Jan. 15, 1874] 



NATURE 



199 



Dr. Balfour Stewart,' however, has not only endeavoured 

 to give to the ideas of Work and Energy their proper 

 position among the most elementary ideas which we can 

 form, but he has displayed an equal amount of freedom in 

 treating the still more modern ideiis of the Dissipation of 

 Energy, and of the difference between exact and statistical 

 knowledge. 



Thus his \"ery first words relate to 



" Oitr Ignorance of Individuals 



" Very often we know little or nothing of individuals, 

 while we yet possess a definite knowledge of the laws 

 which regulate communities. 



"The Registrar-General, for example, will tell us that 

 the death-rate in London varies with the temperature in 

 such a manner that a very low temperature is invariably 

 accompanied by a very high death-rate. But if we ask 

 him to select some one individual, and explain to us in 

 what manner his death was caused by the low tempera- 

 ture, he will, most probably, be unable to do so. . . ." 



" Nor is our knowledge of individuals greater in the 

 domains of physical science. We know nothing, or next 

 to nothing, of the ultimate structure and properties of 

 matter, whether organic or inorganic. 



" No doubt there arc certain cases where a large num- 

 ber of particles are linked together so as to act as one 

 individual, and then we can predict its action, as, for 

 instance, in the solar system, where the physical astrono- 

 mer is able to predict with great exactness the positions 

 of the various planets, or of the moon." 



We regret that we have not space enough to quote the 

 whole of this introductorj' passage, which, in the unpre- 

 tending language of clear thought, expresses ideas which 

 have as yet been appreciated only by a very small number 

 of scientific men, but which will, in due time, greatly 

 modify the popular notions as to the nature of human 

 knowledge. 



The uniformities, therefore, which we observe in our 

 experiments on quantities of matter containing many mil- 

 lions of molecules in continual motion, are uniformities 

 of the same kind as those first explained by Laplace, and 

 in more recent times wondered at by Buckle, and arise 

 from the slumping together of innumerable cases, each of 

 which is by no means uniform with the others. 



This statement acquires still greater significance when 

 it is combined with another consideration which Dr. 

 Stewart, if we mistake not, has already insisted on in his 

 opening lecture at the Owens College. This is the dis- 

 tinction between stable and unstable arrangements of 

 matter and motion. A system, whether at rest or in mo- 

 tion, is said to be stable if a slight variation of its initial cir- 

 cumstances will, at the end of a finite time, produce only 

 a slight variation in the configuration or motion at that 

 time. If, on the contrary, a variation, however slight, in 

 the initial circumstances, may produce, in a finite time, a 

 laro'e disturbance, the equilibrium or motion of the sys- 

 tem is said to be unstable. 



Dr. Stewart illustrates this by several examples, among 

 which we may select a clock as an instance of a stable 

 arrangement in which everything is contrived so that any 

 slight disturbance shall produce as little effect as pos- 

 sible on the position of the hands at any future time. A 

 rifle, on the other hand, is an unstable contrivance, for a 

 very slight pressure on the trigger is sufficient to occasion 

 the motion of the hammer and the explosion of the gun- 



powder — effects, the energy of which is out of all propor- 

 tion to the work done on the trigger. 



Thus we ha\'e stable arrangements which, when at work 

 are not easily put wrong, and unstable arrangements 

 which are characterised by great delicacy of construction. 



The rifle, however, as Dr. Stewart points out, is a 

 machine which, though delicately constructed, is not in- 

 calculably so. Its instability is not like that of an egg 

 bal.mced on its longer axis. But in an animal we find a 

 structure composed of materials which are chemically un- 

 stable, so arranged that on account of the changes to 

 which they are liable, the smallest disturbance may pro- 

 duce the most varied states of motion. If, then, an 

 animal is to be compared to a machine, the delicacy of 

 that machine must be incalculable. 



It is a metaphysical doctrine, that from the same ante- 

 cedents follow the same consequents. No one can gain- 

 say this abstract statement. But it is not of much use 

 in a world like ours, in which the same antecedents never 

 again concur, and in which nothing ever happens twice. 

 Indeed, for aught we know, one of the antecedents might 

 be the precise time and place of the event, in which case 

 experience would go for nothing. 



The physical axiom which has a somewhat similar as- 

 pect is, " That from like antecedents follow like conse- 

 quents." But here we have passed from sameness to 

 likeness, from absolute accuracy to a more or less rough 

 approximation. The axiom is now applicable only to 

 systems of the kind which we have called stable, in which 

 slight variations in the antecedents produce slight varia- 

 tions in the consequents. In unstable systems, like ante- 

 cedents do not produce like consequents ; and as our 

 knowledge is never more than an approximation to the 

 truth, the calculation of what will take place in such a 

 system is impossible to us. 



Dr. Balfour Stewart's discussion of the Dissipation of 

 Energy is perhaps as satisfactory as it could be made in 

 the space allotted to it, and without the use of mathema- 

 tical methods. Energy is indestructible, but it may cease 

 to be available. Here we have a word not familiar in 

 pure science — a word connoting usefulness. We must 

 therefore define what is meant by available, and state 

 the conditions under which we are supposed to be placed 



Energy is available when it can be made to do visible 

 work. The conditions under which we attempt to trans- 

 form energy into work are that we must make use of the 

 interactions of a given system of bodies, moving within a 

 given region of space, out of or into which neither matter 

 nor heat can pass. 



If these bodies are in visible motion, we first reduce 

 them to rest by causing them to do a certain amount of 

 work. We thus obtain their energy of visible motion. 



If they are now at different temperatures, we convey 

 heat from the hotter to the colder bodies by means of a 

 heat-engine, till the whole system is at the same tempera- 

 ture. We thus obtain a second portion of the available 

 energy. 



Finally, if the pressures of different parts of the system 

 are not alike, we allow the portions in which the pres- 

 sure is great to expand, and so compress the portions in 

 which the pressure is less, the volume of the whole system 

 remaining constant. We thus obtain the third and last 

 portion of the available energy. 



