Royal Society. 225 



sure the intensity of physical properties ; adverting, in proof of 

 this, to the acrimonious controversy which took place soon after 

 the application of mathematical expression to the laws of motion ; 

 in which it was contended by some mathematicians, that the weight 

 of a moving body multiplied into its velocity was the measure of 

 the motion ; whilst others of equal eminence maintained that the 

 weight should be nuiltiplied into the square of the velocity, in or- 

 der to obtain the measure. But it was at length discovered that 

 these views were not in reality at variance with each other, and the 

 introduction of the terms momentum and impetus respectively ap- 

 plied to them, terminated the dispute. After referring to some ob- 

 servations on the subject by G. Attwood, Mr. Gilbert remarks, 

 that in the Bakerian Lecture for 1806, by a Fellow of the Society 

 [Dr.WoUaston], who has touched upon nothing that he has not elu- 

 cidated and adorned, it is stated that neither of these terms is usually 

 a correct measure of the effective action of machines. The cri- 

 terion of this is the force exerted multiplied by the space through 

 which it acts ; and this measure, numerically expressed, and with 

 reference to the steam-engine, has been denominated Duty by 

 Mr. Watt, and the raising of one pound one foot high has been 

 made by him the dynamic unit ; according to which estimate the 

 Duty performed by one bushel of coals of 84 pounds has been 

 found to vary from 30 to 50 millions of such units, according to the 

 nature of the engine and the mode of combustion employed. To 

 the measure or function represented by the force multiplied by the 

 space through which it acts, the author, however, proposes to give 

 the name efficiency ; retaining the word duty for a similar function 

 indicative of the work performed ; and by a comparison of these 

 two functions; viz. the efficiency expended on, and the duty per- 

 formed by, any machine, an exact measure of its intrinsic work 

 will be obtained. 



The author then proceeds to show the utility of his new term in 

 investigating the mechanical value of the recoil-engine, and by an 

 algebraic process, taking every thing most favourably to the engine, 

 arrives at the conclusion that the duty cannot, even in the best state 

 of its action, materially exceed half the efficiency, and that in con- 

 sequence it can never be used with advantage. The water-wheel, 

 and the pressure-engine offering much greater duties, while the wheel 

 possesses the advantage of preserving a uniformity of efficiency du- 

 ring the whole action, which is not the case with the recoil-engine. 

 And these considerations lead him to remark on the impossibility of 

 carrying into effect a plan proposed by some eminent engineers for 

 aj)plying steam on a principle of recoil. 



To estimate the efficiency of steam acting uniformly with its en- 

 tire force, the author assumes from experiment, that a bushel of 

 coals can convert into steam l^ cubic feet of water, occupying 1330 

 times that space in the state of steam, and therefore lilting an at- 

 mosphere incumbent on the surface of the water, uniformly to 1330 

 times its depth; — thus giving an efficiency of about 39 millions of 

 pounds raised one foot high. From this he concludes that (all dc- 

 Nas:' Soics. Vol. 1. No. 3. March 1827. 2 G ductions 



