6C2 



NA TURE 



[April 30, 1903 



It may be objected to this explanation that if the 

 rati at which the atoms are being- transformed is very 

 slow, the energy liberated by the transformation of a 

 given number of atoms must be very much greater 

 than that set free when the same number of atoms 

 are concerned in any known chemical combination. 

 It must be remembered, however, that the changes 

 contemplated on this hypothesis are of a different kind 

 from those occurring in ordinary chemical com- 

 bination. The changes we are considering are changes 

 in the configuration of the atom, and it is possible 

 that changes of this kind may be accompanied by the 

 liberation of very large quantities of energy. Thus, 

 taking the atomic weight of radium as 225, if the 

 mass of the atom of radium were due to the presence 

 in it of a large number of corpuscles, each carrying 

 the charge of 3-4 x 10 ~ I0 electrostatic units of negative 

 electricity, and if this charge oT negative elec- 

 tricity wire associated with an equal charge of 

 positive, so as to make the atom electrically neutral, 

 then if these positive and negative charges were separ- 

 ated bv a distance of 10 " s cm., the intrinsic energy 

 possessed bv the atom would be so great that a diminu- 

 tion of it by 1 per cent, would be able to maintain 

 the radiation from radium as measured by Curie for 

 30,000 years. 



Another point to be noted is that the radiation from 

 a concentrated mass of radium may possibly be very 

 much greater than that from the same mass when 

 disseminated through a large volume of pitch blende; 

 for it is possible that the radiation from one atom may 

 tend to put the surrounding atoms in the unstable 

 state; if this were so, more atoms would in a given 

 time pass from the one state to the other if they were 

 placed so as to receive the radiation from their neigh- 

 bours than if they were disseminated through a 

 matrix which shielded each radium atom from the 

 radiation given out by its neighbours. 



J. J. Thomson. 



ENTROPY. 

 The Thermodynamics of Heat Engines. Bv Sidney A. 

 Reeve, Professor of Steam-Engineering at the Wor- 

 cester Polytechnic Institute (U.S.A.). Pp. xiv + 316 

 + 42. (New York: The Macmillan Company; 

 London : Macmillan and Co., Ltd., 1903.) Price 

 10s. 6d. net. 



THIS is a very good specimen of that sort of book 

 which is an amplification of the lecture notes of 

 a professor who has carefully prepared problems for 

 . students. We may not always like the way in which 

 he introduces the subject to his pupils, and we may 

 say that it is unphilosophical and even cryptic, and 

 sometimes too brilliant, but such comments are ofti n 

 due to the fact that his way happens not to be the usual 

 way of presenting the subject. The way of Prof. Reeve 

 probably suits his particular class of unscientific pupil- 

 very well. He uses terms in senses somewhat different 

 from those in common use. He is absolutely correct 

 in many statements with which we would willingly 

 find as much fault as Macaulay did with those of 

 Robert Montgomery. For example : — 



NO. 1748, VOL. 67] 



" The universe is eternal. In the face of its stead- 

 fast continuity man's momentary existence and evan- 

 escent will are as cloud-wreaths against a mountain 

 side." 



We do not know why it should be thought necessary 

 when an engineer is presenting the usual useful appli- 

 cation of the known laws of thermodynamics that he 

 should introduce it in thirty-six pages of this style of 

 writing. 



When the author comes to the actual problems which 

 may be worked out by a simple application of the t,(p- 

 diagram, he is a fairly safe guide to the student, 

 although here and there we should have liked him to 

 point out on what assumptions he is working. 



Perhaps readers of Nature will allow us to give .1 

 short description of the way in which even elementary 

 engineering students are now able to solve what used 

 to be considered very difficult problems. 



We assume that at any instant a pound of stuff is 

 all at tin- same pressure p and temperature I, and that 

 it has a volume ;•. There is some law connecting p. 

 v and t so that any two of these three will define the 

 state of the stuff. During any infinitely small change 

 of state, the stuff gives out mechanical energy or does 

 work p.dv if dv is its change of volume; let it receive 

 the heat energy <?H. Stating all energy in the same 

 units, the net gain of energy by the stuff during the 

 change is dE = dH — p.dv. This E is called the intrinsic 

 energy of the stuff. We assume that there is no other 

 kind of energy to be given to or taken from the stuff 

 than heat and work. The first law of thermodynamics 

 states that, if stuff is carried through a cyclic change 

 and is brought back to its original state, the integral 

 of </H is equal to the integral of p.dv, and E comes back 

 to its original value. The integral of dH is not zero, 

 the integral of the work p.dv is not zero, but the 

 integral of dE is zero. The gain of intrinsic energj 

 in a closed cycle is zero. The second law o; thermo- 

 dynamics is that if we divide liH by ( the absolute tem- 

 perature (on a perfect gas thermometer) of the stufi 

 and call dH/t a gain d(p of entropy, then the integral 

 ol t/(p in a complete cycle is zero. 



The mathematical statements of the first and second 

 laws of thermodynamics are, therefore : — E and <p are 

 properties of the stuff which are known if the state of 

 the stuff is known. Or, dE and d<p are complete 

 differentials. 



Thus in any state of 1 lb. of stuff we know its 



/, z>, /, E and <J>, 



and (except during change from solid to liquid, or 

 liquid to vapour, when p and t are not independent ) 

 any two of these five enable all the others to be calcu- 

 lated. Hence, graphically, a diagram showing how 

 any two of them alter, is a diagram which completely 

 defines the changing stuff. This has been known ever 

 since Rankine and Clausius discovered the second law 

 of thermodynamics. It is owing to Mr. McFarlane 

 Gray's persistency in advocating the use of the </>/ 

 diagram in conjunction with the p,v diagram that 

 engineering students are able so easily to work prob- 

 lems, especially in stuff which is in the liquid-vapour 

 condition. 



Since work is p.dv, the area of a p,v diagram re- 



