Letters Addressed to H.R.H. the Grand Duke of Saxe Coburg and Gotha; On the Theory of Probabilities, as Applied to the Moral and Political Sciences

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1849 Excerpt: ...head or tail the respective probabilities of £ and §, we should have one which would vary slightly in excess or defect from the mean probabilities determined by the mode of procedure, and the substance of the coins. But the principle of Bernoulli is still applicable to this case; and has been demonstrated by M. Poisson by means of analysis. Happily, the aid of calculation is not necessary here to conceive that the small variations which we find in passing from one coin to another may be ranged among the effects of accidental causes, which are obliterated when the experiments are sufficiently multiplied. So that the results are presented as if the trials had really been made with but one coin. In the case before us the experiments should generally be very numerous: it is for this reason that M. Poisson has designated the extension of Bernoulli,s principle as the law of great numbers. We have already had occasion to consider analogous examples, particularly in reference to the measurements taken on a large number of men of the same age. We then saw that-all the heights collected together gave a mean, from which they individually differed according to a well-defined law, and absolutely as if an individual type had been measured a number of times by means more or less defective. This symmetry in the results does not L exist, nor can it exist, but in so far as the elements which give the mean can be referred to an individual type. The measurements of the chests of the Scotch soldiers have presented us with another example of the same nature. They varied more or less from the common mean, as would vary different measurements taken on one and the same chest, but by defective means which would give rise to greater chances of error. Your Highness will, I h...