NA TURE 



[November 5, 190S 



o 



IRE LIME TREE AND ITS PRODUCTS.' 



NE of the most promising of the newer industries of 

 the West Indies is the cultivation of limes. Lime 

 products, at the present time, form the principal exports 

 from the island of Dominica, and are second only to cotton 

 in the island of Montserrat. Large tracts of land have 

 recently been taken up in British Guiana for the cultiva- 

 tion of lime trees, and progress is being made at St. 

 Lucia, Carriacou, and elsewhere. 



Lime fruits in a fresh condition are now largely ex- 

 ported from Dominica to New York, London, and Man- 

 chester. They can be used for every purpose to which the 

 lemon is put, and are considered more economical. Raw 

 lime-juice is e.xported for making cordials, and the concen- 

 trated juice forms one of the principal sources of com- 

 mercial citric acid. The essential oil, both hand-pressed 

 and distilled, is of value in perfumery. 



The tree appears to be confined to tropical and sub- 

 tropical zones, and has not nearly so e.xtensive a range of 

 growth as the orange or lemon. In these circumstances 

 the West Indian Department of Agriculture is well advised 

 to issue clear and popular instructions for planting and 

 cultivating the tree, and for dealing with the various 

 products. The Department has, indeed, gone further, and 

 has distributed many thousands of lime plants ; in con- 

 sequence, the value of the e.xfiorts last year from Dominica 

 was more than 77,000!. Of the two varieties, the ordinary 

 spiny and the spineless, the juice from the latter appears 

 to be the purer and richer in acid. 



" The .A. B.C. of Lime Cultivation " is drawn up by Mr. 

 Joseph Jones, curator of the Botanic Station at Dominica, 

 and Mr. J. C. Marintyre, a large grower. It gives a 

 concise but eminently readable account of the crop, and 

 merits more than a local circulation. 



Dr. Watts deals in the West Indian Bulletin with the 

 question of citric acid. It appears that manufacturing 

 chemists prefer buying calcium citrate rather than the 

 concentrated lime-juice, and Dr. Watts describes methods 

 of preparing the salt. Chalk is added in proper quantity 

 to the juice, and the precipitated citric acid is allowed to 

 settle, is then washed with hot water and dried. At 

 present drying constitutes a great difficulty ; the experi- 

 ments show that a centrifugal machine works well, but 

 the best tvpe still remains to be determined, and many 

 other details of the manufacture have also to be worked 

 out. 



The whole industry appears to be a very promising 

 addition to the resources of the West Indies, and the 

 Department of Agriculture is to be congratulated on the 

 vigorous action it is taking. 



MATHEMATICS AND PHYSICS AT THE 



BRITISH ASSOCIATION. 

 T^HE president of Section A (Mathematical and Physical 

 ■^ Science) delivered his address on Thursday, Sep- 

 tember 3. This address has already appeared in full in 

 Nature of September 3 (p. 425). It was followed by an 

 important discussion on the isothermal layer of the atmo- 

 sphere. Of this, also, a detailed account has already been 

 given in Nature (October 1, p. 550). 



Prof. W. F. Barrett (who was one of the vice-presidents 

 of the section) concluded the morning's proceedings with 

 an account of an ingenious combined optometer and 

 entoptiscope. On meeting again after lunch various re- 

 ports of committees were taken. The committee on 

 improving the construction of practical standards for 

 electrical measurements directed special attention to the 

 conclusion of the electrical measurements of certain of the 

 fundamental units which have been in progress for some 

 time at the National Physical Laboratory. The E.M.F. 

 of the Weston cadmium cell as set up in the laboratorv 

 is given as i-oi83„ at 17° C. Six forms of silver volta- 

 meter give (with proper precautions) the value 1-11827 



1 "The A. B.C. of Lime Cultivation" (Imperial Dept of .'\griculture for 

 the West Indies, 190S.) 



Bulletin 0/ the Department of Ainnculture. Jamaicn, 1008. Vol. vi. 

 Parts ii. and iii. ■ ^ 



West Indian Bulletin. Vol, viii., pp. 167-172. 



milligrams for the silver deposited by i ampere per 

 second. There are two important appendices to the re- 

 port : — (i) on the secular changes of the standards of 

 resistance at the National Physical Laboratory, by F. E. 

 Smith ; and (2) specifications for the practical realisation 

 of the definitions of the international ohm and international 

 ampere, and instructions for the preparation of the 

 Weston cadmium cell. The other reports read were those 

 rendered by the committees on kites, geodetic arc in South 

 Africa, meteorological observations on Ben Nevis, and 

 magnetic observations at Falmouth Observatory. 



The large number of papers down for reading in this 

 section made necessary a separation on three of the days 

 into three departments, which sat concurrently. This 

 trifurcation began on Friday, September 4. The mathe- 

 matical department began with the reading of the report 

 of the committee on the further tabulation of Bessel func- 

 tions. Dr. T. W. Nicholson then communicated some 

 formulae useful for the computation of BcsscI functions 

 when the order and the argument are both large. Dr. 

 E. W. Hobson followed with a paper on Sir W. Hamil- 

 ton's fluctuating functions. In this paper Dr. Hobson 

 reviewed and criticised Hamilton's work, and he specially 

 directed attention to the extraordinarily sure instinct with 

 which Hamilton anticipated many of the results of the 

 modern theory of the definite integral, and steered clear 

 of the many pitfalls which surround this particular sub- 

 ject, in spite of the imperfect and often erroneous ideas 

 on this matter which were current at the time among 

 mathematicians. Prof. Lamb, in the discussion which 

 followed, referred to this point, and remarked that the 

 inaccuracy of the methods of the older analysts was often 

 more apparent than real, because they tooli for granted 

 much of which they were aware, but which it is now 

 the fashion to write down explicitly. 



Dr. S. H. Burbury then read a paper on the law of 

 pquipartition of energy, in which he showed that this 

 law was really independent of the Boltzmann-Maxwell 

 assumption that the variables were uncorrelated. Prof. 

 J. C. Fields gave an account of a new proof of a theorem 

 recently discovered by himself, to which he has given the 

 name of the complementary theorem. The full statement 

 of the theorem, which deals with properties of algebraic 

 functions of a complex variable, is somewhat long, but 

 the theorem is of a most general character, and includes 

 a large number of important results previously known. 

 Mr. Robert Russell explained a new method of introducing 

 the elliptic functions. Denoting the expression 



by /(.v), and by 5 one root of /(.i;) = o, he considered the 

 functions 



" h s.'f(x) '' > vy(j) 



He then showed by simple reasoning that the expression 



x-y 

 U-d){y-S) 



was invariant for transformations of the type 



A- = (/^- + «)/(/'{ + «/) 



and thence that a function <^ existed such that 



NO. 2036, VOL. 79] 



{x-S){y-t) 





This function ^, then, turns out to be no other than the 

 ordinary ir- function, which, in this method, is therefore 

 fundamental. 



Mr. Russell also gave a new proof of Legendre's identity 



EK' + EK-KK' = '' 

 2 



Commenting upon the paper, the chairman (Prof. A. E._H. 

 Love) mentioned that he had recently devised a physical 

 proof of Legendre's identity by considering the magnetic 

 potential of a circular current. 



