depends on the angle between b and c. The effect increases with increasing angle and decreasing width of fringes. As the effect we are looking for (ether drift) must be periodic in each half-turn, we are justified in eliminating the full-period effect. This is done by plotting the single observations, turn by turn of the interferometer; these curves are analyzed by the mechanical harmonic analyzer, and the second harmonic (half-turn effect) is taken as representing the ether drift. If there is an ether-drift effect, the full-turn effect is
necessarily produced, according to Hicks, and its presence may be taken as further evidence of the ether drift. The magnitude and phase of the full-period effect is variable, because it depends upon the adjustment of the mirrors as well as the ether drift. [Slides were shown representing the full-period effect.] It is evident that the magnitude is very different for different sets of observations. The half-period effect, on the other hand, is characterized by a constant magnitude. The full-period effect is small when the width of the fringes is such that five of them cover the mirror (10 cm in diameter). Under other conditions, however, it may be very large. The full-period effect is not new, but has always been present in all the experiments. It is present in Professor Michelson’s original observations.
Kennedy: Are the effects the same in case you use a concrete frame instead of an iron frame?
Miller: Yes, they are essentially the same. The concrete instrument showed smaller temperature effects than did the one with the steel frame, but its mechanical strength was also less. I have always used (as did Kennedy) the method of shifting the fringes by putting weights on the end of the frame; to produce a shift of one fringe, approximately 325 g was necessary. This is less than the corresponding weight in Dr. Kennedy’s apparatus, because
CONFERENCE ON MICHELSON-MORLEY EXPERIMENT 399
the arms of the frame are longer in my apparatus than in his. I should like to mention again that my experiments have been carried out under a great variety of conditions. My assistant moved around the apparatus to see if his position affected the distribution of temperature or the stability or level of the instrument. The light was placed in different positions, both inside and outside the house. At Mount Wilson, the instrument has been mounted in two different buildings, differently oriented. The effect has persisted throughout. After considering all the possible sources of error, there always remained a positive effect.
Professor E. R. Hedrick: Mathematically speaking there cannot be any question as to the correctness of the computations which Professor Lorentz has presented to us. The result for the second-order terms seems beyond question. It is conceivable, however, that there is introduced an error when the path of the beam of light is changed by the motion of the apparatus into a new one. The instrument might not be always in the ideal position assumed in the calculations.
I should like to call your attention to a second point. We start from a certain number of assumptions. Now our aim in mathematics is always to reduce the necessary number of assumptions to a minimum. We make use in this special case of the two principles of Huyghens and Fermat. Can we trust them to terms of the third order? We do not know. Might not a combination of third-order effects eventually affect the magnitude of the second-order effect? Anyhow, if we could reduce the number of physical principles involved in our calculations to a single one, it would be very desirable. That is what Righi and also I have attempted to do.1
Lorentz : I should like to defend my theory. Hedrick says we should try to reduce the number of our assumptions. Now the two
1 It should be stated clearly that the operations of differentiation and integration, freely used in these discussions, cannot be trusted to the extent that is often assumed. The derivative of an approximation to a true formula is not necessarily an approximation to the derivative of the true formula. It is true also that the integrals to successive approximations to a true formula are not necessarily successive approximations to the integral of the true formula, unless the successive approximations are uniform. These conditions cannot be said to hold in such fine approximations as those of the Michelson experiment. Therefore it has seemed to us, and it still seems to us, to be necessary to proceed by direct calculations from definitely stated assumptions, rather than through an intermediate proof (e.g., Fermat’s principle) that is thus questionable.