Christian faith in an age of science . fe. The degree of probability of our con-clusions diminishes rapidly, as those conclusions tran-scend the limits of observation. Again, a curve of one of the higher degrees oftenconsists of two or more branches apparently entirelydistinct from each other; and It may happen that oner)f these branches has in its general form a close re-semblance to a complete curve of lower degree. Thus,the curve which Is represented by the equation,— ay = ±Vx{x — b)(x — c), has, for certain values of the constants, an oval branchwhose form is very similar to that of an ell
Christian faith in an age of science . fe. The degree of probability of our con-clusions diminishes rapidly, as those conclusions tran-scend the limits of observation. Again, a curve of one of the higher degrees oftenconsists of two or more branches apparently entirelydistinct from each other; and It may happen that oner)f these branches has in its general form a close re-semblance to a complete curve of lower degree. Thus,the curve which Is represented by the equation,— ay = ±Vx{x — b)(x — c), has, for certain values of the constants, an oval branchwhose form is very similar to that of an ellipse, and Uncertainty of Scientific Conclusions an infinite parabolic branch. If we had given a num-ber of points of that oval branch, and no points of theother branch of the curve, our conjecture would natu-rally be that the curve was an ellipse; and, if the ob-served points did not exactly correspond with the equa-tion of the ellipse, we should probably suppose that theslight discrepancy was due simply to errors of measure- Y. Fig. 14,—Curve represented by equation, ay — ±^x{x — b){x — c). ment. We should, of course, be in error. The curveis not of the second degree, but of the third part of it is an ellipse. The resemblance of a partof it to an ellipse is only approximate. I believe thatwe must recognize the possibility of an analogouserror in our scientific investigations. A law whichappears to be thoroughly verified by the coincidencebetween prediction and observation may yet be true 333 Law in Nature only approximately and within limits. It is possible,for instance, that the Newtonian law of gravitationmay be only an approximation to the truth. It is pos-sible that the true law may be a vastly more complexone, which would include in a single formula not onlythe relations of sensible masses of matter at sensibledistances, but also the relations of molecules and atomsat infinitesimal distances. Our geometrical illustration may afford us yet an-othe
Size: 1391px × 1797px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1900, bookpublishernewyo, bookyear1903
