, if N be the 

 total number of candidates and 100 be the maximum marks 

 of the paper. This amounts to putting 



l = m = n= . . . . = I ; 



but if it be known that very bad work has come from a 

 certain school, and if in fairness its marks should be 

 valued at (say) one-third of 

 the general run of the 

 schools, then in this case 

 we should put 



Z = m= .... =3 

 for twenty-nine of the 

 schools, and n=i for the 

 school _in question. To add 

 the thirty averages and take 

 one-thirtieth of the result is 

 of no value at all. This is 

 easily seen from the adja- 

 cent diagrams ; in the first, 

 sixty boys have an average /. 

 of 10 marks, fifteen an 

 average of 9, and five an 

 average of 2 ; the mean of 

 the averages is (io-|-q-|-2)/3, 



or 7; in the second case, 5-15" 0.0 



five boys have an average 



of 10 marks, fifteen of 9 marks, and sixty of 2 

 marks ; the mean of the averages is still only 7. Hence 

 the same mean of averages is derived from two obviously 

 different and even independent cases. Is it not fairer, in 

 the absence of any other information, to take 



(600-1- 135+ io)/So = 9-3i and (5°+ 135+ i=o)/8o = 3-8i 

 as the means of the averages, or rather as the repre- 

 sentative index marks of the two groups of candidates? 

 In other words, is not one group about two and a half 

 times better than the other? Hence, for a single paper 

 in a number of schools, the apparently easiest plan is to 

 treat all candidates as equally well prepared, and to take 

 the inde.x mark required by the e.xamlnlng body as equal 

 to the total marks gained by all the candidates in the 

 thirty schools divided by 100 N as before ; and this seems 

 also fair. This inde.x mark may be got as the quotient 

 (ju-\-gv-\-hw+ . . . .)/ioo(f+g+h ....), where u, v . . . . 

 are school averages, and /, g, h . . . . are the numbers at 

 each school, so that f+g+ii+ .... =N. The same 

 problem Is presented to the headmaster of a school who 

 wants to get an Inde.x mark either of a form, or of the 

 work of a master, or of the whole school, for comparison 

 from year to year. J. D. Hamilton Dickso.v. 



Peterhouse, Cambridge. 



