November i6, 1893] 



NATURE 



59 



while each component has a small companion whose 

 intensity is about a fifth of that of the principal lines, at 

 a distance of about one three-hundredth of that of the 

 sodium lines. The green mercury line is made up of a 

 QTOup of five or six lines, the strongest of which is itself 

 double (or perhaps triple) the distance of the compo- 

 nents, being less than a five-hundredth part of that 

 between the sodium lines. 



These distances, small as they are, can be measured 

 within about a twentieth part, so that by this means it is 

 possible to detect a change of wave-length correspond- 

 ing to the ten-thousandth part of that between the two 

 sodium lines. 



The red line of cadmium is the simplest of all the radi- 

 ations thus far examined, consisting of a single narrow 

 line whose intensity falls off symmetrically according to 

 an exponential law, its width (at the points where its 

 intensitv is reduced to half its maximum value) being 

 only 0002 (D^-D.,). The green and the blue cadmium 

 lines are also comparatively simple, and all three of these 

 lines give interference fringes clearly visible at a differ- 

 ence of path of 100 mm., and under appropriate condi- 

 tions they all satisfy the requisites for a definite and 

 inalterable standard of length. 



The most important of these conditions is that the 

 radiating vapour be so rare that the molecules may vibrate 

 freely ; in other words, that the time occupied in the col- 

 tisions between the molecules be so short relativelv tc 



the very large number of waves which pass as the refer- 

 ence plane is moved from one surface to the other. 



This problem has been solved in the following manner. 

 Nine standards were constructed similar in all respects 

 to that of ten centimetres, save that each succeeding one 

 was half as long as the preceding. The last of the series 

 is thus approximately o"39 mm. long, corresponding to a 

 difference of path of 078 mm. The number of waves in 

 this distance in red cadmium light is 1212 plus a fraction, 

 which is corrected by direct observation of the difference 

 of phase of the circular fringes on the upper and the lower 

 (front and rear) surfaces of the standard. This verifica- 

 tion is also made with the green and the blue radiations. 



It is important to note that the measurement of these 

 fractions alone is sufficient to fix the whole number, even 

 if there be an uncertainty of several waves. Thus, the 

 relative wave-length of the three radiations being known, 

 the number of green and of blue waves corresponding to 

 the observed number of red waves can be readily calcu- 

 lated, as is shown in the following table : — 



Number of Waves. 



Wave-length. 



Observed. 



Calculated. 



Fig. 9. 



that of the free path, that its influence in disturbing the 

 Iree vibration may be neglected. Experience shows that 

 in general this limit corresponds to a pressure of one or 

 two thousandths of an atmosphere. 



It may be noted that at atmospheric pressure — even 

 when the radiating substance is introduced in quantity 

 barely sufficient to colour a Bunsen flame — the greatest 

 difference of path attainable is only one or two centi- 

 metres, whereas with mercury vapour in a vacuum tube 

 interference fringes have been observed with a difference 

 of path of 47 centimetres, or about 850,000 waves. 



In order to make any practical use of these minute 

 quantities for standards of length, it is necessary to em- 

 ploy an intermediate standard, such as that shown in Fig. 9, 

 consisting of a bronze bar carrying two plane-parallel 

 glasses, silvered in front, the distance between which can 

 be compared on the one hand with the fundamental 

 standard in actual use— the metre or the yard — and on 

 the other with the length of a light-wave. 



The former process is accomplished by moving the 

 standard (whose length it is convenient to take at 10 

 centimetres) ten times through its own length, the coin- 

 cidence and the parallelism of the. surfaces being con- 

 trolled at every step by the interference fringes in white 

 light formed between these surfaces and that of 

 the re/if c?ice plane (the virtual image of the mirror M.\l 

 in G,, Fig. 8). The position of a fiducial mark on this 

 standard is compared by means of two micrometer micro- 

 scopes with the lines defining the standard metre at the 

 first and last steps. 



In the second process the only difficulty encountered 

 is due to the very great disproportion between the length 

 of a wave and that of the 10 centimetre standard, and 

 the consequent difficulty in keeping the correct count of 



NO. 1255, VOL. 49] 



0-64389 1212-34 I2I2'34 



0-50863 153476 153476 



0-48000 1626-16 1626-13 



If the whole number assumed as the basis of this cal- 

 lation were in error by one or more waves, there would 

 be no correspondence between the observed 

 and the calculated fractions. The length 

 of this standard and the succeeding one 

 are now compared as follows: — The two 

 standards being placed side by side in the 

 refractometer il on a fixed support, and i 

 on a movable carriage, the reference plane 

 (r. Fig. 10) is moved until it coincides with 

 A, the lower (or front) surface of 11, and 

 the interference fringes in white light are 

 adjusted to the proper distance and in- 

 clination by adjusting the inclination of 

 the reference plane. Next, c, the lower surface of i is 

 brought to coincidence with the reference plane, and 

 similarly adjusted, and then all the adjusting pieces are 

 released from the carriages, so that these rest undisturbed 

 on the ways. This completes ihejirst stage of the com- 

 parison. 



Second Stage.— Th^ reference plane R' is now moved 

 back till it coincides with D, the upper surface of 1 and 



R" 



-R' 



Fig. 10. 



Fig. II. 



the adjustment of the interference fringes carried out as 

 before. 



Third Stage.— Tht standard, I, is moved back till its 

 lower surface (C, Fig. 11) once more coincides with the 

 reference plane, r', and its inclination is again adjusted 

 by the interference fringes. 



Fourth Stage. — The reference plane is finally moved 

 back till it comcides with D, the upper surface of i, and 

 its inclination is again adjusted. If now the standard ll 



