The philosophy of biology / by James Johnstone.

  • Johnstone, James, 1870-1932.
Date:
1914
Catalogue details

Licence: In copyright

Credit: The philosophy of biology / by James Johnstone. Source: Wellcome Collection.

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    standard of approximation. It means further that, no matter how small is the number representing this standard of approximation, any pressure-value within the interval will differ from bx by less than this number. This is what we really mean when we say that the interval we are thinking about is an infinitely small one/’ Now corresponding to this interval of pressure- values in the immediate vicinity of bx, there will be an interval of volume-values in the immediate vicinity of bn> and, as before, any one of these volume-values will differ from bn by less than any number representing a standard of approximation to bn. We then find the point on the curve corresponding to both bx and bn, that is b, and we draw the line ffx, and find the tangent of the angle which this line makes with op. The value of this tangent is the limit of the rate of variation of the volume of the gas when the pressure undergoes a change in the immediate vicinity of bx. “ Rate of variation is a function of the argument “ pressure.” This function has the limit l for a value of its argument bx, when, as the argument varies in the immediate vicinity of bx, the value of the function approximates to l within any standard whatever of approximation / We should not, of course, find the rate of variation of volume of the gas by this means. We should calcu- late the value of the differential co-efficient ~ from dp the equation pv=k(/ +at) : this would be - k 1 ^ P But the reasoning involved in the methods of the calculus are those which we have attempted to outline. 1 If the reader does not understand this, he should read Whitehead’s Introduction to Mathematics.” He should read this book in any case.