I saw in this great practical and philosophical idea, the greatest improvement of which the system of representative government is susceptible; an improvement which, in the most felicitous manner, exactly meets and cures the grand, and what before seemed the inherent, defect of the representative system; that of giving to a numerical majority all power, instead of only a power proportional to its numbers, and enabling the strongest party to exclude all weaker parties from making their opinions heard in the assembly of the nation, except through such opportunity as may be given to them by the accidentally unequal distribution of opinions in different localities.
But, after the Restoration, by degrees the practice degenerated, and Englishmen were appointed in numbers to the Irish Episcopate in order to fortify and develop by numerical force what came to be familiarly known as the English interest.
But though the Free State men had a numerical majority of votes, yet the districts had been so arranged that the above returns gave a majority in the Legislature to the Lecompton party. Johnson county, bordering on Missouri, had been united in one district with Douglas county, in which Lawrence is situated, and this district had been given eight members.
In 1896, accordingly, a second, bound to the first by unmistakable numerical relationships, was recognised by Professor Pickering in spectrographs of the 2·5 magnitude star Zeta Puppis, and the identification was shortly afterwards extended to prominent Wolf-Rayet emission lines. The discovery was capped by Dr.
When the numerical superiority is considerable, an attack may be made simultaneously upon both extremities, but not when the attacking force is equal or inferior numerically to the enemy's.
The numerical value of a quantity of energy of any nature should, in the system C.G.S., be expressed in terms of the unit called the erg; but, as a matter of fact, when we wish to compare and measure different quantities of energy of varying forms, such as electrical, chemical, and other quantities, etc., we nearly always employ a method by which all these energies are finally transformed and used to heat the water of a calorimeter.
While forming the approaches, the workmen had been constantly harassed by the fire from the guns on the walls, suffering considerable loss of life; but their numerical superiority was so vast that the loss in no way affected the plans of the pasha.
This result completely agrees with the general experience of breeders and the example given is only an instance of a universal rule. It has the advantage of being capable of being recorded in a numerical way, and of allowing a detailed and definite description of all the succeeding generations.
Further on we read respecting algebraic functions that "most functions were concrete in their origin even those which are at present the most purely abstract; and the ancients discovered only through geometrical definitions elementary algebraic properties of functions to which a numerical value was not attached till long afterwards, rendering abstract to us what was concrete to the old geometers."
The given fact is a mark that a certain relation subsists between the quantities of some of the elements concerned; while the fact sought presupposes a certain relation between the quantities of some other elements: now, if these last quantities are dependent in some known manner upon the former, or vicè versa, we can argue from the numerical relation between the one set of quantities, to determine that which subsists between the other set; the theorems of the calculus affording the intermediate links.