24 HEAT. 



one, where A is the wave-length of the light employed ; so that even 

 if we do not know the absolute thickness at any point, we know the 

 difference in thickness of the film of air at any two points by counting 

 the number of rings between them. Further, it is not necessary to have 

 contact between the curved and plane surfaces. If the lens is gradually 

 raised upwards, the rings contract, disappearing as they reach the centre; 

 but the distances apart of the successive rings remain the same at the 

 same points, corresponding to the same differences in the thickness of 

 the film of air. In Fizeau's experiment the rings were still visible when 

 the air-film was over a centimetre thick. His method, as used at the 

 Bureau International des Poids et Mesures, is as follows * : A flat 

 metal plate T (Fig. 15) is supported horizontally by three screws passing 

 upwards through three holes near its edge. On the three screws is 

 supported a plano-convex lens LL with the plane surface downwards. 

 The so-called plane surface is in reality slightly convex, as is the case 

 with most plano-convex lenses, and if allowed to touch another truly plane 

 surface, Newton's rings are seen round the point of contact. A plate B 

 of the substance of which the expansion is required is prepared with 

 parallel polished faces, and about 1'5 cm. thick, and this is laid on the 

 centre of the metal plate T. The lens is then adjusted, at some small 

 distance above it, so that when sodium light is thrown on it normally, 

 Newton's rings are seen through interference between the rays reflected, 

 at the lower surface of the lens and those passing through and reflected 

 at the upper surface of the plate of the substance. The light of a sodium 

 flame is thrown in and reflected out again by a right-angled prism, and 

 then received by a telescope. The metal plate with the substance and 

 lens is enclosed in a chamber maintained at a uniform temperature by a 

 thermostat. When the temperature is raised, the thickness of air is 

 altered by the difference between the expansion of the supporting screws 

 and that of the substance, and the rings are shifted. By counting the 

 number of rings passing a given point in the field of view of the tele- 

 scope, this difference is measured in terms of the wave-length of the 

 light used. Preliminary experiments are made to determine the expan- 

 sion of the screws, and so the expansion of the substance is known. 

 Since the wave-length of sodium light is about '000589 mm., the 

 method, as might be anticipated, is susceptible of very great accuracy, 

 and by it Fizeau was able to determine the difference of expansion of 

 crystals along their different axes with great exactness. He also 

 succeeded in showing the variation of the co-efficient of expansion with 

 the temperature, taking as the co-efficient the increase per 1 rise in 

 temperature of a length which is equal to 1 at C. 



Applications of Linear Expansions. In many cases in which 



metals are used in construction, account must be taken of variation in 

 their length with variation of temperature. Railway lines must be laid 

 with a small interval between the successive rails, otherwise in hot 

 weather the rails would tend to force each other out of the straight so 

 as to allow the necessary expansion. This is perhaps most easily 

 realised by calculating the total increase on some long line. For 

 instance, the distance from London to Edinburgh is about 400 miles. If 

 the rails are laid in cold weather, we may easily conceive the possibility 



* Vol. i. c., Travaux et Memoircs. 



