In practice the gradient should not exceed i in 221, and even that is too steep, since theoretical conditions cannot always be realized; a wet rail will reduce the adhesion, and the gradients must be such that some paying load can be hauled in all weathers.
The works of the ancient Greek geographers were translated into Arabic, and starting with a sound basis of theoretical knowledge, exploration once more made progress.
Professor Claxton Fidler (Treatise on Bridge Construction, 1887) has made a very careful theoretical analysis of the weights of bridges of different types, and has obtained the following values for the limiting spans.
The theoretical element is the ratio of the parallactic inequality to the solar parallax.
The experiments of Raoult on solutions of organic bodies in water and on solutions of many substances in some dozen organic solvents have confirmed this result, and therefore the theoretical value of the osmotic pressure from which it was deduced.
That they must be studied by the economic historian is equally clear, owing to their practical influence and the fact that they furnished the theoretical bases of much of the economic policy of the 10th century.
His uncompromising antagonism to political blackmail and bribery, and his determination to pursue the right, as he saw the right, only in a common-sense fashion; made bitter enemies on the one hand among the corrupt politicians, and, on the other hand, among theoretical reformers) and discussions raged in the newspapers about his executive acts, his speeches, and his official messages much as they raged during his seven years in the White House.
The average man is pessimist or optimist not on theoretical grounds, but owing to the circumstances of his life, his material prosperity, his bodily health, his general temperament.
Lunar Theory (Cambridge 1896), or the work of Watson or of Bauschinger on Theoretical Astronomy.
The bishops, now increasingly absorbed in secular affairs, were content with a somewhat theoretical power of control, while the archdeacons rigorously asserted an independent position which implied great power and possibilities of wealth.