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SCIENCE. 



[N. S. Vol. I. No. 6. 



the masses involved, their coordinates of 

 position, and the time fi-om any assumed 

 epoch ; while the potential energy is ex- 

 pressed in terms of the masses and their 

 relative positions, irrespectively of the time. 

 From the expressions for these two parts of 

 the energy, all of the properties of the system 

 can be derived by means of the Lagrangian 

 machinery. In the case of most phenomena 

 it is impossible to observe more than a very 

 limited nnmber of the circumstances of 

 motion ; such as, for example, the coordi- 

 nates of one or more of the masses at definite 

 epochs, the rates of variation of those coor- 

 dinates, etc.; but if we can express the two 

 parts of the energy, and if the derived cir- 

 cumstances agree with the observed circum- 

 stances, the mechanical explanation is re- 

 garded as complete. On the other hand, a. 

 phenomenon may not be clearly or obviously 

 mechanical, and it becomes important in 

 many cases to learn whether it is susceptible 

 of mechanical explanation. The criterion 

 supplied by the Lagrangian machinery is 

 this : If the phenomenon can be defined by 

 two expressions or functions having the 

 properties of kinetic and potential energy, a 

 system of masses with appropriate positions 

 may be found to satisfy those functions and 

 hence explain the phenomenon mechani- 

 cally. 



The law of the conservation of energy, 

 then, affords a very comprehensive view of 

 mechanical phenomena ; and when we add 

 that this law is believed to be coextensive 

 with the material universe, one can see why 

 it should have played so important a role 

 in the recent developments of mechanical 

 science. Along with the growth and appli- 

 tion of this law has come a degree of per- 

 fection in the technical terminology of me- 

 chanics surpassing that of most other sci- 

 ences. The terms mass, force, energy, 

 power, etc., as now used in mechanics, pos- 

 sess a precision of meaning which, strange 

 as it may seem, was largely wanting in 



them thirty to fifty years ago. Nothing il- 

 lustrates this fact more forcibly than titles 

 to some of the important papers published 

 during the past half century. Thus, the 

 great memoir published in 1847 by Helm- 

 holtz on what we now call the conservation 

 of energy was entitled ' The Conservation 

 of Force.' In 1854 Prof. Thomson, now 

 Lord Kelvin, published an interesting and 

 important ' Note on the possible density of 

 the luminiferous medium, and on the me- 

 chanical value of a cubic mile of sunlight.' 

 We should now render the ' mechanical 

 value of a cubic mile of sunlight ' as mean- 

 ing the energy of a cubic mile of the ether 

 due to the action of the sun. About thirty 

 years ago the late Professor TjTidall pub- 

 lished his capital work on ' Heat Consid- 

 ered as a Mode of Motion.' "NVe must now 

 translate this into Heat a Mode of Energj'. 

 There was, thus, in the writings of experts 

 of a half century or less ago, much obscure 

 phraseology, while the literature of less 

 careful authors was often provokingly am- 

 biguous. The word force, for example, in 

 a number of treatises published since 1850, 

 has been used to denote the tlu-ee radically 

 different things we now call stress, impulse 

 and energy. 



To the development of the law of energj^, 

 and its applications in electricity and mag- 

 netism especiallj'', are due also an impox-tant 

 fixation of our ideas with respect to the 

 units and the dimensions of units which 

 enter into mechanical quantities. Less than 

 a quarter of a century ago our science was 

 in a certain sense restricted by its terrestrial 

 moorings. So strong, indeed, had been the 

 influence of our earthty abode that onlj' 

 experts like Lagrange, Laplace, and Poisson 

 would have known how to formulate a 

 treatise suitable for instruction in any other 

 part of the universe. Thanks to the half 

 forgotten labors of Fourier and Gauss, how- 

 ever, when it became essential to state the 

 laws of mechanics in a way readily appli- 



