June 29, 1883.] 



SCIENCE. 



607 



The physiology of protoplasmic motion. By Th. W. 

 ExGELMAXN. Translated by C. S. Dolley. 

 Rochester, N.Y., Davis §• Leyden, n.d. 40p. 8°. 



Tliis pamphlet, without date or any state- 

 ment as to the original, is a good' translation, 

 with very poor reproductions of the illustra- 



tions, of Engelmann's chapter in Hermann's 

 well-known Handbuch der physiologic. It is 

 to be regretted that the author did not see iit 

 to date his translation, nor give the source of 

 the original. The latter omission we are for- 

 tunately able to supply. 



WEEKLY SUMMARY OF THE PRO QBE SS OF SCIENCE. 



MATHEMATICS. 



Orthogonal transformations. — Mr. W. J. C. 

 Sharp has iuvestigated the invariants of a certain 

 orthogonal transformation witli special leference to 

 the theory of the strains and stresses of an elastic 

 solid. If a, h, c, f, g, h, are transformed according to 

 the same law as x^, y-, z-, yz, zx, xy {x, y, z, being the 

 rectangular Cartesian co-ordinates of a point, trans- 

 formed without cliange o£ origin), they will have a 

 system, of invariants entirely uuailected by the trans- 

 formation. The author gives the three invariants 

 corresponding to these quantities, and makes a large 

 number of exceedingly interesting applications to 

 different geometrical and physical problems. As Mr. 

 Sharp's paper consists almost entirely of algebraical 

 work, it is impossible to give it more than this brief 

 reference, and to commend it to the notice of those 

 interested in the subjects which he touches upon. — 

 {Proc. Lond. math, sac, xiii.) t. c. [1137 



Elliptic functions.— The Eev. M. M. TJ. Wilkin- 

 son has given a number of general formulae arising 

 from the differentiation of the elliptic functions with 

 respect to the modulus. — [Proc. Lond. math, soc, 

 xiii.) T. c. [1138 



TJnicursal t-wisted quartics. — Mr. R. A. Roberts 

 considers in this pajjer some properties of the unicur- 

 sal twisted quartic curve ; namely, the intersection of 

 a quadric and a cubic which contains two non-inter- 

 secting generators of the quadric. Almost exclusive 

 use is made of the expressions for the co-ordinates of 

 a point on the curve in terms of one independent 

 parameter. A reduction is first given to the canoni- 

 cal form, and, after examining a particular property 

 of the curve, the author obtains the condition that 

 four points of the curve shall be complanar; then 

 certain points on the curve are examined, and inva- 

 riant conditions are obtained for degenerate forms of 

 the curve. The next five sections treat of polygons 

 circumscribed about the curve, and the five conclud- 

 ing sections treat of circular unicursal quartics. — 

 {Proc. Lond. math, soc, xiv. ) T. c. [1139 



PHYSICS. 



Acoustics. 

 Maintained vibrations. — Lord Eayleigh dis- 

 cusses mathematically that type of maintained vibra- 

 tion which is most familiar in the form of Melde's 

 experiment in which a fine string is kept in transverse 

 vibration by connecting it at one end with one prong 

 of a vibrating tuning-fork, the direclion of tlie mo- 

 tion of the point o£ attachment being parallel to the 

 length of the string. The string settles into a state 

 of permanent vibratioh whose period Is double tliat 

 of the point of attachment. The equations indicate 

 that an absolutely rigorous adjustment of pitch is 

 necessary, a conclusion not borne out by experiment. 



This is accounted for by the slight variation of rate 

 with variation of amplitude. The son rauque of 

 Savart is probably caused in a similar way, as the 

 periodic variations of tension accompanying longitu- 

 dinal vibrations will produce associated transverse 

 vibrations. For lecture illustration, a soft-iron pen- 

 dulum vibrating on knife-edges may be placed verti- 

 cally over a vertical bar electro-magnet, through 

 which are sent intermittent currents whose frequen- 

 cy is twice that of the pendulum vibrations. Of the 

 same nature are the crispations observed by Faraday 

 on the surface of water which oscillates vertically. 

 The author has shown that Faraday was correct in 

 his opinion tlrat there are two vibrations of the sup- 

 port for each vibration of the liquid. — (Phil, mar/., 

 April. ) c. E. c. L1140 



Hydrogen-Tvhistles. — Le Conte calls attention 

 to an error in Gallon's calculations, as he assumes 

 that the number of vibrations of the whistle, when 

 blown with different gases, is in proportion to the 

 density, while it is actually in proportion to the 

 square root of the density. Hence 86,533 instead of 

 812,000 vibrations would be given by Mr. Galton's pro- 

 posed whistle. — (Nature, May 17.) c. k. c. [1141 



Electricity, 

 ■Winding electro-magnets. — Professors Perry 

 and Ayrton have experimented upon the following 

 types of electro-magnets : — 



1. Wires wound equally over the whole length. 



2. Wires coned toward each end. 



3. Wire wound equally over half the iron bar, 

 leaving the other end bare. 



4. Wire wound on one half, but coned towards the 

 end. 



It was found that the effect of coning the wire is 

 to produce a strong field very near the pole, but that 

 the force falls off very rapidly as the distance from the 

 pole increases. At considerable distances from 

 the end of the electro-magnet the uniformly coiled 

 magnet, No. 1, produces the most powerful field. At 

 very small distances from the end of the magnet, Nos. 

 3 and 4 give the strongest effects. They conclude 

 therefrom, that with a definite length of wire, of core, 

 and strength of current, the mode of coiling the wire 

 determines the strength of the magnetic field at dif- 

 ferent distances from the end of the electro-magnet. 

 — {Phil, mag., June, 397.) J. T. [1142 



CHEMISTRY. 

 {Analytical.) 

 Amnionic hyposulphite as a reagent in quali- 

 tative ansilysis. — A. Orlowsky suggests the use of 

 ammonic hyposulphite instead of liydric sulphide in 

 a qualitative separation of the metals. In a syste- 

 matic course of analysis which Orlowsky proposes, 

 lead, barium, strontium, and calcium are precipitated 



