AN AWKWARD ELEVATION IN THE PEERAGE. 241

ing a family reputation for sanctity unimpaired. In those times, while one party made an open show and boast of their profligacy, the other party were most rigid and uncompromising with regard to all such failings; carrying their rigour so far that it must in many cases have led to hypocrisy, and induced extreme measures to cover over and conceal irregularities of conduct, or to avenge the disclosure of them. Moreover, although immense reforms had been made since the days when Charles and his fierce archbishop, Laud, cut off noses and ears, and tortured and maimed the images of God upon earth, upon the slightest, or upon no proofs at all, still the stream of justice was far from being so pure as it has since become ; and in spite of the existence of a "Commonwealth," the poor and lowly continued to be but too often oppressed by the rich and powerful.

XLII. AN AWKWARD ELEVATION IN THE

PEERAGE.

In the days of the good Queen Anne, one of the many noblemen who incurred the displeasure of the irascible Sarah, first Duchess of Marlborough, of whom we shall give several stories elsewhere, was my Lord Rivers, then, as she says, more commonly called his Grace of Tyburn.

In one of the MS. defences of her own conduct, there is this concise passage: "Lord Rivers, who robbed his father, lived out of England for some years for fear of being hanged, and since he has always gone by the name of the Duke of Tyburn."

VOL. I.

R

Though evidently not given to invention, Sarah, in her animosities, certainly could over-colour and exaggerate facts; but, in this particular instance, the whole of her short story is confirmed by several contemporary authorities. She was so fond of it that she repeated it several times in her letters to her friends and partisans. It was, indeed, a well-pickled rod!

There are many curious things in this lady's various printed and manuscript defences, which were for the most part not written by herself, but by eminent literary men of the day, who either did the work out of gratitude for former obligations, or in the hope that she might be again restored to favour, and have good livings and other places at her disposal, or were regularly hired to do it by fees. In one of these papers, supposed to have been written by Atterbury, Bishop of Rochester, Dr. Sacheverell, who, after his prosecution, was held by the highchurch and tory party as a martyr, and fêted, feasted, and banqueted wherever he went, is compared to a jolly fat monk, who was sitting down to a rich venison pasty, and exclaiming, "Heu! quantum patimur pro Ecclesiâ !” "Alas! how much do we suffer for the Church!"

or,

The wit of these apologies, however, is not often of so lively a nature. Other persons are gibbeted besides my Lord Rivers; and Dean Swift is set down on more than one occasion as a base, intriguing, and scurrilous fellow, fully qualified for the gallows at Tyburn.

XLIII. WHICH IS THE WORST FATE THAT CAN BEFALL A NEW POEM?

ACCORDING to old Will Winstanley, the most degrading fate that could befall a poem, was to be turned into a pipe-lighter. The chandler's shop, the oil-man's, nay, even to be made "a casing for Christmas-pies," was nothing compared to this-" to be condemned to light tobacco." We presume Will did not love the weed.

XLIV. SIMPLE PROPERTIES OF NUMBERS.

MANY persons are interested in questions of numbers, who are not algebraists, and have nothing to employ their talent upon. They may, by common rules, amuse themselves with multiplying numbers together, or finding how much 61cwt. 23lb. cost, at 5 d. a pound, if they please. But there is nothing interesting in the result of all this; and accordingly, none but those to whom such proceedings are necessary, have recourse to them.

Between the arithmetician, and a great many interesting properties of numbers, stand nothing but a few simple terms, which being once explained, a large field of amusement is open in verifying, upon simple numbers, the results which have been obtained in algebra. The following article contains some of these, in which nothing, will be required but common multiplication and addition. In each succeeding volume, we shall add one or two more to the list. The reader may try high or low numbers, according to his facility in performing the operations.

I. The question often arises how to make up numbers out of other numbers; for instance, how to weigh any certain number of pounds with one set of weights. Suppose, for example, we wish to know what is the smallest set of weights which will do for any number of pounds under one hundred. The common system of arithmetic shows that nine ten-pound-weights and nine poundweights will be sufficient: but here are eighteen weights in all. We shall now show that seven weights only are sufficient, and that it may even be done with five: that is to say, that every number of pounds under 128lbs. may be weighed with seven weights, or, if necessary, every number of pounds under 122lbs. may be weighed with five weights; and that a simple table might be constructed, which would make the process as easy as the common system, or easier.

Firstly. Suppose it is required that no weights shall be put in the scale with the goods weighed. Let the scale with the weights be called W; that with the goods, G. Then it will be sufficient to have weights of the following number of pounds,

with these any number of pounds may be weighed under

and so on.
The reader may satisfy himself
other cases with ease.

The law might be easily so framed that this method of weighing should enable a customer to secure himself against fraud. The necessary enactments would be as follows:

1. Every tradesman must have his weights, beginning from one pound, each double of the preceding, and the same for ounces or grains.

2.

Every one must have his weights marked A, B, C, D, &c. A being one pound, B two pounds (and so on). The same for ounces and grains.

3. Every one must keep a table (to be published by authority), and must show it to his customer, if required. The following is a specimen, and a card would contain all that is necessary for common purposes.

4. Stamped 1 lb. 1 oz. 1 gr. weights, must be sold to all who will buy them: the stamp to be evidence of authenticity, as usual.

5. The tradesman must be bound to go through the process hereafter described, if required: of which it must be observed, that the trouble is great only when the quantity of goods in question is great. The purchaser takes his test-weight (say, one pound) to the shop or warehouse with him. With this one pound he can test every one of the shopkeeper's weights, as follows. Suppose he wants to buy 71 pounds of goods. On his own