72 



SCIENCE. 



[Vol. I., No. 3. 



in the paper noticed above to the solution of those 

 equations of the seventh degree in which a certain 

 function of tlie roots is unaltered by a group of 168 

 substitutions. Such equations arise in connection 

 ■with the modular equations of elliptic functions, and 

 had been previously studied by Hermite, Klein, and 

 others. Klein had pointed out that their treatment 

 sliould be made to depend upon the investigation of 

 the system formed by a certain ternary quartic, which 

 is transformed into itself by a group of 168 substitu- 

 tions and an arbitrary conic. It was this which led 

 Gordan to undertake his researches upon that system. 

 In the present paper he forms certain seven-valued 

 functions of the coefficients of the arbitrary conic; 

 the sums of the powers of these functions are, in 

 virtue of a general theorem previously proved, ration- 

 ally expressible in terms of the fundamental invari- 

 ants of the system ; and the fundamental invariants 

 are I'ationally expressible in terms of the sums of the 

 powers. The seven quantities, then, being regarded 

 as the roots of a given equation, the invariants in 

 question become known, and the solution of tire 

 equation is reduced to the problem of finding the co- 

 efficients of the arbitrary conic when the invariants 

 are given ; the solution of which problem is contained 

 in the preceding paper (No. 177). The whole investi- 

 gation is extremely long and difficult; and Prof. 

 Gordan announces his intention- of recasting the 

 method by which he obtained his results, and giving 

 a presentation of them ' in wliich every trace of the 

 way in which they were readied shall have disap- 

 peared.'— (JfaWi. onn., xx. 4, 1882.) F. F. [178 

 PHYSICS. 

 Acoustics. 



Sounds produced by flovr of liquids. — Tito 

 Martini lias continued the researches of Savart upon 

 the sound produced by a stream flowing through a 

 circular hole at the lower end of a long tube contain- 

 ing liquid. He finds that the pitch does not change 

 gradually, but that a definite number of distinct notes 

 are heard successively as the liquid column shortens 

 by the outflow. The pitch depends on the length of 

 the liquid column and on the velocity of efflux. The 

 number of vibrations is proportional to the velocity 

 of efflux, and the sound is pure only when the sound 

 of the vein is one of the proper sounds of the liquid 

 column. 



A column of constant length gives notes in a har- 

 monic series. When the sound is re-enforced by the 

 column of air above, it becomes quite loud. If the 

 walls of the tube are prevented from vibrating, the 

 sound ceases. The relative velocity of sound in dif- 

 ferent liquids may be determined by finding the 

 lengths of the columns of liquid which give the 

 same note, and the results given in the paper agree 

 very well with determinations by other methods. — 

 (/oiirnaip/iysigue, Nov., 1882.) c. B. c. [179 



Vibrations of loaded bar. — HM. Se'bert and Hu- 

 goniot have investigated by a new method the equa- 

 tions of motion of elastic bars, and especially the 

 case of a bar carrying an additional mass at one end. 

 — (CompJes)-e?idr(s, Oct. 30, 1882.) c. it. c. [180 



Determination of rate of tuning-forks. — 

 Miclielson has devised a new stroboscopic method, in 

 which a fork — for examijle, an Jiij (No. 1) — is com- 

 pared with a second ut.i (No. 2), kept in vibration 

 by electro-magnets, and which last fork is compared 

 directly with the seconds pendulum. The whole 

 number of vibrations of fork No. 2 is supposed to be 

 known. The fractions are found as follows : one prong 

 of the fork carries a mirror; and a few feet in front 

 of this is placed a Geissler tube, illuminated once a 



second, as the circuit of the induction coil in connec- 

 tion witli it is broken by the pendulum. The image 

 of the tube itself in the mirror is a broad band, 

 against which the narrow flash is projected. The 

 number of flashes between their recurrence in two 

 similar positions on the broad image of the tube 

 shows the number of vibrations per second to be 

 added to or subtracted from the known whole number. 



Thus, if there are a flashes in one period, 128 ± - is 



a 



the true rate. As fork No. 2 vibrates continuously, 

 great accuracy can be secured. A mercury globule 

 was used in connection with the pendulum to com- 

 plete the circuit; and, by means of a relay, a break 

 was iiroduced in tlie primary circuit of the induction 

 coil. A very constant battery must be used with the 

 electro-magnets of the fork. The method may be 

 simplified by dispensing with the electric fork, and 

 placing the fork to be rated vertically, and with one 

 edge in the focus of a microscope with ci'oss-hairs. 

 The Geissler tube is placed horizontally behind the 

 ,fork; and the positions of the edge of the fork with 

 reference to the cross-hairs are noted. A table of 

 measurements is given. — {Amer. journ. sc, Jan., 

 1883. ) c. E. c. [181 



Experiments T;vith resonance boxes. — At a 

 recent meeting of the Berlin physical society. Prof. 

 Christiani showed a mi,, fork, which placed on" its 

 box gave a maximum of tone when one side rather 

 than the other was turned to the mouth of the box. 

 The action seemed to be due to the box rather than 

 to the fork, though this had been rusted and re- 

 tuned. It was also found that a singing flame tuned 

 to mi:; was silenced when a mij resonating box was 

 placed liorizontally with its mouth at the top of the 

 tube, while if the corresponding fork was placed on 

 the box no such effect occurred. The same action 

 was noticed with a resonator; the flame being silenced 

 if this was in tune with the flame, but not otherwise. 

 — (iVajTO-e, Jan. 4, 1883.) c. e. c. [182 



Optics, 



Density of luminiferous ether. — Note on Glau's 

 determination of the density of the ether, by E. 

 Wiedmann. If an error in this estimate be corrected, 

 the result is measurably in agreement with that of 

 Sir W. Thomson. — ( Wied. arm., 1882, 986.) c. s. h. 



1 183 



■Whiteness of various sources of light. — The 

 results of a series of observations with an instrument 

 devised by Helmholtz, and by him named 'lenko- 

 scope,' is given by A. Konig. The general principle 

 upon which the instrument depends is the follow- 

 ing : A white surface is illuminated by the light to 

 be tested; and two adjacent images of this surface, 

 polarized at right angles to each other, are observed 

 through a Nicol's prism and a certain thickness of 

 quartz cut perpendicular to the axis. With such an 

 arrangement, the two surfaces would appear of com- 

 plementary colors, the tints being determined by the 

 azimuth of theNicol, and the degree of saturation by 

 the thinness of the quartz plate. With a thin plate 

 the two portions of the field would always be very 

 unlike; with a very thick plate, always nearly white 

 and alike; and, finally, with a plate of intermediate 

 thickness, the similarity would depend upon the 

 azimuth of the Nicol. The value of the azimuth 

 whicli yields the greatest similarity wlien a plate 

 20 mm. thick was employed — and this angle must 

 evidently depend upon the color of the light used — 

 was taken as an arliitrary measure of the whiteness 

 of the light. The table characterizing various fa- 



