form a large folio blue-book.* The instructions framed by Mr Drummond for the guidance of the Commissioners and surveyors are printed with the reports. They are at once an illustration of his powers of organisation, and a proof of the wisdom of the Government in appointing him to superintend the Commission.

While this work was in progress, another and more delicate task was confided to Mr Drummond, as will appear from the following letter addressed to him by

Lord Melbourne:

"WHITEHALL, 24th Nov. 1831.

"SIR,-The Government having determined to found the Reform Bill on a new basis, I request your assistance to enable them to ascertain the relative importance of the smaller boroughs in England and Wales.

"It is proposed to take the number of houses and the amount of assessed taxes for the year ending April 1831 together as the test of disfranchisement. The inquiries of which you have had the direction, and the information obtained in answer to circular letters sent from this office, will put you in possession of the data from which such a calculation can be made.

"You will have the goodness, therefore, to make a scale, containing, in addition to ninety-seven boroughs (the number comprised in Schedules (A) and (B) of the former Bill), the ten or fifteen immediately above them in size and importance. You will arrange these boroughs in such a manner that the lowest may be the first, and the highest the last on the list. I shall be obliged to you to send me, at the same time, an account of the manner in which the calculation has been made.-I have the honour to be, &c., MELBOURNE."

"Lieut. Drummond, R.E., &c. &c."

* "XI. Part I. Parliamentary Representation. Further return to an address to his Majesty dated 12th December 1831 :-For copies of instructions given by the Secretary of State for the Home Department, with reference to Parliamentary Representation; likewise copies of letters and reports received by the Secretary of State for the Home Department in answer to such instructions."

Drummond sent in a first report in execution of this commission on the 12th of December 1831, and the final report on the 16th of January following. The report was accompanied by a list of the boroughs arranged in the order of their relative importance, by the evidence, and a statement of the principle on which that order depended.*

The "new basis for the Reform Bill" was far from being distinctly set forth in the instructions which he had received. Let us see what he made of it. The basis was that the number of houses and the amount of assessed taxes should be the test of disfranchisement. Presumably, it was intended, in estimating the relative importance of a borough, to allow weights to the houses which it contained, and to the assessed taxes which it paid, proportional to their respective numbers, and such that the whole weight of all the houses should be equal to the whole weight of all the taxes in the mass of boroughs considered. On this, as the unexpressed meaning of his instructions, Drummond proceeded. "The method adopted for carrying this principle into effect," he says, "may be stated in the following words :

"1st, Take the average number of houses contained in the boroughs to be arranged; divide the number of houses in each borough by this average number, and a series of numbers will be obtained denoting the relative importance of the different boroughs with respect to houses.

"2d, Take the average amount of the assessed taxes paid by the same boroughs, and proceed in the same manner as described with respect to the houses; a series of numbers will re

*The Report is a considerable blue-book, "Returns relative to the 120 smallest Boroughs at present returning Members to Parliament. 1832."

K

sult, showing the relative importance of the different boroughs with respect to assessed taxes.

"3d, Add together the numbers in these two lists which relate to the same boroughs, and a series of numbers will be produced denoting the relative importance of the different boroughs with respect to houses and assessed taxes combined."

66

This account of the method of computation was contained in the first report to Lord Melbourne, dated 12th December 1831. It was made known in the House of Commons early in January, when the method was immediately called in question and ridiculed by Mr Croker. He declared it "absurd and complicated in the extreme." The principle, judging from the examples in the printed paper, was altogether absurd and inapplicable." He, moreover, expressed his conviction, from the dilatory manner in which information was being supplied to Parliament, that "there was some party desirous of preventing the complete investigation of the facts." These must have been painful observations to be listened to by Mr Drummond. But more annoyance was to come. The principle was thereafter repeatedly canvassed inside the House and out of it. The rumour had gone abroad that parliamentary representation was now to be based on scientific principles, and a new class of combatants entered the arena of political strife. Algebraists arrayed themselves with the opposing factions, and for a time "the Drummond list" became the subject of numerous speeches, pamphlets, and newspaper articles. The first impressions of the public seem to have been against the calculations, and even some of the newspapers usually in the interest of the Government assailed them. When everything connected with the Reform Bill was being made the subject of hot controversy, it was natural

that this list, which marked out the boroughs to be disfranchised, should be vigorously attacked. Much of the controversy to which it gave rise may, indeed, be referred to the keenness with which the boroughs selected to be victims were struggling for existence. How great this was we may see in the reason for “the new basis" of the Bill. The two former bills had taken as the test of disfranchisement a certain amount of population, and put in Schedule A all those which did not reach that amount. The amount of population had been judged of according to the census of 1821. But by the date of the third bill the census of 1831 had been taken, and could not be thrown out of view. And the ostensible and declared reason of "the new basis" was that pains had been taken to raise particular boroughs above the line of disfranchisement by importing into them inhabitants against the time of the census. When such practices could be employed to preserve the franchise, those interested in the returns would, in their discomfiture, spare no pains to discredit the principle on which they were now being, anew, selected for disfranchisement. On the other hand, by the new test some boroughs, originally in Schedule A, got out of it, and some, originally not in it, took their places. The latter might be expected to be foremost in clamouring against the principle which led to such a result.

Among those who had any title to be heard on the mathemetical question, the chief controversy respected Drummond's third step, whether the numbers in the first two series of figures should be added, as in his plan, to obtain those of the third and final series; or multiplied, as some maintained; or multiplied, and the square root of the product taken, as was argued by others. It caused Drummond much annoyance and

pain, inexperienced as he was in party politics, to find the principle thus challenged on which he had founded so important a public document. His instructions had been so general that the responsibility of the list rested with him almost exclusively. How was he to meet and defeat the objectors? The question raised could only be settled by the authority of eminent mathematicians, and to them he resolved to appeal.

The night on which the "principle" was first attacked, he drove, in considerable excitement, from the House of Commons to Woolwich, to consult his old master and friend, Professor Barlow. Miss Barlow remembers the occasion well; the carriage driving to the door at a late hour, and remaining there for hours, during which Drummond was closeted with her father. They discussed the question from about eleven o'clock P.M. till nearly three o'clock in the morning. The Professor would not at first admit the correctness of the calculation; but finally he was convinced, and Drummond returned to town with the first written authoritative approval in his possession. Professors Airy of Cambridge and Wallace of Edinburgh were next consulted, and both of them pronounced in Drummond's favour. The authority of his friend Herschel, could he secure it, would be great, but he he had a delicacy in consulting him. From this he was relieved by Captain Beaufort :

"ADMIRALTY, January 10, 1832.

"MY DEAR SIR JOHN,-Most fortunately for your happiness, you have neither time nor taste to enter into the politics of this stirring period of our history. You have, nevertheless, probably seen some account of the attack made on our friend Drummond by Mr Croker, since reiterated in the newspapers, even in the Courier, which supports the Government. This