Kdtyjb

In Chapter Fifty-Two of The Count of Monte Cristo there is a discussion between the titular count and Madame de Villefort about exposing oneself to poisons:

“Well,” replied Monte Cristo “suppose, then, that this poison was brucine, and you were to take a milligramme the first day, two milligrammes the second day, and so on. Well, at the end of ten days you would have taken a centigramme, at the end of twenty days, increasing another milligramme, you would have taken three hundred centigrammes; that is to say, a dose which you would support without inconvenience, and which would be very dangerous for any other person who had not taken the same precautions as yourself.

I am somewhat confused about the calculations here, and I am wondering if this may be a mistake or if I am simply missing something. The count talks about starting with one milligramme on the first day and adding a milligramme each day. He then says that in this manner you will be up to a centigramme (i.e. 10 milligrammes) by the tenth day. But then he says that after twenty days you will be at 300 centigrammes. This does not appear to make sense. If you continue increasing by 1 milligramme per day then you would be at 20 milligrammes (i.e. 2 centigrammes) by the twentieth day.

Then I thought that perhaps he meant that the total of all the poison from all the days would be 300 centigrams. But, first of all, this would be odd because the number mentioned for the tenth day was only the amount of poison taken on that day and not the total of all days up to that point. And, anyway, the calculation still wouldn't work out:

1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20=210

Thus, the total amount of poison after twenty days would only be 210 milligrammes (i.e. 21 centigrammes). This is still nowhere near the figure of 300 centigrammes.

Is there an explanation for this calculation?

It's a mistranslation.

I checked the original French text (emphasis mine):

—Eh bien, reprit Monte-Cristo, supposez que ce poison soit de la brucine, par exemple, et que vous en preniez un milligramme le premier jour, deux milligrammes le second, eh bien, au bout de dix jours vous aurez un centigramme; au bout de vingt jours, en augmentant d'un autre milligramme, vous aurez trois centigrammes, c'est-à-dire une dose que vous supporterez sans inconvénient, et qui serait déjà fort dangereuse pour une autre personne qui n'aurait pas pris les mêmes précautions que vous [...]

My translation:

"Well then," Monte-Cristo continued, "suppose the poison would be brucine, for example, and that you take one milligram of it the first day, two milligrams the second - well then, at the end of ten days you would have one centigram; at the end of twenty days, adding one more milligram, you would have three centigrams: namely, a dose which you can take without inconvenience, but which would already be very dangerous for someone else who had not taken the same precautions as you [...]

"Three hundred centigrams" would be "trois cent centigrammes" in French, not "trois centigrammes". Someone made a mistake translating. Three centigrammes makes sense, because of the phrase "en augmentant d'un autre milligramme": in the second week of this hypothetical experiment, the dose is increasing by one extra milligram each day, i.e. by two milligrams, which brings us to three centigrams at the end of twenty days.