Oct. 24, 1884.] 



♦ KNOWLEDGE ♦ 



337 



This burning of the skin is accompanied with considerable 

 heat and more or less pain. It is, therefore, necessary to 

 be careful with it, to prevent it spilling. As it is volatile, 

 the bottle containing the acid should be kept stoppered, and, 

 as heat accelerates its evaporation, it should be kept in a 

 cool place. There is, however, no fear of explosion, except 

 with the most powerful acids, more powerful, in fact, than 

 are likely to be procurable. Another point to be borne in 

 mind is, perhaps, more important than either of those 

 hitherto mentioned, and that is, that when a metal is dis- 

 solved in nitric acid, fumes of a most unpleasant and some- 

 what injurious character are evolved. 



The merest tyro in chsmical manipulation knows that 

 when a metal, such as iron or zinc, is dissolved in sulphiu-ic 

 acid, a sulphate of the metal is formed, and hydrogen gas is 

 liberated. This results from the metal taking the place of 

 the hydrogen in the acid. The exchange is expressed 

 thus — 



Zn + SOjH; = SO,Zii + H2 



Zinc and='^'P^']^'<= produce ^^"^'P^^^f and hydrogen. 



With nitric acid the case is somewhat different. The 

 metal, copper, for instance, first decomposes the acid 

 forming the nitrate. Thus : 



Cn + 2XO3H = (S0;);CU0,. + H; 



Copper and nitric acid produce nitrate of copper and hydrogen, 



but this hydrogen does not escape, owing to the unstable 

 nature of nitric acid. A further decomposition takes 

 place, in which the hydrogen splits the acid into water and 

 oxide of nitrogen. Thus : 



3H., 



+ 2XO3H 



nitric 



40H., 



Hydrogen and nitric acid produce • -, and water. 



This oxide escapes into the air and combines with an 

 additional quantity of oxygen, forming nitrous anhydride 

 and nitric peroxide, which appear as pungent brownish 

 fumes. They are intensely irritating to the throat and 

 nostrils, and this portion of the experiment should be con- 

 ducted in a chimney with a good draught, or, failing that 

 in the open-air. In the case of silver, a series of changes 

 takes place similar to the above. The primary reaction of 

 a metal on an acid may be considered identical in all cases, 

 and to consist in the formation of the corresponding salt 

 and hydrogen ; the secondary reactions which occur, and 

 which generally consist in the reduction of a further 

 portion of the acid, depend entirely on the nature both of 

 the acid and the metal employed, on the state of concentra- 

 tion of the acid, and on the temperature at which the 

 reaction takes place. Thus, by the action of various 

 metals on nitric acid, we may obtain at wDl either 

 ammonia, nitrogen, nitrous oxide, nitric oxide, or nitric 

 peroxide. 



To return to the nitrate of silver solution, the whole of 

 the silver being dissolved, a gentle heat is applied to drive 

 off any superfluous nitric acid that may remain. The 

 nitrate being evaporated almost to dryness, half a gallon of 

 distilled or (faOing that) rain water is then added. A pure 

 nitrate of silver solution results. Ordinary drinking water 

 is not available because of its impurities. 



II. Beetz has made a standard cell, which is a modified form of 

 Latimer Clark's mercurous sulphate cell. It consists of a tube in 

 which a compressed cake of mercurous and zincic sulphates is 

 placed ; at one end of the cake the zinc pole is placed, and at the 

 other end the mercury pole. On short-circuiting the following 

 results were obtained : — Five minutes, l--i40 volts ; one hour, 

 1'439 volts ; four hours, 1'439 volts ; six hours, 1'437 volts ; twelve 

 hours, 1-434 volts; forty-eight hours, 1-408 volts. The resistance 

 was 15'700 ohms. 



CHATS ABOUT GEOMETRICAL 



MEASUREMENT. 



By Richakd A. Proctor. 



A. There are few subjects which seem more mysterious to 

 me than the measurement of the lengths of curves, the areas 

 of surfaces bounded by curves, and the determination of the 

 volumes and surfaces of solid figures bounded by.curved 

 surfaces. Surely in all such cases you can suggest approxi- 

 mations to the real values, not those values themselves I 



M. Well, in one sense, all mathematical results are 

 approximations. We cannot even draw a straight line 

 which really corresponds with the definition of a straight line. 

 We are obliged to assume the existence of lines, sui-faces, 

 shapes, and so forth, which we cannot actually picture. 



A. That is not what I mean. I am well content with 

 the geometry of Euclid, which I regard as exact. What I 

 like, indeed, in Euclidean geometry is the exactness of aU 

 its methods and results. Isow, if I understand rightly 

 what is signified by non-Euclidean geometry, it is a system 

 of approximation to the truth, and not exact, like the 

 geometry of Euclid. 



M. I think you mistake altogether. What do you 

 understand by non-Euclidean geometry ? 



A. Why, geometry dealing -with matters outside those on 

 which Euclid enters. 



M. That is a mistake. The awkward term non-Euclidean 

 geometry is not applied to geometry beyond or outside 

 Euclid's, but to geometry inconsistent with ordinary geo- 

 metry. Non-Euclidean geometry requires at our very entry 

 into its domain that we should abandon the axioms, nay, 

 the very definitions of Euclidean geometry. A straight 

 line, for instance, in non-Euclidean geometry, by no means 

 " lies evenly between its extreme points." 



A. I have indeed been mistaken, then, on that point. I 

 certainly want to hear no more about thai geometry. The 

 kind of geometry I was thinking of is geometry dealing 

 with matters outside those dealt with by Euclid. We do 

 not find in Euclid any reference to limiting values, infinity, 

 vanishing quantities, and other such matters, which — to my 

 mind — make the geometry of approximations (if I may 

 invent an expression) unsatisfactory. 



M. Are you fjuite sure of this \ I think you are mis- 

 taken here also. To turn to the veiy beginning of his work, 

 how does Euclid define parallel lines 1 



A. H'm — h'm. Well, certainly in a sense he does seem 

 there to introduce the idea of infinity. 



M. So I think. And does he not introduce the idea of 

 limiting quantities in the twelfth axiom 1 



A. I cannot say that I see what you mean. He says that 

 two lines referred to in the axiom will meet if produced far 

 enough. 



21. Yes ; but he implies that no matter how small the 

 deficiency of the " two angles taken together " from two 

 right angles, those two straight lines will meet on that 

 side where the angles are thus less than two right angles. 

 The idea of a limiting value is here obviously introduced. 



A. I see now what you mean. Let us consider this 

 axiom for a moment. It has little to do, perhaps, with the 

 subject we are upon; but I should like to have your 

 opinion about this troublesome axiom. I suppose you 

 agree with those who consider that is not in reality an 

 axiom ^ 



21. Certainly it is no axiom. The converse is demon- 

 strated in the 1 7th proposition. 

 A. How so ^ 



21. In that proposition it is shown that any two angles 

 of a triangle are together less than two right angles. This 



