[Defining Life] The constant uniformity of phenomena under diversity of external influences.

Absolute, true, and mathematical time, in and of itself and of its own nature, without reference to anything external, flows uniformly and by another name is called duration. Relative, apparent, and common time is any sensible and external measure (precise or imprecise) of duration by means of motion; such as a measure—for example, an hour, a day, a month, a year—is commonly used instead of true time.

Both history of nature and history of humanity are 'historical' and yet cannot dispense with uniformity. In both there is 'uniformity' ('science') as well as non-uniformity ('history'); in both 'history respects itself and 'history does not repeat itself. But, as even the history of humanity has its uniformitarian features, uniformity can still less be dispensed with in 'history' of nature, which, being one of the natural sciences, is less historical and, consequently, more uniformitarian.

Combining in our survey then, the whole range of deposits from the most recent to the most ancient group, how striking a succession do they present:– so various yet so uniform–so vast yet so connected. In thus tracing back to the most remote periods in the physical history of our continents, one system of operations, as the means by which many complex formations have been successively produced, the mind becomes impressed with the singleness of nature's laws; and in this respect, at least, geology is hardly inferior in simplicity to astronomy.

Genuine religion has its root deep down in the heart of humanity and in the reality of things. It is not surprising that by our methods we fail to grasp it: the actions of the Deity make no appeal to any special sense, only a universal appeal; and our methods are, as we know, incompetent to detect complete uniformity. There is a principle of Relativity here, and unless we encounter flaw or jar or change, nothing in us responds; we are deaf and blind therefore to the Immanent Grandeur, unless we have insight enough to recognise in the woven fabric of existence, flowing steadily from the loom in an infinite progress towards perfection, the ever-growing garment of a transcendent God.

Human behaviour reveals uniformities which constitute natural laws. If these uniformities did not exist, then there would be neither social science nor political economy, and even the study of history would largely be useless. In effect, if the future actions of men having nothing in common with their past actions, our knowledge of them, although possibly satisfying our curiosity by way of an interesting story, would be entirely useless to us as a guide in life.

In terms of the way a geologist operates, there is no past until after the assumption of uniformity has been made.

The student of palaetiological sciences is a scientist and a historian. The former tries to be as uniformitarian as possible, the latter has to recognize the contingency of events which will ever be a 'skandalon' to the scientist. Verily, the geologist 'lives in a divided world'.

Uniformity and Evolution are one.

Were the succession of stars endless, then the background of the sky would present us an uniform luminosity, like that displayed by the Galaxy—since there could be absolutely no point, in all that background, at which would not exist a star. The only mode, therefore, in which, under such a state of affairs, we could comprehend the voids which our telescopes find in innumerable directions, would be by supposing the distance of the invisible background so immense that no ray from it has yet been able to reach us at all.

Without the discovery of uniformities there can be no concepts, no classifications, no formulations, no principles, no laws; and without these no science can exist.
Co-editor with American psychologist Henry Murray (1893-1988)

[My] numberless observations... made on the Strata... [have] made me confident of their uniformity throughout this Country & [have] led me to conclude that the same regularity... will be found to extend to every part of the Globe for Nature has done nothing by piecemeal. [T]here is no inconsistency in her productions. [T]he Horse never becomes an Ass nor the Crab an Apple by any intermixture or artificial combination whatever[. N]or will the Oak ever degenerate into an Ash or an Ash into an Elm. [H]owever varied by Soil or Climate the species will still be distinct on this ground. [T]hen I argue that what is found here may be found elsewhere[.] When proper allowances are made for such irregularities as often occur and the proper situation and natural agreement is well understood I am satisfied there will be no more difficulty in ascertaining the true quality of the Strata and the place of its possition [sic] than there is now in finding the true Class and Character of Plants by the Linean [sic] System.