56 



NATURE 



[November i6, 1893 



LIGHT-WAVES AND THEIR APPLICATION 

 TO METROLOGY. 



■pX'ERY accurate measurement of a physical quantity 

 -*^^ depends ultimately upon a measurement of length 

 or of angle : and it will readily be admitted that no effort 

 should be spared to make it possible to attain the utmost 

 limit of precision in these fundamental quantities. At 

 present, lengths are measured by the microscope, and 

 angles by the telescope ; and the extraordinary degree of 

 accuracy already attained by the use of these instru- 

 ments depends entirely on the properties of their optical 

 parts in their relation to light-waves ; so that, in fact, 

 light-v.-aves are now the most convenient and universally 

 employed means we possess for making accurate measure- 

 ments. It can readily be shown that this high degree 

 of accuracy is especially due to the extreme minuteness 

 of these waves. 



Fig. 1. 



Thus it is well known that the image of a luminous 

 point consists of a series of concentric coloured rings 

 surrounding a bright central disc which is smaller the 

 smaller the ratio of the wave-length of the light to the 

 diameter of the objective employed. In fact, it can be 

 shown that the radius of the bright central disc contains 

 as many wave-lengths as the distance of the image from 

 the objective contains the diameter of the objective. 

 Thus in a telescope twenty diameters long, the dia- 

 meter of the bright disc is forty wave-lengths or 002 mm. 

 If the image be magnified "by increasing its distance 

 from the objective, or otherwise, these diffraction rings 

 are magnified in the same proportion ; so that nothing 

 is gained thereby in distinctness, beyond the point where 

 the rings are just large enough to be visible. But, were 

 it not for the inevitable loss of light, it would be advan- 



vibration ; but to determine the position of with respect 

 to a b, this is not at all necessary ; and in fact, if we dis- 

 regard the possible inconvenience due to the dissimilarity 

 between the phenomenon observed and the object whose • 

 position is to be measured, it v/ould be as well to entirely 

 annul the central portions of the lens, leaving only an 

 external annular ring, or better still, only two small por- 

 tions at opposite ends of a diameter. 



This involves no sacrifice of accuracy, but on the 

 contrary a very considerable gain ; for it is now possible 

 to increase the size of the interference fringes up to any 

 desired limit without diminishing the intensity of the 

 light, the result being the same as could be obtained with 

 a perfect microscope of unlimited magnifying power with 

 a source of unlimited intensity. 



For this purpose the two small portions to which the 

 lens is reduced are replaced by plane mirrors or prisms, 

 whose office is simply to bring the two interfering pencils 

 into coincidence. Further, the pencils, in- 

 stead of starting from a point or a line, may 

 be separated by a plane transparent surface ; 

 and a second similar surface may be used to 

 reunite the pencils after reflection. Thus the 

 telescope or microscope will have been con- 

 verted into a refractometer. The exact nature 

 of the analogy will be apparent by a com- 

 parison of Figs. I and 2. 



It may be assumed that under the most 

 favourable circum.stances the utmost attain- 

 able limit of accuracy of a setting of the cross-hair of a 

 microscope on a fine ruled line is about „^,7 of a micron. 

 Now, it is usually admitted that the middle point of an 

 interference fringe, if it be sufficiently broad and clear, 

 can be determined within about ^^ of the width of a 

 fringe. In the refractometer this would mean only ,,Vi of 

 a light-wave, or about o'oi^, from which it would follow 

 that the refractometer is about five times as accurate as 

 the microscope. But a number of trials with the form of 

 refractometer shown in Fig. 8 gave as the mean error of 

 a series of ten observations : 



Fr. Fr. Fr. 



Morley 00056 ... Nicholson 0*0059 ... Xooiio 



The third observer had no previous practice in this 

 kind of measurement. 



tageous for measurements of position to increase the 

 magnification much further. 



This can be accomplished by an extremely useful 

 instrument which has been misnamed the " interferential 

 refractometer.' It will be interesting to note that not- 

 withstanding the apparent difference in form, this 

 apparatus, when used as a measuring instrument, differs 

 in no essential particular from the microscope or the 

 telescope, or (what is perhaps a trifle unexpected) the 

 spectroscope ; and it is possible to change any one of 

 these instruments into the other by unimportant modifi- 

 cations. 



Thus, let 0, Fig. i, be a source of light, ab ?l lens which 

 forms an image of at o'. The operation of the lens, when 

 used to distinguish minute objects, depends upon the 

 accuracy with which all its parts contribute to make the 

 elementary waves reach the focus in the same phase of 



NO. 1255, VOL. 49] 



It is evident from these results that ;j'y of a fringe is too 

 large an estimate of the average error of a setting, and 

 that it is, in fact, less than 001 of a fringe, corresponding 

 to an error in distance of about 0.003/x. 



For angular measurements the microscope is replaced 

 by the telescope. 



Fig. 3 represents a disposition sometimes adopted for 

 observing minute angular displacements of the mirror 

 d c; the light starts from o, is reflected by the plane 

 parallel glass plate/ to the objective a b oi 2l telescope, 

 whence the now parallel rays proceed to the mirror 

 c d. Thence they retrace their path to the plate /, 

 through which they are transmitted, forming an image 

 of the source at o\ which is viewed through the eyepiece. 



Fig. 4 is the exact analogue in the form of a refracto- 

 meter ; and Fig. 5, though slightly different in aspect, is 

 still essentially the same instrument. The path of the 



