158 - -REPORT—1862. 
fluctuation must be detected and exhibited, not only as a subject of study in itself, 
but because we must ascertain and eliminate such periodic variations before we can 
correctly exhibit those which are irregular or non-periodic, and of more interest 
and importance. 
Tables of the average weekly accounts of the Bank of England from 1845 to 
1861, inclusive, having been prepared, it is shown that there are at least three 
kinds of periodic fluctuation observable, during the month, the quarter, and the 
year. The first two kinds are precisely similar in character, though differing much 
in amount, and are due to the payments of dividends or other claims which occur 
at the beginning of the quarter and month. Such payments cause a sudden increase 
of the note-circulation and of private deposits, a considerable decrease of private 
securities, a slight decrease of the bullion, accompanied by a larger but otherwise 
similar variation of the loanable capital. 
Eliminating such variations from those of the whole year, there remain certain 
interesting variations due to natural causes, as distinguished from the artificial 
distinctions of months and quarters. The notes in circulation rise from a minimum 
in January and February to a maximum in the third quarter, and then very rapidly 
decrease during November and December. 
Private securities greatly increase, and private deposits decrease, about haryest- 
time, while the bullion and loanable capital undergo a continuous decrease. 
These variations are probably due to a great absorption of capital in buying up 
the proceeds of the year’s industry, which have to be held in sieke for consumption 
during the succeeding twelve months. 
The bullion and capital, however, have a second maximum in February, and a 
subsequent decrease until May. 
It is also shown, from monthly average determinations, that the rate of discount 
and the number of bankruptcies suffer a sudden rise after the harvest months. It 
may be said that there is a periodic tendency to commercial distress and difficulty 
during the months of October and November. The great commercial panics are 
ageravations of this periodic difficulty, due to irregular fluctuations. 
f 79,794 banlauptcies which were gazetted from the beginning of 1806 to the 
end of 1860, 28,391 occurred in the second month of the quarter, 26,427 in the 
third month, and only 24,976 in the first month, in which occurs the payment of 
the public dividends. 
The price of consols and the price of wheat exhibits a double minimum during 
the year. 7 
Notice of a General Mathematical Theory of Political Economy. 
By W. 58. Jevons, M.A. 
1. The main problem of economy may be reduced to a rigorous mathematical 
form, and it is only the absence of exact data for the inductive determination of its 
laws or functions which will always prevent it from becoming an exact science. 
2. A true theory of economy can only be attained by going back to the springs 
of human action—the feelings of pleasure and pain which accompany our common 
wants, and the satisfaction of those wants by labour exerted to that purpose, These 
feelings are the commonest motives of action ; but other motives of a moral or reli- 
gious nature must be recognized by the economist as outstanding and disturbing 
forces of his problem. 
3. Feelings of pleasure and pain vary in intensity and in duration. They have 
two dimensions. The quantity of feeling, therefore, resembles an area, and is got 
by integration of the function which expresses the relation of the intensity to the 
uration. 
4. Pleasure and pain are opposed as positive and negative quantities. 
5. Anticipation of future pleasure or pain gives a less degree of present feeling, 
related to the anticipated feeling by some vague function of the intervening time, 
peculiar to each person’s character. 
6. A useful object is that which causes pleasure, either by present use or by 
expectation of its future use. 
7. Amount of utility corresponds to amount of pleasure produced. The use or 
