5IO 



NA rURE 



[March 31, 1892 



chapters ; the second of real algebraical quantity ; 

 and the third of complex numbers. The first two 

 parts contain what is requisite for school use, the third 

 is beyond the ordinary run of junior students. The 

 whole has, we believe, stood the test of class 

 work. In the second part the application of trigo- 

 nometry to surveying is made interesting by treat- 

 ing the subject as practically as possible. There 

 is a copy from a photograph of a theodolite, and a con- 

 versational description of the same, and in Part I., through 

 the permission of the publishers, there is printed a portion 

 of the map of the Mer de Glace given in the " Life of 

 Prof. Forbes." These little points are likely to interest 

 young students. Of course the hyperbolic functions are 

 discussed, but they are discussed in a way that is novel 

 to us in some of the details ; for instance, geometrical 

 proofs are given of cosh {u -|- v) and sinh {u -f- v). These 

 strike us as being very elegant and quite within school 

 range, as they need only a moderate acquaintance with 

 the properties of the rectangular hyperbola. A short 

 space is occupied with the Gudermannian function, and 

 a table of approximate values of hyperbolic functions is 

 given in the same section. The section on convergency 

 and continuity of series, and, in fact, the whole discussion 

 of series, is very carefully dorie. 



Our summing up is that the book is one of the best we 

 have met with on the subject, and quite fitted to 

 hold its own against the two or three formidable rivals 

 that have lately appeared in the field. There is a 

 plethora of carefully chosen examples, which we advise 

 the junior student to use with Prof. Chrystal's caution in 

 mind : " I should much deprecate the idea that any one 

 pupil is to work all the exercises (in the * Algebra ') at the 

 first or at any reading. We do too much of that kind of 

 work in this country.^' The text is further illustrated by 

 many ^ra/Zzj' of different functions, and answers, carefully 

 tested from working with pupils, are appended at the end, 

 with tables of the logarithms required for the exercises. 



Les Fleurs a Paris : Culture et Cotnmerce. Par Philippe 

 L. de Vilmorin. (Paris : J. B. BaiUiere et Fils, 1892.) 



The trade in cut flowers is now quite an important de- 

 partment of commerce, and it is rather surprising that a 

 good many attempts have not been made to give a full 

 and connected account of it. In the present volume M. 

 de Vilmorin deals with the subject chiefly in its relation 

 to Paris, and he has brought together many facts which 

 will be of interest both to lovers of flowers and to students 

 of social economy. He describes the various ways in 

 which the trade is organized in the French capital, the 

 sources from which the flowers are derived, the manner 

 in which they are cultivated, and the means by which 

 they are distributed. He then presents an account of 

 the various kinds of flowers used for decorative purposes, 

 giving in simple language such botanical details as are 

 likely to be intelligible and attractive even to non-scien- 

 tific readers. The volume is abundantly and very prettily 

 illustrated. 



Health Springs of Germany and Austria. By F. O- 

 Buckland, M.D. Second Edition. (London : W. H, 

 Allen and Co., 1892.) 

 This little book ought to be of considerable service to 

 invalias who may desire to obtain aid in the choice of a 

 Continental health resort. The author does not profess 

 to present elaborate details as to the various springs with 

 which he deals ; but he says enough about each to give 

 a sufficiently clear idea of its merits and defects. He 

 offers also some good general remarks on the nature and 

 uses of health springs. In the present edition he has 

 made little change, but he has increased the value of the 

 book by adding an index. 



NO. IT 70, VOL. 45] 



LETTERS TO THE EDITOR. 



[ The Editor does not hold himself responsible for opinions ex- 

 pressed by his correspondents. Neither can he undertake 

 to return, or to correspond with the writers of, rejected 

 manuscripts intended for this or any other part of iiA.T\!KK. 

 No notice is taken of anonymous communications. ] 



Heat Engines and Saline Solutions. 



I HAVE nothing to modify in what I have written under the 

 above heading (p. 438) ; but to deal completely with all the 

 questions raised by Mr. Macfarlane Gray (p. 486) would re- 

 quire half a treatise, I will limit myself to a few brief remarks. 



(i) In Carnot's engine there is no (separate) boiler or con- 

 denser. 



(2) When I spoke of the various parts of the working sub- 

 stance being in equilibrium with one another, I referred to com- 

 plete equilibrium, thermal as well as mechanical. If the 

 temperature varies from one part to another there is no equili- 

 brium. 



(3) On the above understanding the pressure of vapour in 

 equilibrium with a saline solution of given strength is a definite 

 function of the temperature. 



(4) Let me suggest that the origin of the difficulty may lie in 

 the phrase "superheated vapour," which has not so definite a 

 meaning as Mr. Gray seems to ascribe to it. Whether vapour 

 be superheated or no, depends, not only upon the condition of 

 the vapour itself, but also upon the bodies with which it is in 

 contact. Vapour which is merely saturated in contact with a 

 saline solution must be regarded as superheated when contact 

 with the solution is cut off. In the first situation it would con- 

 dense upon compression, and in the second situation it would 

 not. 



In conclusion, I will hazard the prediction that, if the heat 

 engines of the distant future are at all analogous to our present 

 steam engines, either the water (as the substance first heated} 

 will be replaced by a fluid of less inherent volatility, or else the 

 volatility of the water will be restrained by the addition to it of 

 some -body held in solution. 



Rayleigh. 



On Earth Vibrations. 



It seems that the earth, once set in vibration, maintains this 

 state for a long time before coming to rest. The observers of 

 Greenwich (see Major H. S. Palmer in the Transactions of 

 the Seismological Society of Japan, vol. iii., p. 148) found 

 that from time to time, at considerable intervals, there was an 

 evening when the usual observations for determining the collima- 

 tion-error of the transit-circle by means of reflection in a tray of 

 mercury could not be taken, on account of the constant 

 trembling of the surface of the mercury, which on such oc- 

 casions continued until long past midnight. These are occasions 

 when crowds of the poorer classes of London flock for amuse- 

 ment to Greenwich Park. A favourite pastime with the young 

 people, often prolonged until after nightfall, is to clamber to the 

 top of the steep slopes of the hill on which the Observatory 

 stands— in fact, to the paling of the enclosure— and then, 

 joining hands in twos or threes, to bolt precipitately to the 

 bottom, where, as may be imagined, they usually arrive "all in 

 a heap." Hundreds join in this sport on fine evenings, and the 

 result, as shown by the behaviour of the mercury, is to set the 

 whole of Flamsteed Hill in a tremor, which does not subside 

 until early next morning, many hours after the people have left. 



Another very beautiful proof of this fact offered itself to me in 

 the Geophysical Observatory of Rocca di Papa, Rome. A slight 

 earthquake coming from Aquila (at no kilometres north-east 

 of Rocca di Papa) was felt and registered by the instruments at 

 9.39 a.m. mean time of Rome, on the 8th of last February. 

 Just at that time I was casually observing through a microscope 

 a pendulum 6 cm, long, which suddenly began to display great 

 agitation. 



Now such a pendulum, when removed from its equilibrium 

 position for an amplitude equal to the observed, ccjmes to rest 

 in about half-an-hour. In the present case the pendulum con- 

 tinued to oscillate till the afternoon. Nor did the character of 

 the vibrations correspond to the gradually and regularly diminish- 

 ing oscillation of a pendulum which has received a single shock. 



'The pendulum is firmly fixed to a big column, deeply founded 



