He has given by means of it a simple proof of the existence of n roots, and no more, in every rational algebraic equation of the nth order with real coefficients.
He ascertained the distribution of electricity among several spheres (whether equal or unequal) placed in contact in a straight line; and he measured the distribution of 2 In 1878 Clerk Maxwell repeated Cavendish's experiments with improved apparatus and the employment of a Kelvin quadrant electrometer as a means of detecting the absence of charge on the inner conductor after it had been connected to the outer case, and was thus able to show that if the law of electric attraction varies inversely as the nth power of the distance, then the exponent n must have a value of 2 t Isua.
In this case the sum to n terms of the series is equal to the nth convergent of the fraction.
Methane and its homologues give origin to the " paraffin " or " fatty series " of the general formula C,H 2, ,+ 1 000H, ethylene gives origin to the acrylic acid series, C n H 27, - 1 000H, and so on.
Dibasic acids of the paraffin series of hydrocarbons have the general formula C n H 2 (000H) 2 "; malonic and succinic acids are important members.
