214 



SCIENCE, 



[Vol. VI., No. 136. 



Let X, in a system of rectangular coordinates, 

 represent mass, and y absolute temperature, then 

 the area, xy^ will be proportional to the energy, 

 or, with a suitable unit of temperature, will equal 

 it. Now, we may cut this area into n equal parts 

 by vertical lines, which will also cut the mass into 

 n equal parts. In such case it requires no scien- 

 tific imagination to see that these parts are similar 

 and * similarly circumstanced; ' but this is altogether 

 too simple for the use to be made of it, and no such 

 statement can pass for a law of thermodynamics ; it 

 is simply the law of homogeneousness. 



Rankine leads up to his statement in an unfortu- 

 nate way, perhaps, emphasizing the fact that every 

 particle is equally hot. Well, so it must be, or the 

 upper line of the figure would not exist, or would be 

 curved, which would interfere with the argument, be- 

 cause there would then be no one temperature for all 

 the molecules. But Rankine intended no such vertical 

 subdivision: in fact, he says, 'Let unity of weight,' 

 etc. ; and we may take a differential unit, and so jDut 

 such a division out of the question. The division 

 intended by Rankine was by horizontal lines, which 

 makes the statement of the law identical with the 

 other: only he says here, 'heat;' and there, 'tempera- 

 ture;' and he commences with heat, because heat is 

 energy, and changes to temperature, because temper- 

 ature is the practical way of estimating this energy, 

 and is proportional to it. 



We believe, then, that this is the one and only sec- 

 ond law; and as our agent is a quantity of energy, 

 and as energy resides in mass, whereas different sub- 

 stances do not differ in their mass, therefore the 

 particular working substance used has no effect. 



We will now look again at the formula for effi- 

 ciency, which flows directly from Rankine' s law, in a 

 simple and evident manner. 



If we could make an infinite-cylinder engine, this 

 formula would not be needed. This engine works at 

 a temperature, not between two temperatures, and it 

 transforms all the heat into work. But mechanical 

 considerations require us to build engines that run 

 in cycles, and we then need it. Every engine run- 

 ning in a cycle is a double engine, consisting of an 

 engine proper and a condenser; i.e., while the piston 

 rises in the cylinder, which we cannot make infinitely 

 high, we transform heat into work completely: then 

 we must use our engine as a condenser for recom- 

 pressing the gas; and, while doing so, we transform 

 work completely into heat; and if we lower the tem- 

 perature of the gas before compressing it, there re- 

 mains a margin of work, according to the efficiency 

 formula. 



It should be remarked, that we have made no spe- 

 cial reference in this address to any thing but a perfect- 

 gas engine; and we believe the theory of this should 

 be made clear before introducing the necessary modi- 

 fications to include liquids and solids: Rankine has, 

 however, framed his formula to cover both. Many 

 other points have been left untouched ; but if I have 

 made plainer how heat, and therefore temperature, 

 may be supposed to consist of any number of equal 

 parts, and convinced you that Rankine' s is the real 



and only second law, my main object will have been 

 accomplished. 



PROCEEDINGS OF THE SECTION OF 

 MECHANICAL SCIENCE. 



The valuable work done by a few in this 

 section deserves the special recognition and 

 support of all its members. The four divisions 

 under which this work may be classified, em- 

 brace wide and interesting fields of thought 

 and study. These divisions are, Technical 

 education, Accurate standards of measure- 

 ment, General, scientific and practical engi- 

 neering work, and Original investigation. 

 These are proper lines of work for the ad- 

 vancement of ' mechanical science and engi- 

 neering,' because they include the education 

 of men for the work ; the production of instru- 

 ments and appliances suited to the work ; ex- 

 cite enthusiasm, and diffuse knowledge, among 

 the workers ; and enlarge the realm subjected 

 to the exact knowledge and control of the in- 

 tellect and will of man. 



The first paper read before this section was on the 

 strength of stay-bolts in boilers, and gave an account 

 of experiments by the writer, Mr. L. S. Randolph. 

 These experiments were designed to furnish data for 

 the explanation of the peculiar manner in which the 

 stay-bolts between the fire-box and boiler-shell had 

 been found to break. The theory was, that the 

 extreme difference of temperature liable to occur 

 between the parallel plates — being at times 200° F. , — 

 caused a shifting of these plates, parallel to one an- 

 other, sufficient to bend the stay-bolts considerably ; 

 and that this bending, occurring near the surface 

 of the plate into which the bolt is screwed, caused 

 the bolts to break at this point. The amount of 

 such bending having been calculated from the known 

 difference of temperature and the length of the 

 plates, the experiments showed that if similar stay- 

 bolts were subjected to this amount of bending, 

 they would ultimately break, thus, apparently, con- 

 firming the theory. In the discussion, different forms 

 of bolts or stays were suggested as likely to remedy 

 the difficulty. The adoption of a link in place of a 

 bolt was thought to be impracticable in this case on 

 account of the small distance between the plates. 

 Proportioning the stays so as to enable them to bend 

 under the stress to which they are subjected without 

 reaching the elastic limit of the material, was sug- 

 gested as a remedy for the difficulty. It was shown 

 that stays are sometimes worn away by being vibrated 

 or bent. This bending causes the scale which has 

 been formed to be thrown off; and oxidation occur- 

 ring again under the action of the water, this new 

 scale is thrown off, and this process continued wears 

 away or ' channels ' the iron. 



A short abstract of a paper on a universal form of 

 pressure-motor by Prof. D. P. Todd was presented by 



