It is clear that for lenses in which the focal length is large compared
with the aperture, the thickness 𝑡 is independent of the shape of the
lens so long as the focal length and aperture remain constant.
Consequently a protuberance may be regarded as a thin meniscus
lens with mathematically sharp edges accurately fitted to a perfectly
regular spherical surface. Substituting for 1/𝑔 the 1156 (𝑓/F)2 obtained
above it follows that
| 𝑡＝A28(μ−1) 1156 (𝑓F)2 | (2). |
The effective aperture of the eye has been supposed to be 18 in.; calling this P, it is then obvious that (since F/𝑓 is the magnifying power) P(F/𝑓) is the theoretical aperture of objective requisite to supply the 18 in. eye-pencil. Substituting P(F/𝑓) for A in equation (2) we obtain
| 𝑡＝P2/8(μ−1)×156 | (3). |
This relation gives the thickness of a meniscus protuberance fitted to an objective (assumed to have an unlimited aperture) which fills the 18 in. pupil and occasions the maximum blurring permissible. If μ be 1·5, 𝑡 is equal to 1/39,936 in.
If the thickness 𝑡 correspond to the aperture A, then for another aperture 𝑎 to produce the same blurring we must have ∆′ (1/F)＝ ∆(1/F)A/𝑎, i.e. the focal length of the protuberance, and therefore the thickness 𝑡 must vary as A. Consider a telescope of 12 in. aperture, focal length of objective (F)＝180 in., focal length of eyepiece (𝑓) 0·3 in. and magnifying power (F/𝑓)=600. The aperture theoretically requisite to transmit the pupillary pencil 18 in. aperture is 18·600＝75 in. If the permissible protuberance cover the entire aperture of 75 in. its thickness would be 1/39,936 in. as above, but if restricted to a diameter of 1 in., then the maximum allowable thickness would be 1/75×1/39,936 in.＝say 1/3,000,000 in. Since the latter protuberance is assumed to fill only 175 of the aperture of the pupil of the eye, it produces an error in focussing equivalent to 75 quarter diopters or 75156. If we take the power of the eyepiece to be 1/·3 in. and subtract from it 75/156, we obtain 1/·35, so that AF is −·05 in.
Either the knife-edge test, or the more usual method of testing figuring by examining the out-of-focus disks formed on the retina when the eye-piece is inside and outside its correct focus, would certainly show the effect of this protuberance as a bright central spot when inside focus, and a dark central patch when outside; a practised eye can detect one-half the above error, and a quarter when the power is 1200 instead of 600. It may be noticed that, under the same circumstances, the error permissible in a reflecting telescope is only one quarter of that admitted in the refractor. In the case of a microscope objective of 10 in. back-focal-length used with a 1 in. eye-piece, the aperture required to transmit the pupillary pencil of 18 in. aperture is 114 in. Regarding the supposititious protuberance or depression as 120 in. in diameter, its thickness or depth must not exceed 1/39,936×0·05/1·25, or say 1/1,000,000 in. Therefore the accuracy of figuring required in the best microscopes does not fall far short of that required in telescopes.
The best optical workmanship, as applied to large reflecting surfaces, aims at reducing local protuberances or depressions to within the limiting height or depth of one twelve-millionth part of their diameter (A) and the optical methods which detect these errors are exceedingly delicate. The finest spherometer detects errors down to about three-millionths of an inch, below which it is valueless. The same applies to the study of the interference fringes formed when a master curve is fitted. It will not show up such fine errors. The figuring of spherical surfaces 12 in. or more in diameter by abrasion with a polisher so that no part of the surface is elevated or depressed above the average level by more than the above defined amounts is commonly practised, but much technical knowledge is necessary for success. It is a sine qua non that the material of the polisher should be as plastic and inelastic as is consistent with a moderate degree of hardness. The best material for large work is Stockholm pitch from which the greater part of the turpentine has been removed by evaporation, and the abrasive used is the finest rouge and water. For small work certain waxes, more or less mixed with rouge or putty powder, are used. Water is used as the lubricant. During delicate figuring temperature changes must be carefully avoided, otherwise buckling and consequent bad figuring of the lens or a variation in the hardness of the polisher may supervene. The motion of the polisher must therefore be leisurely. Moreover, any surface must be allowed to attain a uniform temperature before testing. When, as often happens, an elevation or depression on a large lens apparently refuses to be dislodged by straightforward polishing, recourse is had to local retouching. The faulty parts are localized by optical tests and then rubbed down by small polishers of an inch or more in diameter. In this way a central protuberance 1 in. in diameter and 1/2,000,000 of an in. high standing on the centre of a large objective may be removed by a polisher less than an inch in diameter worked at 200 half inch strokes per minute and at a pressure of 6 ozs. in about a minute. Great care is required, for if the process be carried too far, the whole surface must be re-figured. Local retouching serves to remove those conspicuous zones of aberration to which certain photographic lenses of large relative aperture are necessarily liable. An annular channel is polished out at a mean distance equal to 710 of the semi-aperture from the centre of the lens, and this is carefully shaded off towards the centre and also towards the edge; this corrects the zone of rays which focus at a point short of the focus of the centre and edge rays. This correction is particularly necessary in the case of certain lenses designed for stellar photography. (H. D. T.)
OBJECTIVISM, in philosophy, a term used, in contradistinction to Subjectivism, for any theory of knowledge which to a greater or less extent attributes reality (as the source and necessary pre-requisite of knowledge) to the external world. The distinction is based upon the philosophical antithesis of the terms Object and Subject, and their respective adjectival forms “objective” and “subjective.” In common use
these terms are opposed as synonymous respectively with “real” and “imaginary,” “practical” and “theoretical,” “physical”
and “psychic.” A man “sees” an apparition; was there any
physical manifestation, or was it merely a creation of his mind?
If the latter the phenomenon is described as purely subjective.
Subjectivism in its extreme form denies that mind can know
more than its own states. Objects, i.e. things-in-themselves,
may or may not exist: the mind knows only its own sensations,
perceptions, ideal constructions and so forth. In a
modified form “subjectivism” is that theory which attaches
special importance to the part played by the mind in the
accumulation of experience. See Psychology; Relativity of Knowledge.
OBLATION, an offering (Late Lat. oblatio, from offerre, oblatum, to offer), a term, particularly in ecclesiastical usage, for a solemn offering or presentation to God. It is thus applied to certain parts of the Eucharistic service in the Roman Church. There are “two oblations,” the “lesser oblation,” generally
known as the “offertory,” in which the bread and wine yet unconsecrated are presented, and the “greater oblation," the “oblation” proper, forming the latter part of the prayer of consecration, when the “Body and Blood” are ceremonially presented. The word “oblate” is an ecclesiastical term for persons who have devoted themselves or have been devoted as children by their parents to a monastic life. “Oblate” is
more familiar in the Roman Church as the name of a religious
congregation of secular priests, the Oblate Fathers of St Charles.
They are placed under the absolute authority of the bishop of
the diocese in which they are established and can be employed
by him on any duties he may think fit. This congregation was
founded in 1578 under the name of Oblates of the Blessed Virgin
and St Ambrose by St Charles Borromeo, archbishop of Milan
(see Borromeo, Carlo). There is a similar congregation of
secular priests, the Oblates of Mary the Immaculate, founded
at Marseilles in 1815.
OBLIGATION, in law, a term derived from the Roman law, in which obligatio signified a tie of law (vinculum juris) whereby one person is bound to perform or forbear some act for another. The obligatio of Roman law arose either from voluntary acts or from circumstances to which legal consequences were annexed. In the former case it was said to arise ex contractu, from contract, in the latter quasi ex contractu, ex delicto, or quasi ex delicto—that is to say, from tort, or from acts or omissions to which the law practically attached the same results as it did to contract or tort. Obligatio was used to denote either end of the legal chain that bound the parties, the right of the party who could compel fulfilment of the obligatio, the creditor, or the duty of the party who could be compelled to fulfilment, the debitor. In English law obligation has only the latter sense. Creditor and debtor have also lost their Roman law signification; they have been narrowed to mean the parties where the obligation is the payment of a sum of money. In English law obligation is used in at least four senses—(1) any duty imposed by law; (2) the special duty created by a vinculum juris; (3) not the duty, but the evidence of the duty—that is to say, an instrument under seal, otherwise called a bond; (4) the operative part of a bond. The third use of the word is chiefly confined to the older writers. Simplex and duplex obligatio were the old names for what are now more commonly called a single and a double or conditional bond. The party bound is still called the obligor, the party in whose favour the bond is made the obligee. The
