in Schedule A were also disposed of in their order in the list.

We have Mr Drummond's view of this debate in a letter written to his mother on the day after it :

"We are in the heat of our battle. Last night was the commencement of disfranchisement, and therefore of the attack on the principle adopted by me in the classification of the boroughs. The debate was an animated one for such a subject, and terminated very much to the satisfaction of all our friends, and I was congratulated upon it as a complete triumph, or perhaps a better term would be, vindication from all the previous attacks. Mr Pollock was a senior wrangler at Cambridge, and is a clever man, so that his defeat prevented any other person from following the same course. Croker's tone and manner were very different from what they were the night on which he commenced the attack some weeks ago, so that I could not but feel highly gratified at the result. A great many of us [the commissioners] were collected under the gallery in the House, and we came away in high spirits."

If Mr Croker's language was milder on this than on preceding occasions, he made up for the want of bitterness in the debate on the night of 21st February. The four remaining boroughs in Schedule A were on this night to be disposed of. On the motion that Appleby be not put in the Schedule, Mr Croker again assailed the Drummond list, attacking this time, not the principle, but the returns on which the calculations were founded. "The Government," he said, in referring to Mr Drummond, "have, I think, taken a blind guide to form a new constitution, for than these returns nothing could be more erroneous." This was mere license and discourtesy. The returns were furnished to Mr Drummond, and were just the part of the affair for which he was not responsible. The motion was negatived by a large majority. The other boroughs were then in

order disposed of, and the Schedule stood as it had been drafted.

This was his first triumph, but though it occurred in the heat of the battle, it was far from being his last struggle in connection with the bill. "It required all the energy and all the application for which Mr Drummond was so remarkable," says General Larcom, "to prepare the data, and meet the objections to his calculations; toilsome days and sleepless nights; the Home Office in the morning, and then the House; and after the division, often no sleep till he had satisfied himself the objections which had been raised were futile, and till fresh evidence was prepared to bear upon the doubtful point. Every borough the subject of a contest, even some high names in science for a moment arranged against him; but, some convinced and some defeated, the bill at length was carried. I well remember the calm and solemn feeling with which, the morning after the third reading in the Lords, Drummond stood and summoned to memory a brief review of all its stages, pausing from time to time when objections had been made to his own labours, and finally dismissing all with the firm conviction that he had done his duty to the Government, and aided a cause he conscientiously adopted as his own."

Drummond's services on behalf of the Government on this occasion were rendered gratuitously.* Miss Drummond states, that the Government offered him an honorarium of L.2000, but he declined it. At a later date (1834) these services were made one of the grounds of conferring on him a pension of L.300 a-year. This pension Mr Drummond drew from 15th

* See "Report of the Select Committee on Pensions," dated 24th July 1838.

November 1834 till the 30th June 1835, after which he declined to receive it.

It seems proper to close this account of Drummond's first political services, by saying something of the mathematical controversy to which they gave rise. That controversy may merit notice at a time when a new Reform Bill is under discussion, and when advocates have appeared of principles which demand a general determination of the relative importance, not of the parliamentary districts only, but also of the individual citizens.* The advocates of such principles may see more clearly the difficulties of making an assessment of individual merit, judged of by several criteria, few of which seem capable of being expressed by numbers, when they consider those experienced in determining the relative importance of a mere handful of boroughs, tested by two criteria only, both directly expressible in numbers.

The pamphlets written against the principle of computation applied by Mr Drummond, have fallen into an obscurity from which it would take more trouble than it is worth to rescue them. That there were several, I know from Sir John Herschel, who has obligingly put at my disposal copies of answers which he wrote at the time to two of them, and which give a good idea of the whole pros and cons of the controversy.

The Scheme of Reform propounded by Professor Lorimer of Edinburgh, is one of the class referred to. He would assign to every sane male adult a number of votes proportional to his "social weight," of which his age, wealth, education, profession, and University degree are suggested as the criteria. It seems impossible that the weight of any one, according to such tests, could be expressed in numbers, otherwise than at hap-hazard.

I have been unable to find any of them in the Advocates' Library.

Put algebraically, the question was as follows:-A (a borough's importance), is a function of B (its number of houses) and C (the amount of assessed taxes it pays). A varies with B; it also varies with C. What is to be assumed as the form of the function, when equal weight is to be given to the variations of B as to those of C? Is it B+nC, or BC, or ✔BC; or what is it? This seems all that is necessary to be said in the way of preface to Sir John's lucid letters.

In the following letter he puts "the equitable considerations" which enter into the determination of the form of the function, in a particularly clear commonsense light :

"SLOUGH, February 29, 1832,

"SIR, I acknowledge, as speedily as circumstances permit, your pamphlet on the Borough question; and the inscribed. note, in which you request my opinion of the principle you advocate, viz. [the product principle]. This principle you support in express and pointed contrast to that adopted by Lieutenant Drummond, and of which Lord J. Russell expressed, and correctly expressed, in the House the other night, my approval, as well as that of several well-known mathematical authorities, with whose opinion I then for the first time learned (to my satisfaction) that my own coincided. This latter principle may be thus stated, viz. [the

addition principle.]

"After the best consideration I have been able to give to the subject, and reading the arguments of more than one advocate of the Product' side of the question, I find myself still adhering to the sums, and regarding the products as untenable.

"When I speak of the principles thus, for brevity, as those of the products and sums, of course I suppose them rightly understood and cleared of factitious difficulties, such as that which some have found so puzzling, arising from the different denominations in which money may be reckoned, &c.; and

likewise those which in the latter may arise from different modes of estimating the proportion of importance of one house to one pound. This is quite another consideration. The question mainly put at issue lies between two abstract principles. "My objections against the product principle are these:— "1st, That its representation of extreme cases is radically defective, deviating entirely from common parlance, and from all fair conventional meaning of the word 'importance.'

"2d, That on this principle, a pound of assessed taxes, or a rated house, has no intrinsic fixed importance, but one entirely accidental; so that in some cases the addition of a few pounds assessed taxes or a few rated houses may produce a most extraordinary influence on the estimated importance of a borough, while, in others, the same additions may have very little influence.

"3d, That it places its advocates on one or other horn of the following dilemma :-Either the importance is estimated by the immediate product, or by its square root; if by the immediate product, then the two halves of a borough do not make the whole; a borough of one hundred houses and one hundred taxes is equivalent to four boroughs of fifty houses and fifty taxes, which is manifestly absurd; for, let the latter four be juxtaposed, they will then form a town twice as large and similarly inhabited as to wealth, luxury, &c. On the other hand, if the square root be adopted, what becomes of your theory of ratios? Let there be two boroughs each of one thousand houses, but let one pay three hundred and the other two hundred taxes; then will six of the latter be equivalent only to two of the former. Here, then, all have the fair influence of six hundred taxes annihilated by the mere accident of position.

"To return to my first objection. Usually the argument from extreme cases is one liable to be much abused; but it is always considered a fair trial of a mathematical principle if logically conducted, and in this case it is essential, because the two principles run pretty parallel in cases where the numbers follow an average or medium proportion, and it is only in proportion as the numbers tend towards the extreme cases, that their