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 2, we shall have for 
E—fr' 
Qtr - 
The bar which was used in the experiments of article 9 weighed 
141 1bs. Being adapted to any moveable apparatus, the friction it oc- 
casions would amount at most to d1b. It has been found by experi- 
ments: H = 283°6, r! = 20, r=1, and f= 4, thus x = 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 
this maximum 7 = 
PET a) 
7. ae In short the magnetic power available for practical 
. ne _ (B-fr'y 
Sh ieeernes nf = (Et fr ar 
15. 
In employing a voltaic battery, the ceconomical 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 reported 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. The 
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' EB 
In considering the formula F = —— # , where’ represents the num- 
n'y! +9 
ber of pairs of plates, 7’ 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 n'7’. We 
should not have obtained this striking result if we had employed a con- 
necting wire"of any considérable length, and still less if we had closed 
the circuits of the pair of plates and of the battery by any decomposing 
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 the theory. In admitting the important law 
