282 



SCIENCE. 



[Vol. I., No. 10. 



It will be especialij' welcomed in those labora- 

 tories where considerable attention is already- 

 given to vertebrate work ; and it will do good 

 service in aiding to bring about a more equi- 

 table division of time and opportunities in 



those laboratories where the invertebrates have 

 hitherto received the lion's share of attention, 

 and iu some cases have taken nearly, or quite 

 all, the time in a course supposed to be de- 

 voted to general zoology. 



WEEKLY SUMMARY OF TEE PRO GUESS OF SCIENCE. 



MATHEMATICS. 



Attractions. — M. Aiigelitti discusses the case of 

 the attraction exerted between two masses when the 

 attraction varies as the product of tlie masses and 

 some function of the distance. Tlie particular func- 

 tion of the distance employed is the inverse Jitli 

 power. The author considers the attraction of lines 

 and plane figures upon a point iu the plane, and 

 finally briefly considers the attraction of surfaces 

 and solids upon points external to thera. Nearly all 

 of the results are known, many of them having been 

 given by Jellett and Townsend. — (Giorn. mat., xx.) 

 T. c. [584 



Bernouilli's numbers. — Mr. Ely, in a paper read 

 before the J. H. U. mathematical society, Jan. 17, 

 18S3, gave an accoiuit of the numbers An.m (generally 

 known as A« O'") which occur in the proof of Staudt's 

 theorem concerning Bernouilli's numbers. After giv- 

 ing the definition of these numbers in the form of 

 a series, and stating some of their known properties, 

 Mr. Ely proceeds to enunciate a number of new 

 properties. Without using a great many algebraical 

 symbols, it is impossible to give a fuller notice of 

 Mr. Ely's interesting communication. — (Johns Hop- 

 kins univ. circ, No. 21, 18S3.) T. o. [585 



Partitions. — Professor Sylvester defines partition- 

 graphs, and makes certain applications of their prop- 

 erties to infinite series and infinite products, and 

 particularly to the two forms of representation of 

 the theta functions of one variable by means of an 

 infinite series and an infinite product. A partition- 

 graph is defined as a series of points lying in lines 

 parallel to two fixed lines. The number of points, 

 or lines parallel to one of the boundaries chosen at 

 will, will represent the sviccessive components of the 

 partition, and the number of the lines themselves 

 will be the number of parts in the partition. The 

 lines in question are termed magnitude-lilies, and the 

 ci-ossing ones part-lines. The graph is termed regu- 

 lar when the magnitude-lines never increase as they 

 recede from the rectilinear boundary to which they 

 are parallel. This cannot happen without the same 

 being true of lines parallel to the part-boundary. 

 A regular graph is thus one in which the lines and 

 columns of points neither of them increase as they 

 recede from their respective boundaries. A partition 

 is self-conjugate when its representative graph, after 

 an interchange of the names of the part- and magni- 

 tude-lines, gives the same reading. Such a graph is 

 therefore symmetrical. By application of the prop- 

 erties of the above-described partitiongraphs, Prof. 

 Sylvester proves the equation between the reciprocal 

 of (1— ax) (1— ax'^) (1— ax^) . . . and the infinite se- 

 ries 



1+5 



:+7 



i+- 



1— X ' 1— ax ' (1— x)(l— x^) ' (1— ax){l— a.x-) 

 He also shows how to obtain the development in in- 

 finite series of the infinite products (l-f-ox) (1-f-ax^) 

 il + ax'-) . . . and [l + a-Kt] {l + a-'x^] (l-l-«- V) . . . 



A parallel bipartition of u is defined as a couple of sets 

 of numbers written on opposite sides of a line of de- 

 marcation, so that the number of numbers on the left 

 always exceeds that on the right by a given differ- 

 ence, 6, which may be any number from zero up- 

 wards, and such that the sum of all the elements 

 collectively is equal to n. Then the co-efiicient of 

 x" a' or x''a~' in the above iiroducts is the number of 

 parallel bijiartitions of n to the difierence j, limited 

 to contain only odd numbers, which must not appear 

 in the same arrangement more than once on the same 

 side of the line of demarcation. In vol. v., No. 3, of 

 the American jiiurnal of mathematics, Prof. Sylvester 

 will give a full account of this new theory of parti- 

 tiongraphs. — (Johns Honk. univ. circ, No. 21.) T. c. 



[586 

 PHYSICS. 

 {Photography.) 



Speed of drop-shutters. — M. Vidal has sug- 

 gested a method of measuring short exposures. He 

 employs a large clock-face painted black, with white 

 figures, numbering from 1 to 100, painted upon it. A 

 white index-hand Is revolved from behind at a uni- 

 form speed of one turn per second. Photographs 

 taken of this apparatus themselves register the time 

 of exposure. — (Brit, journ. phot., March 9.) w. H. p. 



[587 



Photographic defects and their remedies. — A 

 short article by Mr. E. H. Farmer gives a list of all 

 the principal photographic defects, together with 

 their remedies. They include gray or metallic, pink, 

 green, yellow, red, and white or opalescent fogs; also 

 frilling, halos, want of density, and spots on the film. 



— (Brit, journ. phot, March 9.) w. H. p. [588 

 Notes. — To make plates tropical. Heat them for 



two hours in a hot oven. 



To clean plates. Soak them in hot water, which 

 will dissolve the gelatine. 



A convenient plate-lifter. Solder a long, pointed 

 piece of metal to an ordinary thimble. By this 

 means, the plates can readily be lifted from the trays. 



— (P/iot. times, Feb.) w. h. p. [589 



Electricity, 



EfBciency of an electric motor. — Professor S. 

 P. Thompson shows very simply, by means of a graph- 

 ical method, the laws of work and efficiency of an 

 electromotor, as dependent upon the ratio of its 

 electromotive force to that of the electric supply. — 

 (Phil, may., ¥e\).) E. H. H. [590 



The electrostatic and electromagnetic sys- 

 tems. — The French have boon tiikiiig their turn In 

 discussing this matter. MM. M<'iva(lier and Vaschy 

 seek to reconcile the two systems by means of co- 

 efficients depending on dielectric and magnetic Induc- 

 tive capacities. Their arguments and experiments 

 are criticised by M. Maurice L^vy. One who has 

 followed the discussion of this matter, as it has 

 appeared in the Philosophical marjazine during the 



