loo 
The Australasian Scwitific Magazine. [Oct. i, 1885. 
of one’s own individual life, or of commerce, or of war and peace.” It 
“ contains the principles on which it is found practicable to induce many 
to join together and consent that all shall bear the average lot in life of the 
whole.” 
Early in the seventeenth century the first step towards the development 
of the doctrine of chances into the regions of science seems to have been 
taken by Galileo in a letter to a now forgotten friend, in which he showed 
the probabilities of any particular numbers turning up in a sequence of 
throws of three dice. This paper, posthumously published, contained a table 
of the permutations of all numbers which can be thrown with three dice. 
The fragment in question is extremely rare and I doubt whether an 
English student will find it outside the great national library of the British 
Museum. Galileo being intent on other scientific researches appears not 
to have devoted further study to this particular one. 
Soon after Galileo’s demonstration, Pascal proved, much to the dis- 
comfiture of the Chevalier de Merve (“a man of talent but no mathe- 
matician”), that his preconceived ideas of the probabilities of gain or loss 
between two players were wholly wrong. The Chevalier was so chagrined 
that he declared that “the science of arithmetic is inconsistent with itself.” 
Fermat and Pascal and others corresponded together on questions of dice 
and cards during the latter middle portion of the seventeenth century. 
These studies were the foundation of the structure on which is based the 
essence of life assurance ; alone a great factor in the daily life of us of 
the present generation. What has been left unaccomplished during these 
two centuries, would take less time to enumerate, than to give even a brief 
catalogue of the labourers and their works whose researches and discoveries 
have placed even the unlearned of this generation on a pinnacle of know- 
ledge far higher than the aspirations of Cagliostro himself. Suffice it to 
mention among the men of science who have followed Galileo and Pascal, 
some few of them who have devoted part of their attention to the fascina- 
tions of the Doctrine of Chances. John De Witt, the great Netherlands 
statesman, was the first to apply the revelations of the doctrine to the 
practical exigencies of human life. He was the first to prove that annuities 
and their congener life assurance were dependent on probabilities. Then 
we have Leibnitz, the Bernoullis, Laplace, Simson, Halley, Price, Morgan, 
Milne, De Moivre, Sir Isaac Newton, Euler, and many others. John Graunt, 
in the days of the great plague of London and its great fire, was engaged not 
so much in evolving questions in probabilities, as in collating statistics and 
exploding errors. The transactions of the Royal Societies of England and 
of Edinburgh teem with brochures by the most brilliant and recondite 
thinkers, as do also the records of the French Academy on questions of 
probability. Paley, the immortal theologian, was eminently a student of 
probabilities. In our own days I think De Morgan is the Jacile princeps of 
students of probabilities, and next to him I may name Mr. Thomas Bond 
Sprague, wbo has combined with what Carlisle might call the most 
thoroughest knowledge of the theory of chances, its practical development 
in the exigencies of our daily life. With signal success he has applied his 
abstruse speculations to the daily routine of the control of the finance of 
life assurance. 
In my next paper I trust to be able to give somewhat of a more 
connected account of the progress of the science than I have been enabled 
to do in the present article, and with the kind permission of the editor, I 
propose subsequently to treat of some of the more interesting problems 
