July 31, 1890] 



NATURE 



331 



The Rocks of the Moon. — M. Landerer, in continua- 

 tion of his memoir last year on the polarizing angle of the lunar 

 surface, has just communicated to the Paris Academy the re 

 suits of some determinations of the angle of polarization of 

 igneous rocks. He finds that specimens from different localities 

 give practically identical results, the probable errors never being 

 greater than ± 5'. The polarizing angle increases from 30° 51' 

 for ophite, through syenite, basalt (31° 43'), serpentine, trachyte, 

 granite (32° 20'), diorite, diabase, andesite (32° 50'), to obsidian 

 (33° 46')- Vitrophyre, a black rock from the Rhodope chain, 

 which contains large crystals of sanidine, magnetite, and horn- 

 blende, in a fluidal, non-perlitic matrix, has a polarizing angle 

 of 2,'^° 18', which approximates very closely to that of the lunar 

 surface. Without presuming too much on this result, the author 

 regards it as at any rate an additional proof of the similarity, 

 and therefore common origin, of our earth and its satellite. 

 The fact that the polarizing angle of ice is more than 37°, is 

 another objection to M. Hirn's hypothesis of lunar glaciation. 



Brooks's Comet {a 1890). — Dr. Bidschof gives the following 

 ephemeris in Asironomische Nachrichtcn, No. 2979 : — 



Epheiiteris for Berliu Midnight. 

 1890. R.A. Dtcl. Log r. Log !^. Bright- 



h. m. s. ness. 



Aug. I. ..13 II I ...-f4S 379 ... 0-3121 ... 03714 ... I 38 



5-13 7 39 - 43 579 -• 0-3160 ... 0-3849 ... 1-27 



9. .13 5 4 ... 42 242 ... 0-3200 ... 0-3978 ... 1-18 



^Z-^Z 3 9 ••• 40 56"5 ••• 03242 ... 0-4100 ... 1-09 



17... 13 I 45 •■• 39 34-5 - 0-3285 ... 0-4215 ... I-02 



21. ..13 o 47 ... 38 177 ... 0-3330 ... 04323 .. 0-95 



25... 13 o 12 ... 37 5-8 ... 03376 ... 0-4423 ... 0-89 



29-12 59 5^5 .•• 35 55^6 ... 0-3422 ... 0-4517 ... 0-83 



Sept.2...i2 59 54 ., 34 56-1 ... 0-3470 ... 0-4605 ... 0-78 



The brightness on March 21 has been taken as unity. 



Brorsen's Comet.— Mr. E. Barnard, of Lick Observatory, 

 notes, in the above number of Asironomische Nachrichten, that 

 he has made many searches for this comet from December of 

 last year to the end of April, but with only a negative result. 

 He notes that during the search he has found several unrecorded 

 nebula". 



Two New Comets {b and c 1890). — M. Coggia, at Mar- 

 seilles, has discovered a pretty bright comet having ihe follow- 

 ing positions {Astronomische Nachrichtcn, 2980), 



Marseilles Kean Time. R.A. Dec!. 



h. m. h. rn. s. o / // 



July 18 ..... 10 31-0 ... 8 48 51-0 ... 4-44 42 48 

 19 ... 9 38*8 ... 8 55 58 ... 44 2 48 

 Mr. Denning discovered a faint comet at Bri-tol on July 23 ; 

 its position at 13 hours Greenwich mean time being R.A. 

 I5h. 12m., and Decl. -f78°. It was moving towards the east 

 {Edinburgh Circular, No. 8). ' 



A New Asteroid (aw). — M. Charlois, of Nice Observatory, 

 discovered an asteroid of the twelfth magnitude on the 15th inst. 



THE SCIENTIFIC PRINCIPLES INVOLVED 



IN MAKING BIG GUNS. 



IL 



Part U. — The Strains in the Gun. 



(29) CO far we have dealt only with the stresses in the metal, and 



•^ we have determined these stresses in the manner given 



l)y Rankine in his " Applied Mechanics," § 273, p. 290, in which 



the only assumption made is that the metal of each cylinder is 



homogeneous. But when the gun-maker wishes to set up a 



given pressure of shrinkage between two cylinders, he has to 



determine, by calculation or experiment, the slight amount by 



which, when cold, the external radius of one cylinder must 



exceed the internal radius of the next cylinder which is shrunk 



on it ; the outer cylinder being expanded by heat and slipped 



on, in order that the given initial pressure may be set up on 



the cooling of the outer cylinder ; and this, too, wlxen other 



cylinders are shrunk on afterwards. 



We must therefore determine the strains and deformations set 

 up in a given cylinder due to given applied pressures, and thus 

 we require the equations giving the strains due to given applied 



Continu.d from p. 309. 



NO. 



1083, VOL. 42] 



pression p(gi 



stresses when the coefficients of elasticity of the metal are 

 known. 



(30) Now, it is proved in Thomson and Tait's "Natural 

 Philosophy," §§ 682, 683, for a substance of which k is the 

 elasticity of volume or bulk-modulus, and n is the elasticity of 

 figure or rigidity, that when the stress is a simple longitudinal 

 tension P, the principal strains in the substance are an exten- 

 sion P{ ~ + -; j in the direction of the tension, and a com- 



-rj in all directions perpendicular to the 

 tension. 



We use the words tension and pressure, as before, to denote 

 stresses measured in terms of pull or thrust per unit area, with 

 our practical units, measured in tons per square inch ; while the 

 words extension and compression are used (in accordance with 

 the terminology of Maxwell, Everett, and Unwin) to mean the 

 strains, measured by the ratio of linear elongation or contraction 

 to the original length. 



Thus, the tension or pressure being the stress, the extension 

 or compression is the corresponding strain ; and Hooke's law 

 of elasticity {ut tensio sic vis), translated into a formula, 



gives ^^ = -^B^B. = P'^^^^"'-.^ = the modulus of 



stram extension compression 

 elasticity. 



(31) Then, by superposition, if ^,/,^ are the extensions pro- 

 duced in three rectangular directions by tensions P, Q, R in 

 these directions — 



= (3^H.^.)p-(^„-i),Q.R).... 



(31) 



with two similar expressions for / and g ; or, in Thomson and 

 Tait's notation, § 694 — 



M^ = P - <r(Q -1- R), (32) 



M/= Q - (r(R -h P), (33) 



M^o-= R - <r(P -1- Q), (34) 



where , 



+ ~-i , or M = — r 



3« 9k ' 3^ + 



so that M is Young's modulus of elasticity, the modulus which 

 is directly observable when a test-piece of the substance (steel) 

 is placed in a testing-machine, and the ratio M = P/e is ob- 

 served of P, the tension, to e, the extension, no lateral tension 

 being applied, or 



Q = o, R = o ; 

 also, 



6h + 2« 



called Poisson's ratio, is the ratio of the lateral compression to 

 the linear extension of the substance when the stress is a simple 

 tension. 



(32) Again, by independent investigation, as in § 692, or by 

 solution of the preceding equations (32, 33, 34), we find — 



p= (k+ i^y + {k- 1«)(/+^).. .(35) 



Q= (^h + A „y + (^i -A„yg + c), . . (36) 



R= (k + ±r^y+ (k- A«j (,+/);. .(37) 



or, in Lame's notation (" Theorie del'Elasticite," § 19) — 



P = A0 + 2fie, 



Q = XO -f- 2nf, 



R = xe + 2itg, 

 with 



e = a + i + c, 



the cubical expansion ; and 



\ = k - '-n, /J. — n. 



The above equations show that when the strain is given as a 

 simple uniform longitudinal extension e, the stresses consist of a 

 uniform longitudinal tension, {h + ^n)e = (A. + 2n)e, in the direc- 



