282 



♦ KNOWLEDGE ♦ 



[J AH. 37, 1882 



Cold n|i|iliiHl lo tho nurfni"*'. orcn in tl»< form of n xontlo current of 

 Kir noninwliut lowiT in tom|H'mtur<< than lh« nkin, will )iro<luc<i the 

 ** fiHtliiiK " of "r)iill." Convpfflcly n thotif^ht will ofUMi f^ivo Hno to 

 tlio " f«i'liii)( " of oohl n|iplii'd to ttio xarfiiei- — for vxiiinpli', of " cold 

 wator riiiitiiiiK ilown Ihi' lim-k." Mniiy of (ho ar-niiiitionii of cold or 

 )i>-at wliii-li nr<' rtiM'rinnriHl liy tlio hyiM'metuiilvo linvo no rxtcniul 

 cauM. 't'lit'V aro |>nn.'ly iduutioiial in th><ir niodo uf origination, iind 

 ideal in fact. — Lanrct. 



^■.llcr ,,r c.niiin s,i..v ON .Soi.rtis. — Ac-cordlnpf to tin- Hnvue 



" ■. II (Innnnn rhomixt. hn^ recently |inb- 



I . pvinff tlio rcMUltH of ii series of experi- 



. :.; ; .1 iiuin tlio effect of powerful compre«Hiou 



on tlio iiiual iliverHx liotlies. Tliu Hiilixlnncea ex|M'riniented witli 

 were taken in the form of fine ])Owder, and fiubmitted, in a Btccl 

 nioalil, to proKKurcg Taryinjf from 2,{KK» to 7,01X) atmospliorcii, or 

 about 7,000 kilo^ramnioa per ii(|Hnre centimetre. The facts observed 

 are pivcii in a series of tables, from whicli wo extract some of 

 tlio moro curious results. Lead filings, at a pri'S.iure of 2,000 

 atmoaphercs, were tran.-<fomiod into a solid block, which no 

 longer nhowod (he least K^ain under the microscope, and the 

 density <if which was 11*6, while that of ordinary lead is 

 113 only. At 5,000 atmospheres the lead became like a 

 lluid and run out through all the interstices of the apparatus. 

 The jMjwders of tine and bismuth, at 5,000 to 6,<i00 aimosphcres, 

 gave solid block having a criiiliiUiiie fracture. Towards G,iiOO at- 

 mospheres zinc and tin appeared to liquify. Powtler of prismatic 

 sulphur was transformed into a solid block of octulieilric sulphui'. 

 Soft sulphur and octahedric sulphur led to the same result as 

 jirismatic. Ucd phosphorus ap|>eurcd also to jmss into the denser 

 stato of black phosphorus. As may be seen from this, simple 

 bodies underi;o chemical transformations by the simple action of 

 |irossure. The chiuigo of amor))hou8 powders, like that of zinc into 

 crystalline ma-ssos, is a .sort of solf-conibination. Certain hard 

 ractals do not lose their pulvendent stmcturo at any pressure. 

 Binoxido of manganese and the sulphides of sine and load in 

 powder weld when compressed, and exhibit the appearance, re- 

 spectively, of natural crystallised pyrolusite, blende, and galena; 

 while silica and the oxides and sulphides of arsenic undergo no 

 agglomeration. A certain number of pulverised salts solidify 

 through pressure, and become transparent, thus provinj; the union 

 of the molecules. At high pressures the hydrated salts, such as 

 sulphate of soda, can be coinplotely liiiuefied. Various organic 

 substances, such as fatty acids, damp cotton, and starch, change 

 their appearand', lose their textnre, and consequently undergo 

 considerable molecular change. 



(Pur iHatbrmatiral Column. 



MATHEJIATICAL QUERIES. 



[30]— I find in " Todhunter's Differential Calculus" the 

 following problem : — What is the greatest equilateral triangle 

 which can bo circumscribed about a given triangle ? I am not 

 able myself to employ the methods of the " DiCfercntial Calculus." 

 Is there any way of solving this problem by geometrical methods ? 

 — No Analyst. 



[Try tlio following : — On the three sides of the triangle, describe, 

 outside tho triangle, segments, each containing an angle of sixty 

 degrees. Then it can readily be .seen that if any straight line be 

 drawn through an angle .4 of the triangle, to meet the two arcs on 

 AH, AC in P and y respectively, then I'B and QC produced will 

 moot on tho arc which has been drawn upon hC, and tho triangle 

 thus formed will be equilateral. All we have to do then is to 

 dot«rniine tho gn'atcst straight line which can thus be drawn 

 through .1 ; and it needs very little familiarity with geometrical 

 mothcHls to see that the gi-eatest straight lino which can be thus 

 drawn is the straight line parallel to the line joining the centres 

 of the arcs on AB, .)('. From this tho formula in " Todhunter's 

 Differential Calculus " for the side of the maximum equilateral 

 triangle follows at once. Ed. J 



[21] — " Znros " a«ks us to give the formulas for solving the 

 problem, Uow fast should the earth rotate that tho centrifugal 

 force at tho oquator should just counterbalance the attractive force 

 of gravity ? 



The followiug is tho solution of " '/ares' " problem : — 

 I<et T bo tho time in seconds in which tho earth should lotute 

 that tho force of gravity y Hhoiild be exactly balanced at the equator 

 by oeiitrifngal force. Let the earth's ecpiatorial radius " r. Then 

 the velocity of a point at tlio equator = i-rr-t-T, and tho contrifngal 

 tondeney whicli gravity ha-! to resiit is represented by (tho vel.)' 



ilivided by (tho nulius). Ho that when tho force of gravity is 

 exactly balanced, wo havo 



•\ T 



V;. 



whuraforc T •• 'iir 



Taking a second for the nnit of time, a foot for tho unit of length, 

 and the earth's equatorial radius as 20,025,000 ft. (the equator is 

 not perfectly circular, its greatest and least diameters differing by 

 about two miles), wo havo, in numbers, 



7-= 0-2432 ^-^^^ 



Now, i log. 20,925,000 = 30603328 

 i log. 32-2 = 0-7539279 



Difference ■= 2 90ftlO19 

 log. C'2432 = 0-7'J5M>72 



Sum = 3-7018121 = log. 5(53283 

 Therefore, T = 5032-S3 seconds 



•= 83 m. 52 83 s. = 1 hr. 23 ni. 52 83 s. 

 If the earth rotated, then, in thi.s time, or roughly in 1 hr. 21m., 

 bodies at the equator would be absolutely without weight. — Ed. 



[22] — Eqcatioxs; .VsTHOxoMiCAt PROBLESts.- Can any of yonr 

 i-eadcra give solutions of the following equations 'f 



(«) 



= a + b 



(li) 2.Cy/.i^ + a'+2x^x''-t-b 



(i.) When is Vonus brightest 



(ii.) My watch loses 5' per day. I travel eastivard at such a rate 

 that it keeps correct time. In what time shall I complete the 

 circuit ? 



(iii.) A star's meridional zenith distance and north declination 

 arc equal (^), how long is the star above tho horizon ? 



(iv.) Find the difference between the synodic periods of Jupiter 

 and Saturn with tho earth, assuming mean distances as 1 .' 5 : 9. — 

 RfEVEETE. 



[15] — By a ridiculous oversight, after sending this question (see 

 11. 258) to the printers, we dealt only with one of the equations we 

 had written down. Of course, there are two, viz. ; — 



.v(v-^5) = 1000 



'/ (i0O-j-) = 100O 

 Or, 01 4 201/ = 400, whence (100-201/) (y -I- 5) = 1000. The rest is 

 obvious. — Ed. 



0m €\)t^5 Column. 



Problem Ko. 1 1. 

 Black. 



PROBLKM No. 15. 

 Black. 



i ± 



White (o play niid "-cU" m«te 

 in two moves. 



Tho two-mover is a prize pi-obleni from the Hi'dftcnfield College 

 Majaiinc Tourney of 1877. A remarkable fact occurred in con- 

 nection with this problem. The Hudderspeld College M(viazine 

 piililished this problem in October, 1877. as composed by W. A. 

 Skinkmann. Simultaneously with this, the Free /'res* published 

 exactly the same position as composed by Mr. (i. K. C-vrponter. It 

 was afterwards ascertained that Mr. Carpenter composed his 

 problem two years prior to Mr. Skinkmann, and it was also ad- 

 iiiilted that Mr. .'Skinkmann had no cognisance of Mr. Carpenter's 

 problem. This forms a remarkable coincidence of ideas by two 



