Here the symmetry points at once to the selection of the three principal axes as the directions for i, j, k; and it would appear at first sight as if quaternions could not simplify, though they might improve in elegance, the solution of questions of this kind.
To simplify this, we take a new unit Y, which is 2 of X.
These equations simplify very much in their application to plane waves.
These points, together with a truly turned and polished cylinder, with carefully planned means of adjustment, much simplify the preparation of making-ready of any kind of type-forme or blocks for printing, which is carried out much in the same way as on the ordinary single cylinder, but in a more convenient manner.
There is not a single branch of the law which he did not simplify and amend, and the iron firmness with which he caused justice to be administered, irrespective of persons, if it exposed him to the charge of tyranny from the nobles, also won for him from the common people the epithet of " the Just."
- 1 or, as (88) and (90) may be written for small angles, (91) sin 20.=2C [I (V) - oS j, (92) sin 20 =2C [O S - I (v)] To simplify the work, so as to look out the value of sin 20 without the intermediate calculation of the remaining velocity v, a doubleentry table has been devised by Captain Braccialini Scipione =S (U) - S (u), = I (U) - I (u); mean angle (70), (Problemi del Tiro, Roma, 1883), and adapted to yd., ft., in.
After the treaties with the Danes, the tendency is to simplify distinctions on the lines of an opposition between twelvehynd-men and twyhyndmen, paving the way towards the feudal distinction between the free and the unfree.
Numerous attempts have been made to simplify the silk-throwing by combining two or more operations on one machine, but not as yet with much success.
The higher life of man is merely a fiction introduced by philosophers and rulers to simplify government and the relations of society.
We have here followed Dillmann's construction of a difficult passage which Duhm attempts to simplify by omission of the complicating clause without altering the general sense.
But it has been demonstrated again and again that, directly the company's interests begin to clash with those of foreign powers, the home government must assume a protectorate over its territories in order to simplify the situation and save perhaps disastrous collisions.
My friends think it very strange that they should hesitate so long, especially when I have not asked them to simplify my work in the least, but only to modify it so as to meet the existing circumstances.
Littoral Deposits (between high andSands, gravels, muds, &c. low-water marks) Kriimmel prefers to simplify this by grouping the deposits in a single category arranged according to their position into: (a) Littoral (including Murray and Renard's littoral and shallow water deposits [II.
To simplify calculation and to enable the assayer to use the metric system of weights employed in all chemical calculations, the "assay ton" ("A.T."
To simplify mechanically the solution of logical problems. These instruments are all more or less elaborate developments of the " logical slate," on which were written in vertical columns all the combinations of symbols or letters which could be made logically out of a definite number of terms. These were compared with any given premises, and those which were incompatible were crossed off.
There is no logical connexion between this theory and the doctrine that appetite of desire has always pleasure (or the absence of pain) for its object; but a materialist, framing a system of psychology, will naturally direct his attention to the impulses arising out of bodily wants, whose obvious end is the preservation of the agent's organism; and this, together with a philosophic wish to simplify, may lead him to the conclusion that all human impulses are similarly self-regarding.
Both here and in the preceding chapters the Septuagint has several variations and omissions, due either to an (unsuccessful) attempt to simplify the present difficulties, or to the use of another recension.
The general terms of language simplify the universe by reducing its variety of individuals to a few forms, none of which exists simply and perfectly.
Robert Willis (1800-1875) has the merit of having been the first to simplify considerably the theory of puie mechanism, by pointing out that that branch of mechanics relates wholly to comparative motions.
Bateson is pre-eminent, would appear to simplify the problem of variation, especially on its mechanical and physiological sides.
In 1789 he published his chief work, the Versuch einer neuen Theorie des menschlichen Vorstellungsvermägens, in which he attempted to simplify the Kantian theory and make it more of a unity.
The reforms which it was to bring about were eagerly and impatiently demanded by the public. This great operation had to be effected without interrupting the public service, and the department had immediately to reduce and to simplify the charges for transmission throughout the kingdom.