St Benedict introduced too into the monastic life the idea of law and order, of rule binding on the abbot no less than on the monks; thus he reduced almost to a vanishing point the element of arbitrariness, or mere dependence on the abbot's will and whim, found in the earlier rules.

Its proximal centrosome (its distal one vanishing as such).

The validity of his fundamental position was impaired by the absence of a well-constituted theory of series; the notation employed was inconvenient, and was abandoned by its inventor in the second edition of his Mecanique; while his scruples as to the admission into analytical investigations of the idea of limits or vanishing ratios have long since been laid aside as idle.

View more

The discriminant, whose vanishing is the condition that f may possess two equal roots, has the expression j 2 - 6 i 3; it is nine times the discriminant of the cubic resolvent k 3 - 2 ik- 3j, and has also the expression 4(1, t') 6 .

This necessitates the satisfying of five equations; in other words, there are five alterations of the 3rd order, the vanishing of which produces an image of the 5th order.

Every other concomitant is a rational integral function of these four forms. The linear covariant, obviously the Jacobian of a x and x x is the line perpendicular to x and the vanishing of the quadrinvariant a x is the condition that a x passes through one of the circular points at infinity.

Lawless and predatory, the English settlers were hardly distinguishable from the native Irish, and the authority of the English king over both had been reduced to vanishing point.

We find that if the series of excitations of the muscle be prolonged beyond the short stage of initial improvement, the contractions, after being well maintained for a time, later decline in force and speed, and ultimately dwindle even to vanishing point.

The disclosures before the Parnell Commission, the O'Shea divorce proceedings, the downfall of Mr Parnell and the disruption of the Irish party, assisted him in his task; but the fact remains that by persistent courage and undeviating thoroughness he reduced crime in Ireland to a vanishing point.

Bidwell 2 accordingly found upon trial that the Wiedemann twist of an iron wire vanished when the magnetizing force reached a certain high value, and was reversed when that value was exceeded; he also found that the vanishing point was reached with lower values of the magnetizing force when the wire was stretched by a weight.