4. By this method, thus getting rid at once, in a great measure, of errours of observation, we obtain data which are _more true than the_ individual _facts themselves_. The philosopher's business is to compare his hypotheses with facts, as we have often said. But if we make the comparison with separate special facts, we are liable to be perplexed or misled, to an unknown amount, by the errours of observation; which may cause the hypothetical and the observed result to agree, or to disagree, when otherwise they would not do so. If, however, we thus take the _whole mass of the facts_, and remove the errours of actual observation[31\3], by making the curve which expresses the supposed observation regular and smooth, we have the separate facts corrected by their general tendency. We are put in possession, as we have said, of something more true than any fact by itself is. [Note 31\3: _Ib._ vol. v. p. 4.] One of the most admirable examples of the use of this Method of Curves is found in Sir John Herschel's _Investigation of the Orbits of Double Stars_[32\3]. The author there shows how far inferior the direct observations of the angle of position are, to the observations corrected by a curve in the manner above stated. 'This curve once drawn,' he says, 'must represent, it is evident, the law of variation of the angle of position, with the time, not only for instants intermediate between the dates of observations, but even at the moments of observation themselves, much better than the individual _raw_ observations can possibly (on an average) do. It is only requisite to try a case or two, to be satisfied that by substituting the curve for the points, we have made a nearer approach to nature, and in a great measure eliminated errours of observation.' 'In following the graphical process,' he adds, 'we have a conviction almost approaching to moral certainty that {208} we cannot be greatly misled.' Again, having thus corrected the raw observations, he makes another use of the graphical method, by trying whether an ellipse can be drawn 'if not _through_, at least _among_ the points, so as to approach tolerably near them all; and thus approaching to the orbit which is the subject of investigation.' [Note 32\3: _Ib._] 5. The _Obstacles_ which principally impede the application of the Method of Curves are (I.) our _ignorance of the arguments_ of the changes, and (II.) the _complication of several laws_ with one another.