140 



SCIENCE. 



[Vol.. II., N<). 28. 



singular point, we may, by giving i the above value, 

 vary the form of the solutions of P {ij) = 0. The 

 author prefers, however, to treat the question directly, 

 inasmuch as he is thus enabled to employ many of the 

 results arrived at by M. Fuchs, and as he can use pro- 

 cesses identical with those employed by Fuchs in his 

 study of the integrals around a singular point. M. 

 Floquet obtains thus a fundamental sj'stem, S, of 

 solutions connected with a certain algebraic equation, 

 A = 0, which he calls the fundamental equation rela- 

 tive to the period u ; the first member of A = is a de- 

 terminant of degree m with respect to the unknown e. 

 The elements of the system S constitute as many 

 groups as the equation A = has distinct roots; and, 

 by apj)lying a process due to M. Hamburger, these 

 groups are divided into sub-groups which are mutu- 

 ally independent. The particular conclusions arrived 

 at are as follows. I. Let s^, e., . . . e„ denote the dis- 

 tinct roots of A = ; let A,- denote the order parting 

 from which the minors of A cease being all zero 

 for e—sj. 1°. P = admits as distinct integrals 

 A, -|- 2,., + ...-)- /l„ periodic functions of the second 

 kind, and no more. 2°. There exists a fundamental 

 system of solutions, including, first, Xj -|- Ao -1- . . . -|- A,, 

 periodic functions of the second kind ; second, 

 m — (/l, 4- A., . . . + Xi) expressions, each having the 

 form of an integral polynomial in x, and having for 

 ,coefiicients periodic functions of the second kind pos- 

 sessing the same multiplier. 3°. The multipliers of 

 the periodic functions which appear in the funda- 

 mental system, either as elements or as coeflicients in 

 the elements, are equal to the different roots £ , , e._, . . . e„ 

 of the fundamental equation. II. In order that P ~0 

 may have m periodic functions of the second kind as 

 distinct integrals, it is necessary and sufficient that 

 each of the roots of A = shall annul all the minors 

 of A up to those of an order equal to the degree of the 

 multiplicity of each root. In the above, a periodic 

 function of the second kind, with a period u, means a 

 function defined by relation F {x + o)) = e F (x); £ is 

 the multiplier; and, if s = 1, the function is said to be 

 periodic of the first kind. — {Ann. I'ecole norm, sup., 

 Feb.) T. c. [134 



PHYSICS. 

 (Phoiograp/ii/.) 

 The effect of pressure ou the gelatine film. 

 — Capt. Abney has shown, that, if pressure is ap- 

 plied to the sensitive surface of the gelatine plates, 

 the same result is obtained as if the plate had been 

 exposed to the light. The editor of the British jour- 

 nal of photography, experimenting further, finds that 

 abrasion, such as may be produced by the motion of 

 a glass rod drawn out to a fine rounded point, is 

 necessary to the action, and that mere pressure, such 

 as would be obtained by a carpenter's vise, produces 

 no effect whatever. A stripped film was next placed 

 upon the other one, and the markings maile with the 

 rod upon it, with very heavy pressure. On develop- 

 ment with pyro, no effect was at first produced; but, 

 by prolonged action, a green fog was created in the 

 adjacent regions of the film, leaving the figures clear 

 on a dark ground. — {Brit, journ. phot, June 1.5.) 

 w. H. P. . [135 



Electricity. 



Unipolar conductivity. — Hugo Sleyer confirms 

 the result previously obtained by him. that the min- 

 eral psilomelan possesses the curious property of uni- 

 polar conductivity for electricity. He finds, also, that 

 the resistance to a constant current is independent of 

 the duration of the current, and that diffei'ent speci- 

 mens of the mineral are radically different in elec- 

 trical properties: hence the inconsistent results of 

 different observers are admissible. — {Ann. phys. 

 chem'., xix. 70.) j. T. [136 



A cheap bolometer. — C Baur describes a ther- 

 moscope which consists of thin gold leaves blackened 

 with platinum chloride, and cut so as to combine large 

 surface with low resistance. These are attached to 

 opposite ends of a cylinder which is hollow and open 

 at the ends, and solid in the middle. These leaves 

 are made the arms of a Wheatstone bridge, and prove 

 to be a much more delicate test for radiant heat than 

 the thermopile. The author terms the instrument a 

 radiometer. — {Ann. ])hys. chem., xlx. 12.) j. T. 



[137 



Measurement of the ohm. — J. Frohlich de- 

 scribes a ' dyuamometric ' method of measuring the 

 ohm: the secondary coil is balanced on a rigid hori- 

 zontal arm, suspended bifilarly so that the plane of 

 winding is perpendicular to the meridian; opposite is 

 placed the inducing coil, in which, by an ingenious 

 arrangement of keys, the ciu-rent is made, shunted, 

 and broken without a sjiark. The consequent attrac- 

 tions and repulsions are measured by the swinging of 

 the suspended apparatus. From a preliminary ex- 

 periment, the author is encouraged to consider the 

 method a practical one. — {Ann. i^hys. chem., xix. 

 106. ) [138 



ENGINEERING. 



Engines of lake steamers. — One of the steam- 

 ers of the Western transportation line has engines of 

 the 'compound' type, two low and two high pressure 

 cylinders, of 20 and of 40 inches diameter and of 40 

 inches stroke. The steam is cut off at 8 inches in 

 the high-pressure cylinder, and the consumption of 

 steam amounts to but 10 pounds per hour and per 

 horse-power. The boat is 2.56 feet long, :3S feet beam, 

 and 16 feet draught. The engines and boilers weigli 

 about 100 tons. The latter have 100 square feet of 

 grate-surface, and 3,366 square feet of heating-sui-face. 

 Another vessel, the E. B. Hale, has simple engines, 

 carries 1,600 tons of freiglit at 14 feet draught, makes 

 about 10 knots an hour on 1,400 pounds of coal. 

 The engines are 36 by 36, and are supplied with 

 steam by one boiler 12 feet in diameter by IS feet 

 long. — {Mechanics, June 23.) B. H. T. [139 



Heating by superheated e:Khaust-steam. — 

 Mr. Levi Hussey lias devised a method of heating 

 buildings in winter by the exhaust-steam from en- 

 gines by first passing it through a superheater in the 

 flue, and there taking up heat which would other- 

 wise be sent up the chimney and wasted. The steam 

 is thus deprived of all moisture, and then heated 

 to so high a temperature that it will heat more 

 thoroughly, and with less obstruction by back-press- 



