due to the mercury green radiation in the two cases, when the components were visible, as exemplified by the photograph given by Fabry and Perot, as referred to above, and when, with the same separation of the silvered plates, the components were not present, as exemplified by fig. 13, Plate XXVI., the question arose Has the change in the conditions given birth to one or more satellites? The sharpness of the fringes in both cases, the unequal change in the intensity of the various components under variable conditions, as is shown when the capillary of a vacuum-tube is heated, and in the fact that the results, given in the above table, upon the distances between the components are in poor agreement, which is probably due to the different circumstances surrounding the radiation, all point to the possibility of the production of satellites. It, must not be forgotten, however, that at the separation of the plates necessary to show the presence of the components the interference-bands are very close to one another, so that it is impossible in this method for an interference-fringe due to the birth of a satellite to appear without overlapping some part of the interference-fringes of the other components and hence producing a new distribution of light in the interference pattern which would naturally lead to different results. The investigations of the variations in the wave-length and intensity of radiations separated by the grating on account of variation in pressure, electrical condition of the discharge, and the chemical nature of the dielectric surrounding the luminous substance, is at present a very fruitful field. For these changes in these widely-separated lines lend themselves to measurement. It is hoped that a method will be found which will more readily show and give measurements of the many changes that occur in radiations whose wavelengths, and hence their frequencies, do not differ greatly, so that ultimately some knowledge as to the mechanics of the systems of moving electrons constituting the atom whose periods differ by small amounts-relative to those obtainable at present-may be obtained. A step in this direction has been made by Lummer. The reproductions in the Ann. d. Phys. x. p. 473 (1903) show excellently the complicated structure of these bright radiations. The method proposed above, employing longer plates, is worthy of a fair trial. My heartiest thanks are due to the professors and lecturers in physics in this University, especially Professor Ames and Professor Wood, and also to my fellow students whose kind assistance in word and deed has greatly facilitated these experiments. Physical Laboratory, Johns Hopkins University. LX. The Whirling and Transverse Vibrations of Rotating Shafts. By C. CHREE, Sc.D., LL.D., F.R.S.* $1.7 CONTENTS. $S 1-5. Preliminary Discussion. 6-11. CASE 1. 12-18. CASE 2. Overhanging shaft, end fixed in direction. supported" at one end, and with its direction fixed at the other end. 28-32. CASE 5. Shaft "supported "at both ends and at inter- 33-35. CASE 6. Shaft fixed in direction at both ends. 40-46. Mathematical Appendix. Preliminary Discussion. LATERAL vibrations are those executed by a bar when bent to one side and then released. They are connected with the "whirling" of rotating shafts, but in a way which has not, I think, hitherto been clearly recognized. The subject of "whirling" has been treated by Professor Greenhill† in a well-known paper dealing with an unloaded shaft rotating under various terminal conditions. More recently the subject has been treated in an elaborate and important paper by Prof. Dunkerley. He employed two ways of calculating the critical speeds of rotation. The first makes use of the ordinary elastic solid equations applicable to thin rods acted on by "centrifugal force"; this is the method followed by Greenhill. On attempting to apply this method to loaded shafts, Dunkerley reached results which he considered hopelessly complicated. In his second method, which is due apparently to Prof. Osborne Reynolds, Dunkerley calculated a critical speed for the loaded shaft, in which the mass of the shaft itself was neglected. Calling the frequency thus obtained Ng, and that found for the unloaded shaft by the first method N1, he deduced a final value N for the frequency from the equation 1/N2=1/N,2+1/N,2. (1) By speed or frequency Dunkerley means the number of revolutions per minute, i. e. where is the angle through which the shaft rotates in one second. *Communicated by the Physical Society: read March 11, 1904. |