The Cephalopods include the nautilus and the cuttle fish, the terrible squid, or octopus, etc. Wonderful tales are told of the tenacity and ferocity of the “Poulpes,” and no doubt in long-past ages these animals attained a gigantic growth. They are very unpleasant enemies, and the cold, slimy grasp of the long tentacles is apt to give one the “horrors,” while the terrible head and beak fill one with dismay. The poulpes are very formidable opponents, and discretion will certainly be the better part of valour when they appear in our vicinity.
We must here close our sketch of the Invertebrates, and we regret that the limits of our volume will not permit us to continue this interesting subject, nor can we find space, at present, for even the barest description of the Vertebrate animals.
The sun-fish (Orthagoriscus).
CHAPTER LVI.
THE ANALYSIS OF CHANCE AND MATHEMATICAL GAMES.
MAGIC SQUARES—THE SIXTEEN PUZZLE—SOLITAIRE—EQUIVALENTS.
We will now proceed to draw our readers’ attention to several experiments very famous at a former period, but which our own generation has completely overlooked. We refer to the Analysis of Chance, a science still known under the title of Calculation of Probabilities, formerly cultivated with so much ardour, but to-day almost fallen into oblivion.
Originating in the caprice of the clever Chevalier de Méré, who in 1654 suggested the game to Pascal, the analysis of chance has given rise to investigations of an entirely novel kind, and attempts have been made to measure the mathematical degree of credence to be given to simple conjectures. We will first recapitulate the principles laid down by Laplace on this subject. We know that of a certain number of events, one only can happen, but nothing leads us to the belief that one will happen more than the other. The theory of chance consists in reducing all the events of the same kind to a certain number of equally possible cases, such, that is to say, that we are equally undecided about, and to determine the number of cases favourable to the event, whose probability we are seeking. The ratio of this number to that of all possible cases is the measure of this probability, which is thus a fraction, the numerator of which is the number of favourable cases, and the denominator the number of all possible cases. When all the cases are favourable to an event, its probability changes to certainty, and it is then expressed by the unit. Probabilities increase or diminish by their mutual combination; if the events are independent of each other, the probability of the existence of their whole is the product of their particular probabilities. Thus the probability of throwing an ace with one dice being 1/6, that of throwing two aces with two dice is 1/36. Each of the sides of one dice combining with the six sides of the other, there are thirty-six possible cases, among which one only gives the two aces. When two events depend on each other, the probability of the double event is the product of the probability of the first event by the probability that, that event having occurred, the other will occur. This rule helps us to study the influence of past events on the probability of future events. If we calculate á priori the probability of the event that has occurred and an event composed of this and another expected event, the second probability divided by the first, will be the probability of the expected event, inferred from the observed event.