598 



NATURE 



[June 2, 1910 



Taking a single vortex at s = Z(, at rest, let 

 w = im log(s-2„). 

 Transform by putting z=f{t), and let z^=f(t^), 

 w=im log {/(/)-/(/o)f 

 = mlog(/-/o) + //«l..g|/'(/o)+/"(/o)^"'9 • • .} 

 expanding in the neighbourhood of t = t^, and at the vortex 



—~ -mi — log (/ - /„) + - -'A 0' 

 dt d( ^^ "" 2 /Vq) ' 



the first part giving the velocity due to the vortex itself 

 and the second the motion of the vortex. The vortex will 

 not be at rest unless f"it^) — o. 



Employing Prof. Bryan's method to obtain a solution 

 giving a vortex at rest in the t plane in the cases con- 

 sidered by him, with the vortex in the t plane not neces- 

 sarily at rest, we have 



U, z — a — tb 

 : + 7M log 



'^ z-a + zd 

 z=/(t) 



Then the velocity at any point is given by 



di I z—a-ib z^a + z6j 



At the vortex the motion is given by 



omitting the infinite term due to the vortex itself. If the 

 vortex is at rest, 



^^ 2 UV,)f . • . . n) 



and if the velocity. at 2 = in the z plane vanishes, 



TT zmb , , 



^-a^ir^^=° ^^) 



Prof. Bryan's first transformation is 2 = f", so the con- 

 dition (i) becomes, since tg" = a + ib, 



m , i/n 11— \ 



+ = o . 



zb z n(a + ib) 



If n is not unity, (i) and (2) give 

 n = \, 



which lies outside the prescribed limits of n. Conse- 

 quently no solution of this type can be obtained giving a 

 vortex at -rest. 



Prot. Brvah 's second transformation is 



U 



(I) 



• Z = V?hT^. 



Condition (i) becomes in this case, since 



U 



which gives 



VI' tin ' ' .c^' 



zb z\a-^tO)\\a.+ ib f - c-\ 



a(a2_3^2_^2), 



U7U , 71 il- 



^ 2b\id'-W-c^\~ 



(1) 



(3) 

 (4) 



Equations (3), (4), and (2) cannot be satisfied by any 

 values of a, b, and m. A solution of the two-dimensional 

 problem of liquid impinging at right angles on a plate of 

 finite breadth with two stationary vortices at the back of 

 the plate and finite velocities at the edges is impossible. 



E. H. Harper. 



Mr. Harper is quite right. It would appear from his 

 investigation that it is impossible to apply the transforma- 

 tions in question to fluid motions with stationary vortices, 

 notwithstanding that a vortex transforms into a vortex, and 

 a fluid particle other than a vortex which is at rest trans- 

 forms into a particle also at rest. It is a pity that this 

 fact was overlooked, and that results were consequently 

 published which are of less interest than was supposed 

 at the time. G. H. B. 



NO. 2 II 8, VOL. St^I 



The Nutriuvtf Value of Black Breaa. 



It appears to me that the contributor of the article on 

 this subject in Nature of May 5 has overlooked one all- 

 important question, viz. how much of the nitrogen present 

 in each form of bread is actually digested. 



I had occasion to look up this question last year, as I 

 happen to be a politician who 15 " particular about his 

 facts," and I agree with your contributor in detesting 

 " allegations," political or otherwise, that are " wanting 

 in scientific accuracy." I referred, accordingly, to 

 Wynter Blyth's " Foods: their Composition and Analysis, "^ 

 and found on p. 173 a table showing " the amount of dry 

 substance, &c., absorbed in percentages of " (a) North 

 German black bread (Pumpernickel) made of whole rye 

 meal with leaven ; (b) Munich rye bread, which is a mix- 

 ture of rye and coarse wheat meal, with leaven ; (c) white 

 wheaten bread. 



The percentages absorbed were : — 



Dry substance Nitrogen 



(«) S07 577 



U') 899 77-8 



(c) 94*4 8o-i 



" It is thus shown," says Wynter Blyth, " that of the 

 black bread a person would have to eat very much more 

 than of white bread." I worked out the corollary of 

 these facts in a letter published in the Western Daily 

 Mercury of February 18, 1909, and showed that, on the 

 basis of these analytical results, it would be necessary to 

 eat 8 lb. of Pumpernickel to obtain the nitrogenous nutri- 

 ment afforded by 53 lb. of wheaten bread. 



My copy of Wynter Blyth's book was published in 1888, 

 and his results are quoted from G. Meyer's experiments. 

 It is, of course, possible that during the last twenty years 

 Meyer's results may have been proved wrong, and that 

 pure rye bread has been proved to yield as much digestible 

 nitrogen as wheaten bread yields. Should this be the case, 

 I shall be much obliged by information as to the latest 

 and most trustworthy experiments. 



Frank H. Perry-Coste. 



Polperro, Cornwall, May 16. 



The criticism is quite to the point, but is not the last 

 word to be said on the subject. It is well known that in 

 the digestion of whole-meal breads there is larger waste ; 

 but, on the other hand, if in the initial material there is 

 a greater amount of certain constituents, then, in spite of 

 a larger percentage waste, the actual quantity of these 

 ingredients utilised in the body may be greater. In 

 Rubner's experiments, cited in " Standardisation of Bread. 

 Bread and Food Reform League," this was found to be 

 the case. The percentage of nitrogen absorbed from white 

 flour being 79-93, and that from whole meal being only 

 69-53, nevertheless the actual amount absorbed from equal 

 weights of the two materials was larger in the case of the 

 whole meal, and this was even more marked with the fat 

 and the inorganic constituents; but at the moment I am 

 unable to find similar analyses relating to. black bread 

 itself. " The Writer of the Article. 



Native Tantalum. 



Since the communication by Mr. P. Walther regarding": 

 native tantalum from the Ural Mountains was published J 

 in Nature of September 16, 1909 (p. 335), another smallj 

 quantity of a few dekagrams of native tantalum has been 

 recognised in the collection of the deceased mining director, 

 having been collected from the Altai Mountains. It was. 

 found in very similar circumstances, and at about the same 

 time, as the tantalum from the Ural Mountains. The, 

 difference is in the impurities ; the Altai tantalum containsr| 

 gold from a slight trace to 0-0095 per cent., but no trace| 

 of manganese, tin, and niobium could be detected ; the 

 latter three have been found in the Ural tantalum. The 

 average percentage of tantalum is 98-99 per cent. The 

 average measurement of the crystals is about o-i mm., and 

 the crystals are of the regular system, as in the Ural 

 tantalum. The hardness (between 6 and 7) and the specific 

 gravity (11-2) are the same. The specific gravity rri' n- 

 tioned in Nature of September 16, 1909, has been for ^ 

 too low, the error being due to air bubbles. 



Newcastle-on-Tvne. W. von Johs. 



