This table is interpreted thus: bettors are willing to lay the same odds against _Rosicrucian_ as would be the true mathematical odds against drawing a white ball out of a bag containing two white and seven black balls; but no one is willing to back the horse at this rate; on the other hand, higher odds are not offered against him. Hence it is presumable that his chance is somewhat less than that above indicated. Again, bettors are willing to lay the same odds against _Pace_ as might fairly be laid against drawing one white ball out of a bag of seven, one only of which is white; but backers of the horse consider that they ought to get the same odds as might be fairly laid against drawing the white ball when an additional black ball had been put into the bag. As respects _Green Sleeve_ and _Blue Gown_, bettors are willing to lay the odds which there would be, respectively, against drawing a white ball out of a bag containing—(1) eleven balls, one only of which is white, and (2) one hundred and seven balls, seven only of which are white. Now, the three horses, _Rosicrucian_, _Green Sleeve_, and _Blue Gown_, all belong to Sir Joseph Hawley, so that the odds about the three are referred to in the last statement of the list just given. And since none of the offers against the three horses have been taken, we may expect the odds actually taken about ‘Sir Joseph Hawley’s lot’ to be more favourable than those obtained by summing up the three former in the manner we have already examined. It will be found that the resulting odds (offered) against Sir J. Hawley’s lot—estimated in this way—should be, as nearly as possible, 132 to 80. We find, however, that the odds _taken_ are 180 to 80. Hence, we learn that the offers against some or all of the three horses are considerably short of what backers require; or else that some person has been induced to offer far heavier odds against Sir J. Hawley’s lot than are justified by the fair odds against his horses, severally.