Which preposition to use with ratios

of Occurrences 275%

To this the larger States were quite unwilling to yield, and when the committee rose they reported, in substance, the Virginia plan, with the proviso that representation in the proposed double-chambered Congress should be "according to some equitable ratio of representation.

to Occurrences 57%

More than one of the young nobles approached the presumably fair peripatetic, and, with courtesy commonly in inverse ratio to the amount of wine he was carrying home, proffered his escort to his gondola.

between Occurrences 27%

The pressure within a viscus is dependent upon the ratio between the amount of contraction of the involuntary muscle in its walls, the external pressure, and the quantity of its distending contents, the internal pressure.

with Occurrences 17%

Again, Swift's flying Island of Laputa is a phenomenon so opposed to all scientific probability, and so directly at variance with natural laws, that it loses in interest in a direct ratio with the violence it does to our feelings.

as Occurrences 13%

We must therefore assume that the second stage in the Government programme will be repression growing in violence in the same ratio as the progress of non-co-operation.

in Occurrences 10%

Normally, there is a certain fixed ratio of the salts in the blood, which keeps them like the ratio in sea-water.

for Occurrences 6%

The actual ratio for the first series given in problem 2 is 1 to 8, while in the second series it is 0 to 10.

than Occurrences 6%

Twenty years of experience show that the diminished cost of transport by railroad invariably augments the amount of commerce transacted, and in a much larger ratio than the reduction of cost.

at Occurrences 4%

Froude himself puts the ratio at six to one.]

from Occurrences 3%

"It has sometimes occurred to me whether Mr. Malthus did not catch the first hint of his geometrical ratio from a curious passage of Judge Blackstone, on consanguinity, which is as follows: "The doctrine of lineal consanguinity is sufficiently plain and obvious; but it is at the first view astonishing to consider the number of lineal ancestors which every man has within no very great number of degrees:

by Occurrences 3%

The conquerors arm themselves in the ratio by which the vanquished disarm, and the worse the situation of our old enemies becomes, so much the worse become the exchanges and the credits of the victorious continental countries.

until Occurrences 1%

The first accident that weakens his structure makes the second more certain and so on in increasing ratio until the end.

among Occurrences 1%

Ann Arundel, Charles, and Prince George, the ratios among the slaveholdings of the several scales, according to the United States census of 1790, were almost identical with those just noted in the selected Virginia counties, but the non-slaveholders were nearly twice as numerous in proportion.

Which preposition to use with  ratios