On certain modular determinants

Abstract

y1 = 0, y2 is negative o r 2/i = 2/2 = 2/3 = 0, 2/4 is negative o r 2/1=2/2 = 2/3 = 2/4 = 2/5 = °. Vo is negative, etc. Further the relation between the sign of dy/dx and the concavity of an arc is often obscurely presented. Take an x or time axis horizontally and a y axis vertically and consider an arc AB everywhere concave down. Let C be a point on the arc such that AC and CB have equal horizontal projections, and let their vertical projections be ac and cb. Then algebraically we have from a figure ac > cb, that is, heights gained in equal successive times are diminishing and therefore there is a retardation and d'-y/dx is negative. And we similarly associate concavity upwards with positive values of* d-y/dx.