144 



SCIENCE. 



[Vol. I., No. 5. 



erties of ruled spaces. He defines a point a, and a 

 plane a through this point, as a couple, wliicli he in- 

 dicates by tlie symbol (a, a). Among the co '' couples 

 situated upon a straight line A (i.e.,' the point a lies 

 on a straight line A, which is itself contained in the 

 plane a), tliere is a simple infinity satisfying a given 

 condition; their aggregate constitutes a correlation. 

 If this condilion consists in the equality of the an- 

 barraonic ratios of the four points and the four 

 planes of four arbitrary couples of the correlation, 

 the correlation is said to be anharmonin. An impor- 

 tant application is inade of a theoi-em of Chasles', con- 

 cerning the distribution of the tangent planes to ruled 

 surfaces. If m, u.i u^ u^ are parameters upon which 

 depend a knowledge of a right line (u), and u, + dui, 

 etc., those which refer to an infinitely near line 

 {u + cla), the vanishing of a homogeneous function 

 of the differentials da expresses a property of the 

 system bf lines (ii) and {u + du), and, consequently, 

 of the correlation which they determine relatively to 

 one of the group (u). The differentials du, or finite 

 quantities t proportional to them, may be considered 

 as homogeneous co-ordinates of the different anhar- 

 monic correlations existing upon the line Ji. Among 

 these correlations those which destroy one or two 

 kinds of i-co-ordinates constitute, respectively, a 

 plexus or a series of correlations. These plesi and 

 series replace the cones of elementary directions in 

 punctual space. The condition for the meeting of 

 two lines (u) and {u+ du) is expressed by the vanish- 

 ing of a quadratic form N{du); and, obviously, all 

 forms such as KN(du), where K is only a function 

 of the variables u, express the same property. The 

 author remarks that it is possible to choose K in such 

 a manner that the resulting form shall represent the 

 moment of the two lines: i.e., the product of the short- 

 est distance between them by the sine of the angle of 

 their mutual inclination. A number of analogies are 

 here given with punctual spaces. The author makes 

 use of a theorem of Sturm's, concerning pencils of 

 lines; and, particularly, of a method of Darbou.'c', 

 referring to the linear representation of surfaces. A 

 special system of co-ordinates is examined, in which 

 the linear complex possess the properties of spheres; 

 and from this is deduced a system analogous to pento- 

 spherical co-ordinates, of which the Pllickerian co- 

 ordinates and Klein's sextuply-orthogonal system are 

 particular cases. 



The third part of the memoir refers entirely to in- 

 finitesimal properties of the second order. The prob- 

 lem treated is an extension of the theory of geodesies, 

 and coiulucts to a geometrical interpretation of Lip- 

 schitz' normal co-ordinates. — [Bull. sc. math., etc., 

 18S2.) T. c. [289 



PHYSICS. 

 {Photographi/.) 



Photographic halos and reversals. — When a 

 brilliant point of light is photographed, we often find 

 that it is surrounded by a black circle on the negative, 

 whose inner edge is distinctly marked, while its outer 

 shades off imperceptibly into the surrounding regions. 

 Capt. Abney shows that this is not a diffracUon phe- 

 nomenon as has been asserted, but is due to reflection 

 from the back surface of the glass; and that the di- 

 ameter of the ring depends on the thickness of the 

 glass, and on its critical angle of reflection. All 

 trouble from halos may be avoided by coating the 

 back of the plate with Brunswick black, which re- 

 flects back no light to the film. 



It is a well-known fact, that, if we greatly over-ex- 

 pose a plate, we shall get a reversal 6t the image, — 

 the lights taking white, and the shades black, instead 

 of Dice versa as usual. Now, it has been shown that 



this is due to the action of the bromine, which has 

 been freed in the lower layers of the film by tlie ac- 

 tion of light, and rises, attacking the metallic silver 

 and sub-bromide in the upper layers. This difficulty 

 is avoided by soaking the film in a solution of potas- 

 sium nitrite, which absorbs the bromine as fast as it 

 is formed, and before it can do any damage. — {Brit, 

 journ. phot., Jan. 5.) w. H. p. [290 



Keeping-qualities of gelatine plates. — Mr. 

 William Brooks has been making some experiments 

 on the keeping-qualities of gelatine plates, and finds, 

 that, though they may work well for a few months, 

 they become slower after that time, the images 

 thinner, and that they develop a tendency to fog. 

 Emulsions were made up with the different silver 

 salts: and it was found that plates coated with the 

 pure bromide of silver would keep well for six 

 months; those coated with bromo-iodide would keep 

 fovir months; those with bromo-chloro-iodide, three 

 months; and bromo-chloride, two months. The latter 

 plates gave by far the best results when new; but un- 

 .exposed plates very soon deteriorated, especially if 

 the weather was damp. — {Brit, journ. phot., Feb. 2, 

 188-3. ) w. H. P. [291 



Lead as an intensifier. — Herr Grehner recom- 

 mends the following intensifying solution: nitrate 

 of lead, 4 parts; potassium ferricyanide, 6 parts; 

 water, 100 parts. When this solution has acted suf- 

 ficiently long upon the plate, it is taken out and 

 washed; it is then placed in a mixture of one part 

 of a saturated solution of potassium chromate, and 

 five parts of ammonia, after which it is washed for 

 a short time. If washed too long, the film has a 

 tendency to peel. This formula is applicable to 

 collodion plates. — {Brit, journ. phot., Feb. 2, 188.3.) 

 w. H. P. [292 



Electricity. 



Determination of the ohm. — G. Lippman pro- 

 poses to measure the resistance of a column of mercury 

 by opposing the cui'rent induced by a rotating mag- 

 net to another current measured by a galvanometer. 

 Then 



_ 2TnimK 

 K'H tana' 

 where K is a constant of the electro-magnetic appara- 

 tus, m the moment of the magnet, n its velocity of 

 rotation, K' the galvanometer constant, and H the 



m . 



glS 



determined by Gauss's method. The author claims, 

 that in a resistance of one to five ohms the fractional 

 error would be within -ni\rn- — {Comptes rendus, xcv. 23. ) 

 Another method, by the same author, is to revolve 

 a coil inside of a bobbin which carries a current pass- 

 ing through the resistance to be measured. The cur- 

 rent induced in the revolving coil is opposed to the 

 difference of potential at two points in the resistance 

 to be measui'ed. The condilion of equilibrium is r = 

 2 7r)iC S, where n is the velocity of rotation, S the 

 dislance between the jjoiuts of contact, and C a con- 

 stant of the bobbin. The author gives an experi- 

 mental method of finding S', the value which S would 

 assume if the bobbin were extended to infinity in both 



directions. The value of C for such a bobbin is 4 =-> 



d 

 d being the distance between two turns of the wire. — 

 {Comptes rendus, xcY.2(}.} j. T. [293 



Aerial navigation by electricity. — M. Gaston 

 Tissandier has found that an electric motor of the 

 Siemens iiattern, driven by a bichromate battery, the 

 whole not exceeding the weight of three men, is 



horizontal resultant of local magnetic forces. 



