Remarkable as Hellriegel's discovery was, it merely furnished the explanation of a fact which had been empirically established by the husbandman long before, and had received most intelligent application when the old four-course (or Norfolk) rotation was devised.
But, at the same time, the constants in the above relation are not identical with those in the corresponding relation empirically deduced from observations on fatty hydrocarbons; and we are therefore led to conclude that a benzene union is considerably more stable than an ethylene union.
The method of preparing these gores was originally found empirically, but since the days of Albert Darer it has also engaged the minds of many mathematicians, foremost among whom was Professor A.
By the laryngoscope, invented about 1850 by Manuel Garcia the celebrated singingmaster, and perfected by Johann Czermak (1828-1873) and others, the diseases of the larynx also have been brought into the general light which has been shed on all fields of disease; and many of them, previously known more or less empirically, submitted to precise definition and cure.
On the other hand, if laws of social phenomena, empirically generalized from history, can, when once suggested, be affiliated to the known laws of human nature; if the direction actually taken by the developments and changes of human society, can be seen to be such as the properties of man and of his dwelling-place made antecedently probable, the empirical generalizations are raised into positive laws, and sociology becomes a science."
Under the older-fashioned methods of treating physical geography, the prairies were empirically described as level prairies, rolling prairies, and so on.
The limits set to the furnace builder's natural desire to make his furnace as large as possible, and its present shape (an obtuse inverted cone set below an acute upright one, both of them truncated), have been reached in part empirically, and in part by reasoning which is open to question, as indeed are the reasons which will now be offered reservedly for both size and shape.
At a time when social subjects were as a rule treated empirically, he brought first principles to bear at every point.
In order to allow for the finite stiffness and strength of materials, the least distance of the centre of resistance inward from the nearest edge of the joint is made to bear a definite proportion to the depth of the joint measured in the same direction, which proportion is fixed, sometimes empirically, sometimes by theoretical deduction from the laws of the strength of materials.
These were formerly given empirically, simply because they had been found to do good.