552 



NA TURE 



[ Si PTl MB] i: '). 1922 



understanding oi various .1 >pei ts ol animal life. \ et 

 the In 1 1 1 :_ creature is fundamentally a unity. In trying j 

 i" make the " how ' ol an animal existent e intelligible 1 

 to "in impei feet know ledge we have, for purpo 1 oi 

 study, to whole into part-aspects and part- 



mechanisms, but thai eparation is artiiici.il. It is as 

 a whole, a single entitj . thai the animal, 01 for that 

 matter the plant, has finally and essential!) to be 

 ■ n\ 1 .1 ed We ( annol real!) understand one pari 

 without tlic other. Can we suppose a unified entity 

 part mechanism and part not ? 1 »ne pn\ il< ge 

 open to the human intellect is to attempt to comprehend, 

 not leavinj oul ol account an) ol its properties, the 

 " how " oi the In ing creature as a whole. The problem 

 is ambitious, bul its importance and its reward are all 

 the greater if we seize and attempt the lull width ol its 



icope. In the biological synthesis oi the individual it 



teemed with mind. It includes examination of 



man himsell as acting under a biological trend and 

 process which is combining individuals into a multi- 

 individual urbanisation, a social organism surely new 

 in the historj of the world. This biological trend and 

 process is constructing a social organism the coin ion oi 

 which depends mainly on a property developed so 



l" 1 hi. all) in man as to be, broadly speaking, hi alone, 



namel) . a mind actuated by instincts but instrumented 



with reason. Man. often Nature's rebel, as Sir Ray 

 Lankester has luminously said. can. viewing this great 

 supra-individual process, shape his coui ;e conformabl) 

 with it even as an individual, feeling thai in this case 



to rebel would be to sink lower rather than to continue 

 his OW n e\ olution upw aid. 



Scientific Problems and Progress. 

 Addresses oi Presidents of Sections of the British Association. 



I'm Theory of \i mbi rs. 



In his presidential address to Section A (Mathematics 

 and Physics), Prof. G. II. Hard) propounded a series 

 oi five problems ol general interest in the theory of 

 numbers, which are still awaiting solution. 



(a) 11 hen is a number the sum of too cubes, and what 

 is the number oj its representations .' The densit) oi the 

 distribution of such numbers tend-, to zero as the 

 number tends to infinity, but no simple criterion by 

 w hieh these numbers can be rei 0| nised 1- know n. The 

 least number expressible in more than one wa\ as a 

 1 729, which is t2 3 I 1 :; 0) to 3 9 s , 

 Four representations oi [9x363510 s are known, and 

 tins is apparently the largest number of such forms 

 which has been obtained. 



. . lumber the sum of Jive cubes ? Two 

 numbers. 23 and 239, require nine cubes; then are 

 fifteen numbers requiring eight, and I21 numbers 



requiring seven, the largesl ol the latter being 8042. 

 numbers probabl) disappear before reaching 



1.000.000. and possibh ii\ccuhc numbers -il-" dis 

 appear, but in huge numbers, for four-cube numbers 

 pi 1 ist for ever. 



(c) Is 2 13 ' 1 prim< 1 problem belongs to the 



.'. .1 ' perfed ' numb 1 -. ea< h ol 

 which is the sum of all its divisors including unity. 

 The numb. 1 \ 1 can be prime onl) when n is prime, 

 and lyj is the least value ol n for which the answer is 



still doubtful. Two oilier problems connected with 



the perfect numbers, for which solutions arc still sought 



are : Can a perfect number be odd ? and. are there an 

 infinite number ol perfed numbers ? 



(d) Are there infinitely many primes of the form it- + 1 t 

 The genera] di I primes is. in all i 

 solved, but much remains to be done among numbers ol 

 special form. ITc form <■/- 1 is the simplest case ol 

 the general form an- ■ 2bn 1 C, and although an approxi- 

 mate formula, which has been well tested, has been 

 obtained for determining the number of prim... theri 



immediate prospect oi an accurate proof. 

 e there infinitely many prime pairs. 

 ■ ■■ particular case of the question whether any 

 group of primes recur indefinitely. Apparently all 

 ps recur for ever with definite frequency] 



NO. 2758, VOL. HO] 



and so far as the first million numbers are con. , , tl( d 

 the propositi, in has been tested, but there is no rigid 



pi.... 1 oi its accuracy. 



Chemistry of the Sugars. 



PrINCIPAI [rviN] spent the first part of his 

 address to Section 1! (Chemistry) in discussing the 

 new responsibilities which devolve upon scientific 

 who take advantage oi the Eacilitie 



b) the Departmenl Oi Scientific and Industrial Re- 

 search (sec \ \ I 1 RE, Jill)' 22. p. 131 ). 



la. iecond section of the address was devoted to an 

 account oi how investigations on the sugars cat ried ou1 

 in the St. Andrews' Laboratories for many years are 

 \ doped so as to include the structural problems 

 of the polysaccharides. These compounds are shown 

 to be composed oi comparatively simple units, as 



indicated below . 



re. a-Cellulose gives a trimethyl derivative as 

 the maximum substitution product, and this in turn 

 yields on hydrolysis only 2-. 3-, 6-trimethyl glucose. 

 The simplest formula for cellulose would thus be an 

 anhydro-di-glucose, each hexose residue being sub- 

 stituted in positions r and 5, but, in order to 

 modate the yield of cellobiose obtained from cellulose, 

 the molecule for the latter is held to be that oi .1 111- 

 ;-anhydi oglui ose). 



Starch. The methylation of starch gives a product 

 ontains seven methyl groups for every unit of 

 eighteen carbon atoms. These are distributed in such 

 a manner that one glucose residue contains three meth\ 1 

 groups, while two such groups are present in each of 

 the remaining glucose residues. Starch is thus based 

 on an anhydro-trisaccharide to which a structure has 

 been as< ribed. 



Inulin. — This polysaccharide is known to be com- 

 posed entirel) oi ; fructose residues, and each oi these 

 has now been shown to be identical in structure. It is 

 in the meantime premature to say if inulin is derived 



from the simple unit l', ; ll 1(l 5 or from the double or 



triple multiple oi this, but in any event the 

 residues are symmetrically disposed. 



A .lose Structural relationship has thus been estab- 

 lished between \a) cellulose and starch. (6) starch and 

 I . (c) inulin and sucrose. 



