312 



SCIENCE. 



[Vol. I., No. 11. 



functions. He limits liimself to tlie examination of 

 geodesic polygons traced upon central surfaces of the 

 second degree. Section 3 of the paper is an ex- 

 cursus upon the thread construction {fadenconstruc- 

 tioii) of the lines of curvature on quadrics. For an 

 intelligible reading of the paper, a previous paper of 

 the author's, ' Ueber fadenstructionen des ellipsoi- 

 des,' must be referred to. — {Math, mm., xxi. 1883.) 

 T. c. [639 



Complexes of the second order. — M. Genty 

 discusses Kunimer's sixteen-nodal quartic by the 

 methods of vector analysis. No new results or prop- 

 erties of this surface are given; but the paper is in- 

 teresting as an application of this particular method. 

 — {Journ. de math., 1SS2.) T. c. [640 



Hypergeometric series. — M. Mathieu studies 

 the differential equation of the second order, satis- 

 fied by Gauss's function F (a, /3, y, x), and examines 

 briefly the cases when the general solution of this 

 equation can be expressed in a finite form, and ob- 

 tains, in consequence, the cases when the function F 

 (". A y, X) can be expressed in finite form. He de- 

 termines also the cases when the function F (a, /3, y, 

 sin- ^) is periodic with respect to (S, and has 2 it for 

 its period. — {Journ. demath., 1882.) T. c. [641 



Parallel surface to the ellipsoid. — Dr. Craig 

 discusses the general equation of this surface, and its 

 principal sections. Certain of its singularities are 

 enumerated, and formulae are given for the ratios of 

 corresponding elements of area and length upon the 

 parallel and primitive ellipsoid. A number of for- 

 mulae are given, referring to the curvature of the 

 surface. Elliptic co-ordinates are employed through- 

 out the greater part of the paper. — (Journ. fur math., 

 xciii. ) T. c. [642 



PHYSICS. 

 Heat. 



Specific heat of ivater. — The results of experi- 

 ments on the specific heat of water at different 

 temperatures diflfer, not only quantitatively, but quali- 

 tatively. Rowland and Miinchhausen, whose experi- 

 ments are the most reliable on this subject, have shown 

 that the specific heat of water decreases to about .30°, 

 and thence increases. In order to test these results, 

 Hr. F. Neesen has made some experiments upon this 

 subject with Bunsen's ice-caloriineter. The calorime- 

 ter was constructed according to the plan of Schuller 

 and Wartha, in order to avoid the errors caused by the 

 iiupuritles of the snow. Hr. Neesen points out that 

 it is of importance not to begin the e.Kperiment until 

 some indications of melting appear in the ice of the 

 calorimeter. If tliis point is not observed, the change 

 of volume will be too small. The thermometers used 

 were two mercury thermometers, graduated respec- 

 tively to 0.2° and 0.1°. The results obtained by Nee- 

 sen are to be considered merely approximate, as 

 suflicient determinations of the specific heat at each 

 temperature were not made. The results, however, 

 agree qualitatively, though not quantitatively, with 

 those of Rowland. — (Ann. phys. chetn., xviii. 3.) 

 C. B. P. [643 



Electricity. 



High-pressure electric accumulator. — Mr. 

 Frederick J. Smith describes an arrangement for pro- 

 longing the life of a gas-battery. The tubes contain- 

 ing tlie electrode are inverted in a tank nearly filled 

 with dilute sulphuric acid. The tank is closed air- 

 tight, and the gases, as they are evolved, generate a 

 pressure, which, as shown by a manometer, amounts 

 to several atmospheres by the time the tubes are 

 filled. The amount of gas which can be thus col- 



lected in the tubes is, of course, much greater than 

 that collected under ordinary conditions, and the life 

 of the gas-battery correspondingly longer. When a 

 Faure accumulator is treated in the same way, the 

 electromotive force of the polarization is affeced, but 

 to what extent is not yet definitely determined. — 

 (Phil, may., March.) e. h. ir. [644 



Bifllar suspension and absolute measurement. 

 — F. Kohlrausch gives a mathematical treatment of 

 the bifilar suspension, obtaining, as the complete ex- 

 pression for the directive force, 



!> = ![" 



616-2 

 "IT 



Sttp^E ■ 



where m is the mass of the suspended body increased 

 by half the mass of the wires; e, and e^, the distance 

 apart of theupperand lowerends respectively ; p the ra- 

 dius, and E the modulus of elasticity, of the suspend 

 ing wires; g, the acceleration of gravity; and Z, half 



the mean length of the wires, diminished hyp -'V-— E. 



Hence he deduces two methods of measuring the 

 horizontal intensity of terrestrial magnetism, which 

 he calls the bifilar-galvanic and bifilar-magnetic re- 

 spectively. The first method consists in observing 

 the deflections a of a magnet, and if of a circular coil 

 suspended at a distance a from the magnet, when 

 D tan a 



B.' = —TT T, subject to certain corrections. The 



a' tan (p^ ■> 



second method consists in observing the deflections 

 a and f of two magnets, oiie large in respect to the 



other, when H'^ = „.(i + t) (i " ' ^ + rf^ " ^ o^) 

 sin a 



T — T (1 — 2 tan a tan «), where d is the distance be- 

 tan « ' ^ " 



M 

 tween the poles of the larger magnet, K = ^ for 



the smaller magnet, A its length, and T its torsion- 

 co-efficieut. On the 21st of October, 1881, the first 

 method gave .10J07, and on the 16th of February, 

 1882, the" second method gave .19389, cm-ig^ sec — ^ 

 at Wiirzburg. — (Ann. phys. chem., Dec, 1882.) J. T. 



[645 

 ENGINEERING. 

 Boston ■wrater-TBTorks. — An elaborate description 

 of the additional supply of water for the city of Bos- 

 ton from Sudbury River, compiled by Mr. A. Fteley, 

 the resident-engineer upon the work during lis con- 

 struction, has just been issued by the city government 

 in a large, finely printed, and copiously illustrat'-d vol- 

 ume. The works for supplying Boston with water 

 from Sudbury River consist of three storage-reservoirs 

 in Framingham, and a conduit from that town to 

 Chestnut-hill reservoir in Brookliiie. In 1881 Sud- 

 bury River furnished to Boston more than twice the 

 quantity of water supplied from Lake Cochituate; and 

 steps have already been taken to increase still further 

 the storage-capacity of the system. The volume be- 

 gins with a discussion of the sources of supply, the 

 rainfall, and the storage-capacity of the reservoirs. 

 Next follows a general description of the dams and 

 reservoirs, and of the several sections of the work, 

 in all its engineering features. The quality of the 

 water, the gauging of the river, and a discussion of 

 the capacity of tlie conduit, and the flow of water 

 over weirs, conclude the body of the work. The 

 appendix contains valuable tables on water-supply hy- 

 draulics, and a large amount of information for the 

 practising engineer. The wor]< is illustrated with 69 

 large plates, commencing with a map of the Sudbury 

 River watershed, and giving very fully the construe- 



