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Singular Perturbation Methods in Control

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9. F. and resistance. Let us take a horizontal scale along the line A B of 8 ohms to the inch. F. F. and 2 ohms resistance. F. will be 16 volts and resistance 22 ohms, so that the latter will be represented on our scale of 8 ohms to the inch by placing the poles of the battery -^ 8 inches apart, so that the line c 2 PRACTICAL NOTES 20 " A B must be 2f long. Each cell may now be marked off along this line, the distance from one connection to the next being Fullers. The plates may |" for the Leclanch6s and J" for the then be sketched in their right positions, as shown.

Leakage. F. accumulated, or, in other words, with the number of connected in series. F. ; in the that a small leak at the base of a tank may cause PRACTICAL NOTES 18 only a trifling escape of water but might allow when the tank is nearly empty, water and conIt should be raised from within. of serious loss as the level of sequently the pressure is the object, therefore, with large batteries, especially when they are employed in delicate measurements, to place them on insulating supports, and also to prevent leakage from cell to cell by keeping the outer surfaces of the cells clean and good method is to coat with paraffin wax the outer of the cells and the trays or brackets on which they A dry.

Proportional to the same length the cross-section of its and a Given Length Cross Section. of Wire Inversely With conductors of material, the resistance increases as reduced, just as the resistance to the flow of water through a pipe is increased as the pipe is reduced in cross-section. , and B, are is A length and material, but B has twice the cross -sectional area of A, then B may be regarded as being made up of two wires very close together, each of A's cross- of the same section, and therefore equal to A in every respect.