June 8, 1906.] 



SCIENCE. 



875 



confined to the ' irreducible case ' will apply 

 to all cubics, and for numerical calculation 

 ■ this process is as short as any other trigono- 

 metric solution, and has the advantages of a 

 uniform procedure. If, in order to use only 

 trigonometric functions, we introduce the 

 auxiliary Gudermannian angle to calculate 

 the hyperbolic functions that occur, the for- 

 mulas reduce, in the case of real coefficients, 

 to the ones commonly given for cases other 

 than the irreducible. 



Mr. A. Press spoke by invitation on ' Some 

 Problems in Electrical Design.' 



The question of heat-flow and temperature- 

 rise was dealt with for the direct-current 

 dynamo, the alternater, turbo-alternater and 

 induction motor. It was shown that each 

 type of machine comprises an entirely dif- 

 ferent physical problem, and that the enor- 

 mous discrepancies between ordinary theory 

 and practise rested on an incomplete applica- 

 tion of Fourier's theorem of conservation of 

 heat-flow. The closed types of machines were 

 also pointed out as again offering a new series 

 of problems. 



With respect to sound problems of dynamo 

 electric apparatus very little work had been 

 done, although a satisfactory theory of these 

 phenomena would be greatly welcomed by the 

 engineering profession. In all probability 

 there were radial vibrations set up in the 

 laminse of the cores, and, by virtue of the 

 alternating character of the air-flow stream 

 lines in the cores, sounds induced thereby 

 superimposed upon the other sounds gave the 

 chief characteristic difference between the 

 kind of note emitted by the alternating types 

 of machines and that by direct current types. 

 There were problems of air-flow that also 

 needed elucidation. These latter had in- 

 timate relationship with temperature-rise 

 problems. The method of attack in factory 

 work has necessarily to be modified in accord- 

 ance with whatever tests have already been 

 made, rather than have the experiments made 

 to comply with some preconceived plan. In 

 consequence of this the physical constants 

 may be very wide of the truth. 



Problems dealing with the determination of 

 self -induction and resistance for very high 



frequencies (2,000 per second) had also to be 

 attacked. As far as known only two types of 

 conductor-arrangements have been completely 

 solved. They are, respectively, the round con- 

 ductor in free air and the rectangular con- 

 ductor surrounded on three sides by iron. 

 Frictional problems were also discussed, air 

 friction and bearing friction being more spe- 

 cifically dealt with. 



This paper led to an interesting discussion, 

 especially with respect to the relative con- 

 tributions made by the theoretical students of 

 electricity and the constructors of machinery. 



Informally Mr. White spoke of the galvan- 

 ometer as a motor. 



The meeting falling due on April 21 was 

 omitted on account of the meeting on April 

 20 and 21 of the American Physical Society. 

 A luncheon was served by the Philosophical 

 Society on Saturday at the Bureau of Stand- 

 ards, and in the evening a dinner in honor of 

 Professor H. A. Lorentz, of Leyden, was at- 

 tended by about fifty persons. Vice-president 

 Bauer presided and Professor Newcomb was 

 toastmaster. 



The 618th meeting was held on May 5, 

 1906. 



It was anuounced that the society had ac- 

 cepted an invitation to be represented at the 

 semicentennial celebration of the St. Louis 

 Academy of Sciences on March 10, and had 

 appointed Dr. W J McGee to represent it; a 

 brief report from him was read and the medal 

 sent by the academy was exhibited. Also the 

 invitation to be represented at the bicentennial 

 Franklin celebration in Philadelphia on April 

 18-20 had been accepted and the president 

 had been appointed in response to it; he made 

 an oral report. 



Mr. W. J. Humphreys described some ' Re- 

 cent Experiments on Arc Spectra under Heavy 

 Pressures.' The Zeeman effect leads to the 

 conclusion that an atom must have a magnetic 

 field; therefore, a change in pressure should 

 cause a change in the spectrum. The older 

 experiments with high pressures were very 

 unsatisfactory, being tedious and the arc un- 

 steady. The speaker used a steel bomb, with 

 a quartz window and a rotating electrode, and 



