From this beginning the succeeding terms of the progression could be determined mathematically.
The formula of Dalton would make the pressure increase in geometrical progression for equal increments of temperature.
For, if the members of a natural kind had no common idea to unite them, scientific research, having nothing objective in view, could at best afford a Aoyos or definition of the appropriate particulars; and, as the discrimination of the One and the Good implied the progression of particulars towards perfection, such a Xbyos or definition could have only a temporary value.
For such is the wonderful skill, prescience of experience, and invincible confidence acquired by some great natural geniuses among the Nantucket commanders; that from the simple observation of a whale when last descried, they will, under certain given circumstances, pretty accurately foretell both the direction in which he will continue to swim for a time, while out of sight, as well as his probable rate of progression during that period.
Sombart (Der moderne Kapitalismus, 2 vols., Leipzig, 1902), have propounded the doctrine of one gradual progression from an agricultural state to modern capitalistic conditions.
The two modes of progression overlap in human life, but the child's tendency when learning is to rest on the soles of the feet and the palms of the hands, unlike the apes, which support themselves on the sides of the feet and the bent knuckles of the hands.
I believe in the future I describe not out of a childish wish, but because it seems the obvious and natural progression of history.
From the regular progression of the lines in the X-ray spectra of different elements Moseley was able tc indicate the number of elements yet to be discovered, and he cleared up certain anomalies in the periodic tables of the elements.
He generalized Weber's law in the form that sensation generally increases in intensity as the stimulus increases by a constant function of the previous stimulus; or increases in an arithmetical progression as the stimulus increases in a geometrical ratio; or increases by addition of the same amount as the stimulus increases by the same multiple; or increases as the logarithm of the stimulus.
As a believer in the progression of the human race, he placed the principle of moral approbation in the attainment of perfection.