May 29, 1903.] 



SCIENCE. 



861 



Professor H. F. Blichfeldt : ' Note on linear 

 substitution groups of tinite order.' 



Professor E. E. Ailardice: 'On some curves 

 connected with a system of similar conies through 

 three points.' 



Dr. Saul Epsteeu : ' Necessary and sufficient 

 condition for the existence of invariant subgroups.' 



Professor G. A. IIeller: 'On reciprocal 

 groups.' 



Dr. H. C. Moreno and Professor G. A. Miller : 

 ' On the non-abelian groups in which every sub- 

 group is abelian.' 



Mr. W. a. Manning : ' On the class of primitive 

 substitution groups.' 



Miss Ida M. Schottenpels : ' Generational def- 

 inition of an abstract group simply isomorphic 

 with the simple substitution group GjoW-' 



Dr. T. M. Putnam : ' Certain subgroups of the 

 quaternary linear fractional group of deter- 

 minant unity, in the general Galois field.' 



The paper by Dr. Epsteen was presented 

 by Professor Wilczynski. The secretary read 

 the paper by Miss Schottenfels. The other 

 papers were presented by their authors. The 

 next meeting of the section will be held in 

 December at the University of California. 



G. A. MiLLEE, 



Secretary. 



NEW YORK ACADEJ:Y OF SCIENCES. 



section of astronomy, physics and chemistry. 



At the meeting of the section on May 4, 

 Professor Ernest E. von NardrofF read a paper 

 on ' A New Interferometer Method for Meas- 

 uring the Refractive Index of a Transparent 

 Plate.' 



This method was planned to avoid the 

 use of compensation, which leads to grave 

 errors unless in the compensating material 

 the ratio of the velocities for any two wave- 

 lengths is the same as in the substance being 

 measured. It is frequently impracticable to 

 fulfil this condition, as for example by using 

 as a compensator a second plate of the same 

 material. Air compensation is of course out 

 of the question. 



In the present method, in which no use is 

 made of white light fringes, the transparent 

 plate, a microscope cover-glass for instance, 

 is mounted on a special stage perpendicular 

 to the path of one of the beams in a Michelson 



interferometer. With sodium light, bands are 

 seen that are generally distorted through lack 

 of perfect parallelism between the surfaces of 

 the plate. The stage is now rotated forward 

 about a vertical axis through an angle of 45° 

 up to a fixed stop, thus increasing the path 

 through plate. Slowly turning the stage 

 backward, the bands passing a fixed point in 

 the field are carefully counted until the plate 

 returns to the perpendicular position, when 

 the motion of the bands reverses. A new 

 count is now made while the stage is turned 

 past the perpendicular, backward 45° to a 

 second fixed stop. Generally these counts 

 differ by a few tenths of a band, owing to im- 

 perfect mounting of the stage as a whole on 

 the interferometer, but they may be averaged 

 without sensible error. Since the light passes 

 through the plate twice, one half the number 

 of bands counted should be taken to represent 

 the increase of optical path, N. The thick- 

 ness, t, of the plate at the part of it observed 

 in the interferometer may be measured by 

 means of a micrometer caliper or a spherom- 

 eter. The following exact formula, much 

 simplified through the use of precisely 45° 

 of rotation, gives the value of the refractive 

 index, ^ . 



i^ = i + 



,+ (.-/!- = )■ 



i' 



t) 



For sodium light where the wave-length, ^^ 

 is 0.0005893 mm. 



0.5 -+- 



(o., 



:(.. 



2929- 



This method has been extended to the meas- 

 urement of doubly refracting plates, such as 

 mica. The plate must contain in its plane at 

 least one of the axes of the so-called ellipsoid 

 of elasticity, and must be mounted with this 

 axis vertical. The bands may be observed 

 through a Nicol prism having its shorter 

 diagonal vertical. 



A second paper was presented by Dr. G. B. 

 Warring, on ' Some Peculiarities of the 



