LONDON.Physical Society, October 28.—Dr. J. FT. Gladstone, F.R.S., past president, in the chair.—The discussion on Mr. Williams's paper, “On the relation of the Dimensions of Physical Quantities to Directions in Space,” was opened by Prf. Perry readiog a communication from Prof. Fitzgerald, president. The writer said Mr. Williams disagreed with the suggestion that and magnetic inductive capacity are quantities of the same kind principally because he had not got over the curious prejudice that potential and kinetic energy are different. No theory of the ether could be complete unless it reduced its energy to the kinetic form. Flectric and magnetic inductive capacity would probably be found to be similar in the ether, and ultimately have the same dimensions. The analogies were not yet complete, but only in respect of maiter was it probable that any difference existed between them. Diamagnetism corresponded to electrostatic induction, but paramagnetism had no definite electrical analogue. He was inclined to regard the phenomena of paramagnetism as connected with the arrangement of the material molecules, whilst diamagnetism depended on the electric charges on those molecules. So far no matter had been fund which conducts magnetism, and such may not exist in our universe, but it may be gravitationally repelled by matter as we it.-Mr. Madan remarked that in the first part of his paper Mr. Williams recognized that dimensional formuhe were originally change-ratios, but puts this aside for the higher conception which regards the e formul as expressing the nature of the quantity. Fourier showed how to find the dimensions of units by making the size of the fundamental units vary. But (specific inductive capacity) did not vary with the fundamental units, for it was merely the ratio of the capacities of two condensers, and therefore, by Mr. Williams's definition, a pure number. It was difficult, he said, to see how k could have dimensions, but Mr. Williams regarded it as a physical quantity, and therefore possessing dimensions. The object in giving dimensions to k and p. seemed to be to get over the double system of units. Mr. Madan did not think that dimensions could express the nature of physical quantities, and said differ of opinion existed amongst authorities on this point. For eicample, Dr. J. l-Iopkinson, at the last B. A. meeting, said that because a co-efficient of self-induction had the dimensions of length it must be a length, whilst other learned professors objected to this view. Even if one admitted that dimensions are a test of the nature of physical quantities it was not necessary that the two systems of units should be identical. The connecting link between the two systems was Q = C 1, and the validity of this equation had been questioaed. If this objection be confirmed, then there would be no current in electrostatics and no Q in the electromagnetic system, and the units would not clash. Referring to dynamical units, Mr. Madan pointed out that two units of mass were used in astronomy, but astronomers got over the difficulty by using a co-efficient. Dimensional formulse, he said, are the result of a convention that certain definitions should hold true generally, bat they contain no further information respecting the nature of the quantities beyond that involved in those definitions. As an example of the inability of such formuke to expres the nature ofquantities he pointed out that whilst physical differences were known to exist between and electricity the dimensional formuke showed so signs of such differences.-Prof. Rflcker said every correct physical equation consisted ofa numerical relation between physical quantities of the same kind, and might be written either as a mee numerical equation or as a relation between the physical quantities themselves. The equation 2 + I 3 may correspond to 2 feet + I foot = 3 feet, and the latter may be written 2[Lj + r[Lj = 3[Lj, where [Lj reprelines sents the unit of length. So far as he was aware, nobody but a recent writer in the Electrician had denied that in such an equation [U represented a concrete quantity. Maxwell cxplicitly stated that it does in his article on "Dimensions"("Encyl. Britt.") and elsewhere, and Prof. J. Thomson, in his paper on the same subject, makes no statement contrary to this. The above equation might also be written 2[feet] + i[foot] i[yardj. Another equation involving time is 6o[sec.j = I[minute], and dividing one by the other one gets 2 rfoot rfoot 1 ryard 651 I WII I I LSeC.J Lsec.J LmLII.