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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.”
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, he 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
point will be undoubtedly much canvassed in the House, and as ninety-nine out of every hundred of its members have no means of deciding such a question, and would be ready to bow to the opinion of any one who stands high in that of the world, it would be a great relief to poor Drummond if (purely as a mathematical question, without reference to its application) you would simply state your opinion of the principle that he has adopted. He is, however, far too delicate to risk the annoyance of your feelings by either inducing you to do what would be disagreeable, or compelling you to refuse. I have, therefore, taken the great liberty of enclosing some of the papers to you; and if you would hint to me that you had no great reluctance to give your opinion, he would immediately write to you clearly on the subject; or, on the other hand, a single word from you will put a stop to the whole affair.-I am, very faithfully yours,
To this appeal Sir John immediately responded, examining at great length the whole conditions of the calculation, and giving a general adherence to the method which Mr Drummond had followed.
The discussion of the question was resumed in Parliament on the 20th February 1832, on the question being put “ that Old Sarum, Wiltshire, should be inserted at the head of Schedule A, instead of Alborough, Yorkshire." The attack on Drummond was led by a distinguished mathematician, Mr (afterwards Baron) Pollock. He was listened to as Englishmen know how to listen to a senior wrangler on a question of computation. He contended at considerable length that the method of adding the numbers in the two series was erroneous, and that the only mode of giving equal weight, in estimating of the relative importance of a borough, to the number of houses which it contained and the amount of assessed taxes which it paid, was by multiplying together the numbers in the
two lists which related to the same boroughs. He was immediately followed by Lord John Russell, who, after some general reasoning on the subject, said
"He replied upon it not on his own authority, but on that of the greatest mathematicians of the country, and had no hesitation in saying that the principle of Lieutenant Drummond was the only one that could with propriety be adopted. It was a strict mathematical question, and he had the opinion of a distinguished mathematician upon the subject at present in his hand—a gentleman, he was sure, who was well known to the majority of the House—he alluded to Professor Airy of Cambridge—which was distinctly in favour of the principle adopted by Lieutenant Drummond; and he had also the opinion of another learned mathematician, Professor Barlow, who stated that the principle was not only correct, but indispensable, according to the provisions in the instructions given. The same question had been put to Professor Wallace of Edinburgh, who not only in his reply approved of the principle, but went much into the details, thereby showing he had studied the problem, and after consideration had come to the result that the principle was a correct one. There was another opinion which he had the authority of Captain Beaufort to mention. It was that of Sir John Herschel, also approving of the principle. He thought he had said sufficient to satisfy the House that the principle pursued by Lieutenant Drummond had not been adopted in ignorance of a science which, on the contrary, was one he had long studied."*
After some observations from Mr Pollock, the debate became general. But the mathematical question was now settled by the weight of authority, and further attempts within the House to show that there was a “ radical error" in the computation were rested on general considerations merely. Old Sarum was in the end duly placed at the head of the list for disfanchisement, and thereafter fifty-two of the fifty-six boroughs
* Times' Report.