two couples, the number seven, coming next after the sum of the three sacred numbers, determines the largest group which we can distinctly imagine.  Reciprocally, it marks the limit of the divisions which we can directly conceive in a magnitude of any kind.”  The number seven, therefore, must be foisted in wherever possible, and among other things, is to be made the basis of numeration, which is hereafter to be septimal instead of decimal:  producing all the inconvenience of a change of system, not only without getting rid of, but greatly aggravating, the disadvantages of the existing one.  But then, he says, it is absolutely necessary that the basis of numeration should be a prime number.  All other people think it absolutely necessary that it should not, and regard the present basis as only objectionable in not being divisible enough.  But M. Comte’s puerile predilection for prime numbers almost passes belief.  His reason is that they are the type of irreductibility:  each of them is a kind of ultimate arithmetical fact.  This, to any one who knows M. Comte in his later aspects, is amply sufficient.  Nothing can exceed his delight in anything which says to the human mind, Thus far shalt thou go and no farther.  If prime numbers are precious, doubly prime numbers are doubly so; meaning those which are not only themselves prime numbers, but the number which marks their place in the series of prime numbers is a prime number.  Still greater is the dignity of trebly prime numbers; when the number marking the place of this second number is also prime.  The number thirteen fulfils these conditions:  it is a prime number, it is the seventh prime number, and seven is the fifth prime number.  Accordingly he has an outrageous partiality to the number thirteen.  Though one of the most inconvenient of all small numbers, he insists on introducing it everywhere.

These strange conceits are connected with a highly characteristic example of M. Comte’s frenzy for regulation.  He cannot bear that anything should be left unregulated:  there ought to be no such thing as hesitation; nothing should remain arbitrary, for l’arbitraire is always favourable to egoism.  Submission to artificial prescriptions is as indispensable as to natural laws, and he boasts that under the reign of sentiment, human life may be made equally, and even more, regular than the courses of the stars.  But the great instrument of exact regulation for the details of life is numbers:  fixed numbers, therefore, should be introduced into all our conduct.  M. Comte’s first application of this system was to the correction of his own literary style.  Complaint had been made, not undeservedly, that in his first great work, especially in the latter part of it, the sentences and paragraphs were long, clumsy, and involved.  To correct this fault, of which he was aware, he imposed on himself the following rules.  No sentence was to exceed two lines of his manuscript, equivalent to five of print.  No