November 25, 1915] 



NATURE 



337 



English-Kafir dictionary. Such works as those 

 under review are, of course, valuable, but they 

 would be twice as useful if, in addition to Kafir- 

 Kng-lish, an Eng-lish-Kafir section was added. 

 English-speakinjj;^ people ia South Africa will not 

 find the work now under review of as much use 

 or importance as philologists, because it will need 

 endless searching to find therein the equivalent 

 of some English word which they wish to translate 

 into Kafir. 



Mr. McLaren, in compiling the work under re- 

 view, acknowledges his great indebtedness to the 

 previously published monumental dictionary by 

 Dr. Kropf, and to the great Zulu Dictionary of 

 Bryant. Unfortunately, like most writers on the 

 Kafir dialects, he adopts the South African ortho- 

 graphy, which is devised without any regard to 

 the existence of other languages in the world re- 

 quiring to be speHt phonetically, and which ignored 

 most of the suggestions made by Lepsius in his 

 standard alphabet. To express the three or the 

 four clicks used in the South African Bantu the 

 letters c, q, and x are borrowed, oblivious of the 

 fact that all are required and have long since been 

 used in other phonetic systems to express the 

 English ch, the Arabic (j, and the Greek \. The 

 Arabic guttural Q is of such common occurrence 

 all over the world in languages too numerous to 

 catalogue, that the symbol q is required for its 

 expression, and is made use of more logically 

 since this Semitic letter, borrowed by the Greeks 

 and the Romans, had in Phoenician almost cer- 

 ^ tainly the sound of the Arabic ^J. In my own 

 work on phonetic spelling, and in my study of 

 the Bantu languages, which is gradually being 

 printed by the Oxford University Press, I have 

 been obliged to devise sf>ecial type to indicate 

 the clicks, because the symbols offered by 

 Lepsius were too confusing to the eye when 

 written or printed. 



The term " Kafir " is, of course, exasperating 

 to the logical mind, as it is nothing more than 

 the Arab term "unbeliever," but it seems to have 

 become permanently established in South Africa, 

 and cannot be set aside — though why linguists 

 like Mr. McLaren should wish to spell it with 

 two f *s instead of one is what I cannot understand. 

 There is no general term other than Kafir to in- 

 clude the closely allied western dialects of the 

 Zulu species-^Xosa, Tembu, Pondo, Pondomisi, 

 Xesibe. The other well-marked dialects on the 

 t ast and north are Zulu and Swazi. The 

 "Angoni" of Gazaland (reaching also to Nyasa- 

 land) is perhaps a fourth sub-species. To those 

 who cannot afford the big, heavy, and expensive 

 (but most valuable) Kafir-English Dictionary of 

 NO. 2404, VOL. 96] 



Dr. Kropf, the work under review will be useful, 

 as it is light, compact, clearly printed, and priced 

 at only 35. 6d. 



(2) Chikaranga is, as Mr. C. S. Louw informs us 

 in his preface, the language spoken by the natives 

 of Mashunaland in southern Rhodesia. It is a lan- 

 guage divided into several well-marked dialects, 

 and the general name of these is more correctly 

 spelt (as it is pronounced) Karana. The 

 Karana language is the southernmost member of 

 that far-spread Nyanja group, which extends over 

 the Shire basin half-way up Lake Nyasa, and 

 includes most of the tongues of the lower Zambezi 

 and of the Zambezi valley as far west as the 

 j vicinity of the Victoria Falls. The book under 

 review is quite the best manual as yet published 

 I on this important speech. It consists of a gram- 

 1 mar, exercises, and a copious vocabulary, virtually 

 j a dictionary, English-Karana and Karana-English. 

 ! It is published by Philpott and Collins, Bulawayo, 

 and it is a pity that no indication is given of any 

 London agency, for the work is sure to be in re- 

 quest in that ever-widening circle of Bantu stu- 

 dents, not only for its philological interest, but 

 because a knowledge of Karafia is of really great 

 importance to those who are proposing to settle 

 and work in southern Rhodesia and adjoining 

 portions of Portuguese south-east Africa. 



H. H. JOHNSTOX. 



FINITE DIFFERENCES FOR ACTUARIES. 

 Elements of Finite Differences, also Solutions to 



Questions set for Part I. of the Examinations 



of the Institute of Actuaries. Second edition. 



By J. Burn and E. H. Brown. Pp. iii + 289. 



(London : C. and E. Layton, 1915.) Price 



I05. 6d, net. 

 ''1~^HE first edition of this work, which is in- 

 X tended for students preparing for the first 

 examination of the Institute of Actuaries, ap- 

 peared in 1902. The present edition only differs 

 from its predecessor in the addition to part i. of 

 an alternative demonstration of Lubbock's formula 

 for approximate summation, and of three chapters 

 dealing with Stirling's Interpolation Formula, 

 Interpolation for functions of two variables, and 

 Interpolation of inverse functions. 



The first two chapters give a clear and straight- 

 forward exposition of the elementary processes 

 and formulae. In the chapter on Interpolation, 

 the usual Finite Difference methods and that of 

 Legrange are given. In the case of a function 

 which is given for n non-equidistant values of 

 the variable, it is suggested that a possible method 

 of procedure is to assume 



U^ = A + B.r+C.t«+ . . . +D.r"-'. 



