mal du premier ordre, qui se peint dans chaque esprit. Une injure corporelle irréparable, par exemple, produira plus d'allarme que n'en produira une injure corporelle simple; un homicide, plus encore qu'une injure corporelle simple; un homicide, plus encore qu'une injure corporelle, bien qu'irréparable, qui ne s'étend pas à la vie : et ainsi du reste. C'est ici sans doute du mal du second ordre la mesure la plus simple et la plus saillante. Cependant nous allons en voir encore sept autres dont l'importance n'est rien moins que triviale.

ordre qui se peint dans l'imagination de chacun. Mais il y a

d'autres circonstances qui modifient l'alarme.

APPENDICE II

LE CALCUL DES PLAISIRS et des Peines.

Noux extrayons les fragments qui suivent d'un manuscrit qui semble avoir été rédigé vers la même époque que les essais intitulés << Indirect Legislation » et «< Influence of Place and Time », c'est-à-dire aux environs de 1782. Il constitue presque la totalité du numéro 27 des Mss. d'University College (Legislation t. Preface to a Body of Law.

The limit of the quantity of a pleasure in respect of intensity on the side of diminution is a state of insensibility: the degree of intensity possessed by that pleasure which is the faintest of any that can be distinguished to be pleasure, may be represented by unity. Such a degree of intensity is in every day's experience: according as any pleasures are perceived to be more and more intense, they may be represented by higher and higher numbers: but there is no fixing upon any particular degree of intensity as being the highest of which a pleasure is susceptible.

The limit of the quantity of a pleasure in respect of duration is the least portion of duration that can be distinguished: suppose a moment. If then a moment be taken for the least portion of time that is distinguishable, it is certain that no pleasure, to exist at all, can last for less than a moment. Such

La limite de la quantité d'un plaisir par rapport à l'intensité dans le sens de la diminution est un état d'insensibilité : le degré d'intensité possédé par le plaisir le plus faible qui puisse être distingué en tant que plaisir, peut être représenté par l'unité. Ce degré d'intensité fait partie de l'expérience quotidienne; selon que des plaisirs sont perçus comme étant de plus en plus intenses, ils peuvent être représentés par des nombres de plus en plus élevés ; mais il n'y a pas moyen de déterminer un degré particulier d'intensité qui soit le plus haut dont un plaisir soit susceptible.

La limite de la quantité d'un plaisir par rapport à la durée est la moindre portion de durée qui puisse être distinguée: soit un moment. Si donc on prend un moment comme étant la moindre portion de temps qui puisse être distinguée, il est certain qu'aucun plaisir ne pourra exister, s'il dure moins qu'un

a degree of duration for a pleasure is within every day's experience. But there is no fixing upon any particular number of moments as being the greatest during which any pleasure can continue.

The quantum of the value of a pleasure in point of proximity has for its limit on the side of increase actual presence. No pleasure can be nearer, no pleasure can, on the score of proximity, be more valuable, than one that is actually present. Pleasures that are actually present are within every day's experience. But there is no fixing upon any number of moments, months, or years, that shall constitute the greatest interval, which can subsist between any present time, and the time at which the event of a pleasure's being enjoyed is to take place. The greatest possible duration of a man's life, were it determined, might indeed determine the greatest degree of remoteness of a pleasure as far as a single person were concerned but in the first place the greatest possible duration of a man's life is a quantity that never can be determined; in the next place it often becomes material to consider the pleasure not of a single person only but of many persons in succession.

The quantum of the value of a pleasure in point of probability, or certainty, as it is more convenient to call it on the present occasion, has for its limit on the side of increase that absolute certainty which cannot be deemed to take place but where the pleasure is actually present. No pleasure can be more certain than one that is actually present. But there is no fixing upon any number of chances which shall be the greatest there can be against the event of any pleasure's taking place.

Now then whole numbers increase continually from the same fixed point (var. unity): fractional numbers decrease continually from the same fixed point. Hence it appears, I imagine, pretty plainly, why the degrees of intensity and duration must be express'd by whole numbers, that of proximity and that of certainty by fractions.

So much for the circumstances that are ingredients in the value of a pleasure as far as concerns a single individual :