582 



NATURE 



[Oct. 



1 1 



A similar remark applies to temperature, the range experimentally 

 treated for water and for sea-water being only o° to .15° C. Also 

 it has been stated that the recording indices are liable to be 

 washed down the tube, to a small extent, during the relief of 

 pressure, so that the results given are probably a little too small. 



Compressibility of mercury, per atmosphere COOOO036 



,, ,, gla^S CTOO0O02O 



Average compressibility of fresh water per atmosphere — 



[At lowpressures 520 . 10" 



For 1 ton = 152*3 atm. 504 



2 ,, = 304-6 ,, 490 



3 » = 456-9 » 478 



355 . TO' 9 / + 3 . 10- 9 / 2 ] 

 360 4 



365 5 



370 6 



The term independent of I (the compressibility at 0° C.) is of 

 the form — 



I0" 7 (520 - 17/ + f), 



where the unit of p is 1S 2 '3 atmospheres (1 ton-weight per 

 square inch). This must not be extended in application much 

 beyond p = 3, for there is no warrant, experimental or other, 

 for the minimum which it would give at p = 8*5. 



The point of minimum compressibility of fresh water is 

 probably about 6o° C. at atmospheric pressure, but is lowered 

 by increase of pressure. 



As an approximation through the whole range of the experi- 

 ments we have the formula — 



o - ooi86 



I - 



2L 



400 



f 2 

 1 0000 



)'. 



36 + J> 



while the following formula exactly represents the average of all 

 the experimental results at each temperature and pressure — 



to" 7 (52o - 17/ + pi) - io _9 (355 + ip)t + io- 9 (3 + fY 1 - 



Average compressibility of sea*water (about o - 92 of that of 

 fresh water) — 



481 . io -7 - 340 . io _! V 



462 



447-5 



J [At low pressures 

 For 1 ton 



2! ,, 



3 ». 



34o 

 320 



305 



295 



io" 9 ; 2 ] 



- 437-5 

 Term independent of / — 



io" 7 (48i ~ 21*25/ + 2'25/ 2 ). 

 Approximate formula — 



S^U9(i -JL + fi \ 

 38 + p \ 150 10000/ 



Minimum compressibility point, probably about 56 C. at 

 atmospheric pressure, is lowered by increase of pressure. 



Average compressibility of solutions of NaCl for the first p 

 tons of additional pressure at o° C. : — 



o '00186 



36 + p + s' 



where s of NaCl is dissolved in 100 of water. 



Note the remarkable resemblance between this and the formula 

 for the average compressibility of fresh water ato° C, and/ -f s 

 tons of additional pressure. 



[Various parts of the investigation seem to favour Laplace's 

 view that there is a large molecular pressure in liquids. In the 

 text it has been suggested, in accordance with a formula of the 

 kinetic theory of gases, that in water this may amount to about 

 36 tons-weight on the square inch. In a similar way it would 

 appear that the molecular pressure in salt solutions is greater 

 than that in water by an amount directly proportional to the 

 quantity of salt added.] 



Six miles of sea, at lo c C. throughout, are reduced in depth 

 620 feet by compression. At o° C. the amount would be about 

 663 feet, or a furlong. (This quantity varies nearly as the 

 square of the depth). Hence the pressure at a depth of 6 miles 

 is nearly 1000 atmospheres. 



The maximum-density point of water is lowered about 3° C. 

 by 150 atmospheres of additional pressure. 



From the heat developed by compression of water I obtained 

 a lowering of 3 C. per ton-weight per square inch. 



From the ratio of the volumes of water (under atmospheric 

 pressure) at 0° C, and 4 C, given by Despretz, combined with 

 my results as to the compressibility, I found 3°'i7 C. ; and by 

 direct experiment (a modified form of that of Hope) 2°7 C. 



The- circumstances of this experiment make it certain that the 

 last result is too small. 



Thus, at ordinary temperatures, the expansibility of water is 

 increased by the application of pressure. 



In consequence, the heat developed by sudden compression of 

 water at temperatures above 4° C. increases in a higher ratio 

 than the pressure applied ; and water under 4 C. may be 

 heated by the sudden application of sufficient pressure. 



The maximum density coincides with the freezing-point at 

 - 2° - 4 C, under a pressure of 2" 14 tons. 



SCIENTIFIC SERIALS. 



In the Journal of Botany for August and September, a con- 

 siderable portion is occupied by the continuation of papers, to 

 which reference has already been made — Messrs. Britten and 

 Boulger's biographical index of British and Irish botanists, 

 and Mr. G. Murray's catalogue of the marine Alga; of the 

 West Indian region. — Mr. W. H. Beeby records an addition 

 to the British Phanerogamic flora in Callitriche polymorpha. — 

 Mr. A. Fryer has some critical remarks on Potamogetpn Jluitans. 

 —A number of new ferns from Western China, and from Mani- 

 pur, in India, are described by Mr. J. G. Baker and Colonel 

 Beddome. 



The numbers of the Botanical Gazette for June-August con- 

 tain quite an unusual number of articles of general interest. 

 Bryologists will find a description of eight new species of moss 

 from North America, each illustrated by a plate ; in fact, the 

 plates in these three numbers are very numerous and excellent. 

 — Mr. Chas. Robertson discusses the origin of zygomorphic 

 (lowers from the point of view of evolution. — Of flowering 

 plants, we have descriptions of new species from Western 

 America (chiefly Umbelliferae) and from Guatemala, by Messrs. 

 Coulter and Rose and Mr. J. D. Smith. — Mr. F. C. Newcombe 

 describes the mode of dissemination of the spores of Equisetum 

 in the splitting of the sporange and the carriage of the spores 

 by means of the elaters. — Mr. A. F. Forste describes (with a 

 plate) the adaptation to cress-fertilization in various species. 



American Journal of Mathematics, 1888 (Baltimore, Johns 

 HopkinsUniversity).- — The object of M. R. Liouville's paper, " Sur 

 les lignes geodesiques des surfaces a courbure constante," with 

 which vol. x. No. 4 opens, is stated by him to be " d'indiquer 

 la signification geometrique des equations differentielles du 

 second ordre ayant leur integrale geneiale lineaire par rapport 

 aux constantes arbitraires, et de former leurs invariants pour 

 toutes les substitutions qui ne changent point, soit l'inconnue, 

 soit la variable independante " (pp. 283-292). — The following 

 memoir, on the primitive groups of transformations in space 

 of four dimensions, by James M. Page, is likely to be very 

 serviceable, as it is the first continuous account in English of the 

 researches of Sophus Lie on the theory of groups of trans- 

 formations. Lie himself has developed the theory in a series 

 of papers which date from 1873, and has not published any con- 

 nected work on the subject (pp. 293-346). — W. C. L. Gorton 

 writes on line congruences. He treats the subject by 

 quaternions, and obtains all Rummer's results (Crelle, vol. lvii. ), 

 and is enabled by his method to carry out certai.i steps which 

 are only indicated by this writer (pp. 34.6-367). — The volume 

 closes with a notelet by Prof. Franklin, entitled " Some 

 Theorems concerning the Centre of Gravity." This contains 

 "almost instantaneous" proofs of Lagrange's two theorems on 

 the centre of gravity. 



With vol. xi. No. 1, we have what strikes us as being an 

 admirable likeness of the great French mathematician, Charles 

 Hermite. We have previously expressed our pleasure at 

 this new departure of the editors of this journal, and hope 

 their catering for mathematicians will meet with material 

 approval. — The first communication is a memoir on a new 

 theory of symmetric functions, by Captain P A. Mac- 

 mahon, R. A. This prolific young mathematician is doing ex- 

 cellent work, and the pages of the journal are just suited to 

 present his results in the most effective form. The paper fa 

 intimately connected with a recent one, by the same writer, com- 

 municated to the London Mathematical Society, in which he 

 gives a sketch of an extension of the algebra of the theory of 

 symmetrical functions, and establishes the basis of a wide de- 

 velopment. " The main object of the memoir is to show clearly 



