D PREFACE. 



The third and fourth chapters are incidental applications of the displace- 

 ment interferometer and contain experiments on the expansion of metal tubes 

 by internal pressure and on a promising method of measuring the refraction 

 of glass, irrespective of form. To carry out the experiments in the last case 

 with requisite rigor, optic plate-glass apparatus would unquestionably be 

 essential. Nevertheless the tentative data obtained are noteworthy. 



I have begun in Chapter V the development of displacement interf erometry 

 in connection with the older Jamin-Mach interferometer, an instrument 

 which has certain peculiar advantages and is in a measure complementary 

 to the Michelson interferometer. The work was undertaken in connection 

 with the micromeasurement of the difference of heights of communicating 

 columns of liquids, though the latter had to be abandoned in consequence 

 of the excessive tremor in a laboratory surrounded by active city traffic. 

 I shall hope, however, to carry out such work elsewhere. 



The chief result of Chapter V is the detection of the achromatic inter- 

 ferences, as I have called them for convenience interferences which are 

 ultimately colors of thin plates seen at oblique incidence; but with the new 

 interferometer, and obtained with white light, they are peculiarly straight 

 and vivid and resemble a narrow group of sharp Fresnellian fringes with the 

 central member nearly in black and white. They are capable of indefinite 

 magnification and their displacement equivalent is a fraction of a mean wave- 

 length per fringe. Notwithstanding their strength and clearness, they are 

 so mobile in connection with micrometric displacement that in general it 

 would be almost hopeless to attempt to find them but for the fact that they 

 coincide in adjustment with the centered ellipses or hyperbolas of the spectrum 

 fringes of the displacement interferometer. 



The fine white slit-image which is dispersed to produce the latter carries 

 the achromatic fringes when the slit is indefinitely broadened or removed. 

 Once found, moreover, they are not sensitive to small differences of adjust- 

 ment if a change of focal plane is admissible. The chapter shows a curious 

 method for the measurement of vertical displacements, possibly available 

 for the detection of ether drag, which, though just insufficient in connection 

 with the spectrum fringes, would be promising in connection with the achro- 

 matic fringes. Finally, the chapter contains some repetitions of the old 

 experiments of Fizeau on the periodic evanescence of fringes due to the sodium 

 lines. Curiously enough, the achromatic fringes also show periodic recurrence 

 sometimes, which as yet remains unexplained. 



The peculiar adaptability of the new interferometer to the measurement 

 of small angles, either in a horizontal or a vertical plane, is developed in the 

 final chapter. The ratio of the angular displacement of fringes to the angle 

 to be measured (i.e., the rotation either of the paired mirrors or of an auxiliary 

 mirror in the apparatus) may be made enormously large, and the paper shows 

 cases in which, with strong luminous fringes, the angle to be measured is mag- 

 nified 500 times. Moreover, this is by no means a limiting performance. Again, 

 while angles as small as a few tenths of a second or less are measured, angles 



