TO THE MOVEMENT OF MACHINES. 523 



effect obtainable will depend on the value of f or of the friction. By- 

 differentiating the second member with respect to n, we shall have for 



tins maximum n = •- — . 



The bar which was used in the experiments of article 9 weighed 

 14|^lbs. Being adapted to any moveable apparatus, the friction it oc- 

 casions would amount at most to ^ lb. It has been found by experi- 

 ments : E — 283-6, r' = 20, r = 1, and/= i, thus n = 273-6 ; that 

 is to say, there would be the greatest possible advantage in employing 

 about 273 bars wound round with helices of the same size. This 

 number varies with the size of the plates : for a surface m, we have 



11 = ^ — . In short the magnetic power available for practical 



2fmr 



. nE . (E-fr'Y 



inirposes is w f = -^^ — •'„ ,/ . 



15. 

 In employing a voltaic battery, the oeconomical effect will be dimi- 

 nished, unless at the same time the helices united in the same wire be 

 multiplied ; for Mr. Faraday has proved by the experiments rejjorted in 

 the articles 990, &c. of the Eighth Series of his Researches, that the same 

 quantity of electricity passes through a voltaic battery of any number 

 of pairs of plates which traverses a single pair of the same size. Tlie 

 quantity of gas disengaged at the surface of each plate of the battery 

 is the same as at the surface of a single pair ; this at first sight appears 

 astonishing, and seems to contradict numerous experiments which have 

 been made upon the pile ; for every one knows that the quantity of 

 gas disengaged by the decomposing apparatus, and at the same time the 

 deviation of the needle, increase up to a certain point, by multiplying 

 the number of plates. 



n'E 

 n'r' + r' 



ber of pairs of plates, r' the resistance of each pair, and r that of the 

 connecting wire, or of the body which we wish to decompose, we must 

 suppose that in the experiments of Mr. Faraday (990.) the connecting 

 wire of the battery and of the single pair of plates were so short that 

 its resistance r might be entirely neglected in relation to w' r'. We 

 should not have obtained this striking result if we had employed a con- 

 necting wire'of any considSrable length, and still less if we had closed 

 the circuits of the pair of plates and of the battery by any decomjjosing 

 apparatus. Mr. Faraday has established a very exact distinction be- 

 tween the quantity and intensity of electricity set in motion. The first 

 may be measured in different ways ; but it will be difficult to find 

 an exact measure for its intensity, nevertheless this would be very 

 necessary for completing tiie theory. In admitting the important law 



In considering the formula 7^ = , ^ — , where »' represents the num- 



