540 



♦ KNOVS/LEDGE ♦ 



[June 26, 1885. 



wool iu the experiment must have had originally a bulk of 



— — times that of the 'whole quantity of original 



fibre, i.e., more than 293 times the bulk of the fibre itself. 

 Such a quantity thus grasped by the fibre almost forces us 

 to suppose that the condensation by adhesive attraction 

 must have effected some degree of liquefaction, but if it 

 reached actual liquefaction in the nearest contact layer, 

 such liquefaction due to adhesion would differ from con- 

 densation by cooling in the important fact that the latent 

 heat of the gaseous water would still be retained, and with 

 it the property of gaseous expansive energy. 



OPTICAL RECREATIOXS. 



By a Fellow of the Eotal Asteokojiical Society. 



( Continued Jtota 'gage 321.) 



HAVIXG arrived at this stage in the treatment of our 

 subject, we are placed in a certain amount of difli- 

 culty, since the next natural division of it is that dealing 

 with the phenomena of chromatics. This, however, can 

 scarcely be treated without reference to prismatic, or 

 spectrum, analysis ; and on this particular subject the Con- 

 ductor of Knowledge has himself promised a series of 

 papers (under the title of "Light-sifting"). Now until 

 these appear, our reference to the nature of colour and the 

 mode of its production can scarcely be other than dis- 

 jointed and incoherent. A? an introduction, however, to 

 the whole subject, it may not be entirely out of place if 

 we essay to give some idea of the method by which the 

 immortal Xewton first measured the thickness of the film 

 of any material sufiioiently attenuated to exhibit chromatic 

 phenomena. This primarily depends upon that principle 

 of " similar triangles," which underlies the determination 

 of lunar, planetary, and even stellar distances. 



The practical photographer knows how, when printing 

 from his plates, he screws the back of the glass negative 

 very tightly up against the glass of the printing-frame, 

 curved bands of beautiful colours often become visible. The 

 same thing may be seen, too, between two lamina? in a 

 mass of mica, on ancient glass, ic. JTow these colours are 

 produced in the thin film of air between the plates, or 

 oxidised film in the case of old glass vessels, and what 

 Newton set himself to do was to measure the thickness 

 pertaining to each particular one. His actual apparatus 

 was of the very simplest, consisting merely of a plano- 

 convex lens with a radius of convexity of li feet, and a 

 double-convex one with a radius of .50 feet. Upon the 

 plane surface of the first lens was placed one of 

 the surfaces of the other or double-convex lens of 

 •50 feet radius, and then, by the aid of three binding 

 screws round their edges, the surfaces were brought into 

 close apposition, as shown in Fig. 42, where we see that 



Fv'. 42. 



I etween the convexity of the 50 feet radius lens and the 

 plane surface of the 14 feet one a film of aii- is en- 

 closed, gradually increasing in thickne-s outwards from the 

 central point where the lenses are in contact, and where 



of course, it has no thickness at all. Now if we look down 

 on to such an arrangement as this in daylight, we see a 

 series of concentric coloured rings, as shown in the figure. 

 The centre of the circles, where, as we have said, the two 

 lenses are in actual contact, is a black spot, outside of 

 which, in succession, appear rings of pale blue, white, 

 yellow, orange, and deep red. Following these is another 

 series of violet, indigo, blue, greenish-white yellow, orange, 

 bright red and crimson red (the popular " colours of the 

 rainbow "). This is succeeded by a third, fourth, fifth, 

 sixth, and seventh series, the colours gradually be- 

 coming more diluted as we proceed outwards, until they 

 vanish. Now these successive alternations grow narrower 

 and narrower as they recede from the central spot, in such 

 sort that the ana of each bright ring, measured from the 

 darkest part of one alternation to the darkest part of the 

 next, is equal We shall presently see the meaning of this, 

 and what are the numerical relations subsisting between the 

 thicknesses that produce the same colour, in the successive 

 orders or series of colours of which we have been speaking. 

 The practical calculation, or rather the principle on which 

 it is made, will be understood from Fig. 4.3, in which, how- 



Fig. 43. 



ever, the curvature of the double convex lens is grossly 

 exaggerated, in order to show how the film of air, F M, 

 gradually thickens as we proceed outwards. Let us 

 suppose that we wish to find the thickness of the film 

 of air which forms the ring B C, the radius of whose 

 upper or concave surface, G B, is 50 ft. ; in other words, 

 the thickness, E C, in our figure. We will imagine that, on 

 measuring to the point C from the central black spot, we find 

 BC = 25inch. Draw the chords A E and B E. Then 

 (Euclid III., 31) A E B is a right-angled triangle, and if 

 we further draw D E perpendicular to A B and = B we 

 get two other right-angled triangles A D E and B D E. 

 These two last triangles are similar (Euclid VI , 8), and 



