CHAPTER II. PASCAL’S SCIENTIFIC DISCOVERIES.

“But the most remarkable part of his treatise on the ‘Equilibrium of Fluids,’” continues Sir David Brewster, from whose exposition we quote, ¹⁹ “and one which of itself would have immortalised him, is his application of the general principle to the construction of what he calls the ‘mechanical machine for multiplying forces,’ ²⁰—an effect which, he says, may be produced to any extent we choose, as one may by means of this machine raise a weight of any magnitude.  This new machine is the *Hydrostatic Press*, first introduced by our celebrated countryman, Mr Bramah. “Pascal’s treatise on the weight of the whole mass of air forms the basis of the modern science of Pneumatics.  In order to prove that the mass of air presses by its weight on all the bodies which it surrounds, and also that it is elastic and compressible, a balloon half filled with air was carried to the top of the Puy de Dôme.  It gradually inflated itself as it ascended, and when it reached the summit it was quite full and swollen, as if fresh air had been blown into it; or page 47what is the same thing, it swelled in proportion as the weight of the column of air which pressed upon it diminished.  When again brought down, it became more and more flaccid, and, when it reached the bottom, it resumed its original condition.  In the nine chapters of which the treatise consists, he shows that all the phenomena or effects hitherto ascribed to the horror of a vacuum, arise from the weight of the mass of air; and after explaining the variable pressure of the atmosphere in different localities, and in its different states, and the rise of the water in pumps, he calculates that the whole mass of air round our globe weighs 8,983,889,440,000,000,000 French pounds. “Having thus completed his researches respecting elastic and incompressible fluids, Pascal seems to have resumed with a fatal enthusiasm his mathematical studies: but, unfortunately for science, several of the works which he composed have been lost.  Others, however, have been preserved, which entitle him to a high rank amongst the greatest mathematicians of the age.  Of these, his ‘Traité du Triangle Arithmétique,’ his ‘Tractatus de Numericis Ordinibus,’ and his ‘Problemata de Cycloide,’ are the chief.  By means of the *Arithmetical Triangle*, an invention equally ingenious and original, he succeeded in solving a number of theorems which it would have been difficult to demonstrate in any other way, and in finding the coefficients of different terms of a binomial raised to an even and positive power.  The same principles enabled him to lay the foundation of the doctrine of probabilities, an important branch of mathematical science, which Huyghens, a few years afterwards, improved, and which the Marquis la Place and M. Poisson have so greatly extended.  These treatises, with the exception of that on the Cycloid, were composed and printed in the year 1654, but were not published till 1668, after the death of the author.”