Page:The Sources of Standard English.djvu/452

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It is hoped that the methods of solution here explained, and the instances exhibited, will be found sufficient for application to nearly all the important problems of Physical Science, which require for their complete investigation the aid of Partial Differential Equations.

In order to spare astronomers and observers in natural philosophy the confusion and loss of time which are produced by referring to the ordinary treatises embracing both branches of probabilities (the first relating to chances which can be altered only by the changes of entire units or in&shy;tegral multiples of units in the fundamental conditions of the problem; the other concerning those chances which have respect to insensible grada&shy;tions in the value of the element measured), the present tract has been drawn, ''up. It relates only to errors of observation, and to the rules, derivable'' from the consideration of these errors, for the combination of the results of observations.