Eratosthenes (276-196 B.C.) used most probably a solstitial armilla for measuring the obliquity of the ecliptic. Hipparchus (160-125 B.C.) probably used an armillary sphere of four rings.
Those who have not seen the animal in life, or who did not believe in the possibility of the valves crossing each other with a slight obliquity, would not consent to appropriating any of its muscles to that purpose, and consequently attributed to all the lateral muscles the simple function of keeping the valves in an opposite position, or holding them adjusted.
All that it is necessary to assume is that the effects of the successive zones gradually diminish, whether from the increasing obliquity of the secondary ray or because (on account of the limitation of the region of integration) the zones become at last more and more incomplete.
We have seen that the problem before us is independent of the law of the secondary wave as regards obliquity; but the result of the integration necessarily involves the law of the intensity and phase of a secondary wave as a function of r, the distance from the origin.
The obliquity, corresponding to u =7, is such that the phases of the secondary waves range over a complete period, i.e.
12 -7r2R4 x2 f 2 The roots of Jo(z) after the first may be found from We may compare this with the corresponding result for a rectangular aperture of width a, tlf = X/a; and it appears that in consequence of the preponderance of the central parts, the compensation in the case of the circle does not set in at so small an obliquity as when the circle is replaced by a rectangular aperture, whose side is equal to the diameter of the circle.
Again, if we compare the complete circle with a narrow annular aperture of the same radius, we see that in the latter case the first dark ring occurs at a much smaller obliquity, viz.
V sin ?i, where a is the grating-interval and 43, the obliquity, the closeness of the grouping increasing with the number of intervals.
Among his happy conjectures may be mentioned that of the sun's axial rotation, postulated by him as the physical cause of the revolutions of the planets, and soon after confirmed by the discovery of sun-spots; the suggestion of a periodical variation in the obliquity of the ecliptic; and the explanation as a solar atmospheric effect of the radiance observed to surround the totally eclipsed sun.
Besides these complications there is another drawback to the use of the coelostat for general astronomical work, viz., the obliquity of the angle of reflection, which can never be less than that of the declination of the star, and may be greater to any extent.
If the conditions of equilibrium require an obliquity greater than this, sliding will take place.
The angle NCR is the obliquity of the resistance.
Consequently the condition of stability of friction is fulfilled if tht angle PCR is not greater than ~ that is to say, if the obliquity o~ the resistance required at the joint does not exceed the angle of repose and this condition ought to be fulfilled under all possible variation~ of the load.
Stable at a given point, conceive that point to be traversed by plane in all oossible positions, and determine which position gives thi greatest obliquity to the total pressure exerted between the portions of the mass which abut against each other at the plane.
The condition of stability is that this obliquity shall not exceed the angle of repose of the earth.
Parallel Projections of Figures.If any figure be referred to a system of co-ordinates, rectangular or oblique, and if a second figure be constructed by means of a second system of co-ordinates, rectangular or oblique, and either agreeing with or differing from the first system in rectangularity or obliquity, but so related to the co-ordin.
If the first structure have stability of friction, the second structure will have stability of friction also, so long as the effect of the - projection is not to increase the obliquity of the resistance at an~ joint beyond the angle of repose.
The obliquity of the action of the teeth is the angle EIT=
In practice it is found desirable that the mean value of the obliquity of action during the contact of teeth should not exceed 15, nor the maximum value 30.
Let C1, C1 be the centres of two wheels, B~IB1, B2IB1 their pitch-circles, I the pitch-point; let the obliquity of action of the teeth be constant, so that the same straight line P1 I?z shall represent at once the constant line of connection of teeth and the path of contact.
It is evident that the radii of the base-circles bear to each other the same proportions as the radii of the pitch-circles, and also that CiPi=1C1.cos obliquity ~ (27)
C2P2=IC2cos obliquity (The obliquity which is found to answer best in practice is about 143/4; its cosine is about i3/4, and its sine about 3/4.
Consequently, one of the forms suitable for the teeth of wheels is the involute of a circle; and the obliquity of the action of such teeth is the angle whose cosine is the ratio of the radius of their base-circle to that of the pitch-circle of the wheel.
To find the length of the path of contact on either side of the pitch-point I, it is to be observed that the distance between the fronts of two successive teeth, as measured along PiIPi, is less than the pitch in the ratio of cos obliquity: I; and consequently that, if distances equal to the pitch be marked off either way from I towards P~ and Pi respectively, as the extremities of the path of contact, and if, according to Principle IV.
In practice it is usual to make the path of contact somewhat longer, viz, about 2.4 times the pitch; and with this length of path, and the obliquity already mentioned of 143/4, the addendum is about 3~I of the pitch.
The obliquity of the action in passing the line of centres is nothing; the maximum obliquity is the angle EID=EID; and the mean obliquity is one-half of that angle.
It appears from experience that the mean obliquity should not exceed 15; therefore the maximum obliquity should be about 30; therefore the equal arcs DI and ID should each be one-sixth of a circumference; therefore the circumference of the describing circle should be six limes the pitch.
Nearly Epicycloidal Teeth: Williss Method.To facilitate the drawing of epicycloidal teeth in practice, Willis showed how to approximate to their figure by means of two circular arcsone concave, for the flank, and the other convex, for the faceand each having for its radius the mean radius of curvature of the epicycloidal arc. \Villiss formulae are founded on the following properties of epicycloids Let R be the radius of the pitch-circle; r that of the describing circle; 8 the angle made by the normal TI to the epicycloid at a given point T, with a tangent-to the circle at Ithat is, the obliquity of the action at T.
Forces applied to Mechanism Classed.If 0 be the obliquity of a force F applied to a piece of a machinethat is, the angle made by the direction of the force with the direction of motion of its point of applicationthen by the principles of statics, F may be resolved into two rectangular components, viz.
The total pressure exerted between the rubbing surfaces is the resultant of the normal pressure and of the friction, and its obliquity, or inclination to the common perpendicular of the surfaces, is the angle of repose formerly mentioned in 14, whose tangent is the coefficient of friction.
The side on which it touches that circle B C is determined by the fact that the obliquity A of the reaction is such as to oppose the A rotation.
The following are the principles on which this equality of wear depends: The rapidity of wear of a surface measured in an oblique direction is to the rapidity of wear measured normally as the secant of the obliquity is to unity.
129) be the axis of a pivot, and let RPC be a portion of a curve such that at any point P the secant of the obliquity to the normal of the curve of a line parallel to the axis is inversely proportional to the ordinate PY, to which the velocity of P is proportional.
Now let PT be a tangent to the curve at P, cutting OX in T; PT=PYXsecant obliquity, and this is to be a constant quantity; hence the curve is that known as the tractory of the straight line OX, in which PT = OR = constant, This curve is described by having a fixed straight edge parallel to OX, along which slides a slider carrying a pin whose centre is T.
U1=T~-+-~-);u2=Tf\+ also, let 0 be the obliquity of the action; then the times occupied by the approach and recess arc respectively Ci Ci -
His success as a dramatist had by this time gone some way to disabuse hostile critics of the suspicions as regards his personal character which had been excited by the apparent looseness of morals which since his Oxford days it had always pleased him to affect; but to the consternation of his friends, who had ceased to credit the existence of any real moral obliquity, in 1895 came fatal revelations as the result of his bringing a libel action against the marquis of Queensberry; and at the Old Bailey, in May, Wilde was sentenced to two years' imprisonment with hard labour for offences under the Criminal Law Amendment Act.
He taught, if he did not discover, the obliquity of the ecliptic, is said to have introduced into Greece the gnomon (for determining the solstices) and the sundial, and to have invented some kind of geographical map. But his reputation is due mainly to his work on nature, few words of which remain.
The obliquity of the ecliptic is the angle which its plane makes with that of the equator.
The motion of the ecliptic produces a secular variation in the obliquity which is now diminishing by an amount nearly equal to the entire motion of the ecliptic itself.
Attempts have been made by Laplace and his successors to fix certain limits within which the obliquity of the ecliptic shall always be confined.
It can, however, be shown that the obliquity cannot vary more than two or three degrees within a million of years of our epoch.
The formula for the obliquity of the ecliptic, as derived from the laws of motion of it and of the equator, may be developed in a series.
From this expression is derived the value of the obliquity at various epochs given in the following table.
The load, supported by the lower hook, is raised by hauling on the free end and, neglecting any slight obliquity of the plies of rope, the free end moves six times as fast H L C FIG.
The obliquity continually increases until the observer reaches the equator.
In or near Iioo B.C., Chou Kung, an able mathematician, determined with surprising accuracy the obliquity of the ecliptic; but his attempts to estimate the sun's distance failed hopelessly as being grounded on belief in the flatness of the earth.
540-510 B.C.) learned on his travels in Egypt and the East to identify the morning and evening stars, to recognize the obliquity of the ecliptic, goras.
He invented, or improved armillary spheres, the chief implements of ancient astrometry, determined the obliquity of the ecliptic at 23° 51' (a value 5' too great), and introduced an effective mode of arc-measurement.
This excess is, however, subject to wide variation, owing to the obliquity of the ecliptic and of the lunar orbit to the equator, and therefore to the horizon.
Gradually people became sick of openly avowed gallantry, of shameless libertinism, of moral obliquity and of the flattering artifices of vice; a long shudder ran through the selfish torpor of the social body.
Of the meridian circle, which gives 23° 51' " for the obliquity of the ecliptic. His astronomical poem Hermes began apparently with the birth and exploits of Hermes, then passed to the legend of his having ordered the heavens, the zones and the stars, and gave a history of the latter.
If the obliquity of illumination be so great that the principal maximum passes through the outermost edge of the objective, while a spectrum of 1st order passes the opposite edge, so that in the back focal plane the diffraction phenomenon shown in fig.
For exceptionally accurate work microscope objectives are sometimes used as condenser systems. When using immersion objectives, an immersion condenser must also be used if rays of extreme obliquity are wanted, for, in consequence of the total reflections, rays can only come from the upper plane surface of the condenser, which have not a larger inclination to the axis than about 41°, varying according to the refractive index of the glass.
If we begin with a blue glass, we may observe the gradually increasing obliquity of the direction of maximum polarization; and then by exchanging the blue glass for a red one, we may revert to the original condition of things, and observe the transition from perpendicularity to obliquity over again.
So long as the particles are all very small in comparison with the wave-length, there is complete polarization in the perpendicular direction; but when the size is such that obliquity sets in, the degree of obliquity will vary with the size of the particles, and the polarization will be complete only on the very unlikely condition that the size is the same for them all.
He has alluded to a childish fancy for a young girl with a slight obliquity of vision; but he only mentions it 1 Ouvres, x.