PRESENT FUNDAMENTAL CONCEPTIONS OF PHYSICS. 505 



matter and energy was not rigorously established by experiment, as the 

 respective measurements could never attain perfect accuracy ; that this 

 theory, unconsciously impressed on us from the beginning, might there- 

 fore have been conjectured by the ancient philosophers without con- 

 firmation from experiment. We would, however, point out that the 

 measurements relative to those propositions possess that degree of ac- 

 curacy which is indispensable in the determination of a law in natural 

 science; that in the latter, only laws thus proved are admissible, and 

 that the theories of the persistence of matter and energy had never 

 been definitely expressed with mathematical precision before the above 

 named epochs. At any rate, the really scientific and highly fruitful 

 application of these two fundamental laws falls in the last decades 

 of the past century and in our time. It was only after the perma- 

 nence of matter had been experimentally demonstrated with the aid 

 of delicate precision-scales by Lavoisier (1772-'S0), Wenzel (1772 to 

 1777), and Iiichter (1792), and on these grounds definite statements 

 had been made, that chemistry really became truly scientific in form 

 and character by reason of the development of the doctrine of definite 

 proportions. 



If on the one hand the theory of the persistence of matter created 

 chemistry as a science proper, on the other the theory of the persistence of 

 energy threw a full light on physics, chemistry, physiology, and in fact 

 on the whole philosophy of the investigation of nature. The last step 

 in the establishment of the theory of the conservation of energy was 

 produced by the theory of heat. The premises of this theory existed 

 however already in mechanics, it having been observed in the latter at 

 an early date that by machines no power was ever gained, but that by 

 the use of machines power could only be employed more easily and to 

 better advantage. 



The ancients knew that in the lever the greater weight moves just as 

 many times more slowly as it exceeds the smaller weight in quantity. 

 Galileo observed more generally (1592) that in lifting a weight by 

 means of a simple machine as much is lost in space and consequently 

 in time as is gained in power. Johann Bernoulli (1717) in an ingenious 

 manner transformed this proposition as the " principle of virtual veloc- 

 ities" into the first principle of the theory of equilibrium, from which 

 emanates the solution of every statical problem. Subsequently 

 d 'Alembert embodied this principle in its widest analytical form (1743). 

 We find then that in simple and consequently in complicated machines 

 (these being composed of the former) absolutely no power and therefore 

 no energy can be gained. Machines cannot produce powers; they can 

 onl,\ apply them more advantageously to a useful purpose. 



Since by means of a machine the work performed by the first motor 

 could at the utmost but reappear in undiminished quantity at the last, 

 (and this could be only if there were no losses by impediments to motion 

 from friction and resistance of the air,) it is evident that a jperpetuum 



