382 



NATURE 



{^Mar. 14, 1872 



them the placenta has no claim to be a primary index of affinity. 

 And if we only seek for the most practically convenient way of 

 arranging Mammalia, it is to the bones and teeth, rather than to 

 the maternal organs of generation, that we must look. 



P. H. Pye-Smith 



Potential Energy 



While on the subject of Thomson and Tait's Natural Philo- 

 sophy, I should like to call attention to the definition of Potential 

 Energy, given in Art. 273, p. 1S9. 



I think it will be found tliat this definition gives the wrong 

 sign, because the potential energy in any configuration is the 

 amount of work the forces of the system perform in i-diiniiiiglo 

 the zero configuration, the ideal position of stable equilibrium. 



Thus when a spring is stretched or compressed the po'ential 

 energy is measured by the kinetic energy which is generated by 

 the work done by the elastic force of the spring by the time the 

 spring has returned 10 its unstretched condition. Wiih this 

 change of sign the definition now agrees with that given in 

 Art 484. 



Infinite distance being taken as the zero configuration, the 

 potential energy is a positive quantity for such forces as electric 

 and raagiietic forces. 



With this zero the potential energy for gravitating particles is 

 negative, which is expressed by saying that the exhaustion of 

 potential energy is positive, because as the particles approach 

 their kinetic energy increases, and their potential energy suffers 

 exhaustion and diminishes. 



In Art. 4S5 we read, "The potential at any point, due to any 

 attracting or repelling body or distribution of matter, is the 

 mutual potential energy between it and a unit of matter placed 

 at that point. But in the case of gravitation, to avoid defining 

 the potential as a negative quantity, it is convenient to change 

 the sign. Thus the gravitatio'i potential atany point, due to any 

 mass, is the quantity of work required to remove aunit of matter 

 from that point to an infinite distance." 



Although the gravitation potential has had its sign changed, 

 nevertheless the potential at any point P for gravitation and for 

 electric and mrgnelic forces, is defined in the same way as the 

 sum of the quotients of every portion of the mass divided by its 

 distance from P. 



Thi; is the Potential Fimciion of Green, usually called by the 

 n.ime given by Gauss, the Potential, and is the function which 

 satisfies Laplace's equation. 



The gravitation potential is the old force function of Sir W. 

 Hamihon and Jacobi, such that its rate of increase in any di- 

 rection is the resolved part of the force in that direction on the 

 ■unit of mass. 



The potential, defined as the potential energy in the unit of 

 mass is of opposite sign to the free function ; its rate of de- 

 crease in any direction is the component force in that direction. 



These perplexing changes of sign arise from the fact that in 

 gravitation we hive only one kind of matter, the particles of 

 which naturally attract ; hence the potential energy is negative, 

 or it diminiihes as the particles approach ; it is, therefore, con- 

 venient to make a change of sign. 



In the general case of which electrical and magnelical pheno- 

 mena may be taken as the type, like particles repel, unlike 

 attract, and the potential energy increases as the particles 

 approach. 



These definitions and conventions of signs are, of course, in 

 accordance with those given by Thomson and Tait ; the proper 

 signs and names are given also in Briot's " Theorie Mecanique 

 de la Chaleur," but in all the other French books there is great 

 confusion ; for instance, in the "Theorie Mecanique de la Chaleur" 

 of Verdet, the potential goes by Green's name, the potential func- 

 tion, but has its sign changed, while the potential energy is called 

 the potential, after Clausius. This also seems to be the nomen- 

 clature adopted by the Germans. 



It is very necessary that all doubt as to the meaning and value 

 of these important functions should be set at rest ; the system 

 adopted in Thomson and Tail's "Natural Philosophy" leaves 

 nothing to be desired. A. G. Greenhill 



St. John'9<:ollege, Cambridge, March 6 



Development of Barometric Depressions 



I LEAVE to those who are equal to it the task of reconciling 

 g,nd discussing "J. K. L.'s" propositions in reference to Indian 



meteorology, which appear to be these :— i, "The rainfall in 

 the Himalayas " (instanced by him in proof that rainfall is not 

 the cause of depression), " probably causes a very great de- 

 pression" (meaning, I now suppose, the great Asiatic depres.-ion 

 really due to the rarefaction of the air in Central Asia) ; 2, " but 

 certainly not any currents such as I have described " (viz., cur- 

 rents in accordance with Buys Ballot's Law, having the lowest 

 pressure on their left) ; 3, " the circuit of the wind in the region 

 of the Himalayas is, so far as we know, in exact accordance with 

 Ballot's Law." 



My complaint was that the critic had ignored, not, of course, 

 Part II. of my book, but certain propositions in Part I., as "dis- 

 tinctly enunciated " as those on which he comments, and in- 

 separable from them, though not yet fully discussed. 



I will now close, as far as my part is concerned, a discussion, 

 for the opening of which I was responsible, but which his, con- 

 trary to my intention, become rather personal than scientific. Tlie 

 question, however, really at issue between us I believe to be one 

 of some interest in meteorology. " Djes the fact that precipi- 

 tation in certain cases, and especially in the warmer regions of the 

 globe, fails to produce baric depression, disprove, or render im- 

 probable, the theory (based on substantial evidence) that the 

 depressions which occur in Western Europe are results of pre- 

 cipitation?" 



March 10 W. Clement J^ey 



A Safety Lamp 



The article in this week's N.A.TtTRE on " Foul Air in Mines, 

 and how to live in it " calls to mind a contrivance made use of 

 by the watchmen of Paris in all magazines where explosive or 

 inflammable materials are stored, and suggests the idea that the 

 same may possibly be of service to our miners. 



The Paris Figaro ^zyi, " Take an oblong vial of the whitest 

 and clearest glass, put in it a piece of phosphorus about the size 

 of a pea, upon which pour some olive oil, heated to the boiling 

 point, filling the vial about one-third full, and then seal the vial 

 hermetically. To use it, remove the cork, and allow the air to 

 enter the vial, and then re-cork it. The whole empty space in 

 the bottle will then become luminous, and the light obtained 

 will be equil to that of a lamp. As -oon as the light grows 

 weak its power can be increased by opening the vial and allow- 

 ing a fresh supply of air to enter. Thus prepared the vial may 

 be used for six months." 



4, Moreton Place, S.W. B. G. Je.nkins 



Beautiful Meteor 



1 ENCLOSE a description of meteor, apparently of unusual 

 brilliancy, recently seen by my assistant at Parsonstown, think- 

 ing that it may perhaps be interesting to some of your readers. 



Carlton Club, London, March 12 Rosss 



" Observed an intensely brilliant meteor. It was first seen in 

 the region about Lepus, whence it moved with a slow and steady 

 motion across the heavens to the S.E. horizon, where it gr.adually 

 disappeared in a bank of cloud at about 9'> 5™ 19% Greenwich 

 mean time, having occupied seven or eight seconds in moving 

 over 50° of a great circle. The time given may be a few seconds 

 wrong, as it was noted by an ordinary watch. The head was 

 intensely brilliant, of a bluish white colour, and lighted up the 

 whole sky. 



"Its brightness was maintained during its entire visibility, and 

 may have been as great as the moon at quadrature. Apparent 

 diameter of the head 42'. It was followed by a very narrow tail 

 about 3° in length and of a reddish hue. It did not leave any 

 phosphorescent train behind it, but at the latter part of its course 

 it threw out some reddish luminous masses, that gradually faded 

 away. Its apparent course was in a great circle through jS Canis 

 Majoris to a point near the S.E. horizon, in azimuth S. 28i° E., 

 and altitude 8i°. For Canis Majoris the azimuth was S. 

 20° 52' -4 \V., and altitude 16' 43''3. 



' ' Observatory, Birr Castle, March 8 " 



While travelling last night, at about twenty minutes to nine 

 o'clock, as we were descending a tolerably high hill, about 5 miles 

 from this city, our road leading S.S.W. , I found myself very 

 favourably circum.stanced for seeing a beautiful meteor which was 



