736 



SCIENCE 



[N. S. Vol. XXX. No. 777 



tJie developments in Bessel functions of order 

 zero." 



The Southwestern Section of the society will 

 meet at the University of Missouri on Saturday, 

 November 27. The winter meeting of the Chicago 

 Section will be held at the University of Chicago 

 on Friday and Saturday, December 31 and Jan- 

 uary 1. The annual meeting of the society will 

 be held at Boston, in affiliation with the Amer- 

 ican Association, Tuesday to Thursday, December 

 28-30. P. N. Cole, 



Secretary 



THE PHILOSOPHICAL SOCIETY OF WASHINGTON 



The 669th meeting was held in the West Hall 

 of George Washington University, on October 23, 

 1909, President Wead in the chair. The following 

 papers were read: 



A Mechanical Means for Effecting Certain Con- 

 formal Transformations: Dr. R. A. Habbis, of 

 the Coast and Geodetic Survey. 

 Attention was called to the fact that a mech- 

 anism which sums continuously and simultane- 

 ously two trigonometrical series, the one consist- 

 ing of sine terms, the other of cosine terms, may 

 be readily adapted to conformal transformations. 

 The independent variable » is assumed to describe 

 circular paths concentric about the origin in the 

 «;-plane, and through interruptions at regular in- 

 tervals, to indicate the orthogonal paths which 

 are radiating straight lines through the origin. 

 Z will describe a system of curves in the Z-plane 

 corresponding to the circles, while the interrup- 

 tions in the Z-motion will define a system of 

 orthogonal curves corresponding to the radial 

 lines in the a-plane. 

 We have in general: 



Z — Az<^ + Bz»+.-.=X + iY 



= mod Ar" [cos (a8 -\- a) + i sin (aS + a) ] 

 + mod Br^ [cos (6e-f /3) + i sin (69 + j3)] 

 + 



where r denotes the modulus, and d the argument, 

 of s. The arguments oi A, B, ... are a, /3, — 

 The exponents a, b, ■ ■ ■ are real numbers and 

 may be positive or negative, integral or fractional. 

 The motion of Z is the resultant of the motions 

 along X and Y. These two rectilinear motions 

 can be produced simultaneously by a mechanism 

 similar to that described by W. H. L. Russell in 

 the Proceedings of the Royal Society of London, 

 Vol. 18, 1869. 



When only two powers of a are involved in the 

 expression for Z, a very simple instrument can 



be used in effecting the required transformation; 

 viz., an instrument which continuously combines 

 two circular motions. Such an instrument con- 

 sists essentially of two graduated arms or cranks, 

 made to revolve with the required angular veloci- 

 ties by means of suitable gears, and a parallelo- 

 grammic arrangement so connecting the revolving 

 arms that at each instant the half sum of the two 

 circular motions is indicated by a tracing point. 



Attention was called to numerous examples, 

 such as Z^g -\- Bsr^, Z^z — Bz^, where B and 

 6 are real positive quantities ; Z = z-{- 1/g, 

 Z^z-\- ^, Z = z -\- z/v, etc. 



A mechanism capable of performing a consider- 

 able variety of transformations like these was 

 exhibited before the society; also a small copper 

 plate upon which several curves had been etched 

 mechanically by means of the instrument. 



The International Unit of Light; Photometric 

 Units and Nomenclature: Dr. E. B. Rosa, of 

 the Bureau of Standards. 



The speaker gave the definitions of seven pho- 

 tometric magnitudes and derived the equations 

 showing the relations between them. These quan- 

 tities are : ( 1 ) the intensity, ( 2 ) luminous flux, 

 (3) illumination, (4) radiation, (5) hriglitness, 

 or specific intensity, (6) the surface integral of 

 the latter over the source, (7) quantity of light, 

 or the time integral of the flux. The first three 

 of these quantities are most used in practical 

 photometry and illuminating engineering, but the 

 others are required in a complete system, and it 

 contributes to clear thinking and concise expres- 

 sion to have a separate name for each different 

 quantity. The corresponding names in French 

 and German were given, and some changes in 

 these names suggested that would make the no- 

 menclature in the three languages more nearly 

 uniform. 



R. L. Faeis, 



NEW YOBK ACADEMY OF SCIENCES — SECTION OP 

 ASTRONOMY, PHYSICS AND CHEMISTBY 



A MEETING of this section was held on Monday, 

 October 18, at the American Museum of Natural 

 History. Mr. Edward Thatcher read a paper on 

 " Some Principles in Art Metal Work " ; W. Camp- 

 bell, " On the Structure and Constitution of some 

 Alloys and Metals used in the Arts," and Pro- 

 fessor D. W. Hering, on " Wave-length of Light 

 by Newton's Rings." 



Wm. Campbell, 



