Page:Scientific Papers of Josiah Willard Gibbs - Volume 2.djvu/150

 are nearly satisfied. Approximate values of $$r_{1}, r_{2}, r_{3}$$ may suffice for the following computations, which, however, must be made with the greatest exactness.

VII. Test of the first hypothesis.

$$\log r_{1}, \log r_{2}, \log r_{3}$$ (approximate values from the preceding computations). The value of $$s - s_{2}$$ may be very small, and its logarithm in consequence ill determined This will do no harm if the computer is careful to use the same value—computed, of course, as carefully as possible—wherever the expression occurs in the following formulæ:

For adjustment of values: $$\tfrac{1}{2}(v_{3} - v_{1}) = \tfrac{1}{2}(v_{2} - v_{1}) + \tfrac{1}{2} (v_{3} - v_{2})$$}}