Paperback
-
PICK UP IN STORECheck Availability at Nearby Stores
Available within 2 business hours
Related collections and offers
Overview
Starting with the introduction of the basic Kolmogorov-Bochner existence theorem, the text explores conditional expectations and probabilities as well as projective and direct limits. Subsequent chapters examine several aspects of discrete martingale theory, including applications to ergodic theory, likelihood ratios, and the Gaussian dichotomy theorem. Prerequisites include a standard measure theory course. No prior knowledge of probability is assumed; therefore, most of the results are proved in detail. Each chapter concludes with a problem section that features many hints and facts, including the most important results in information theory.
Product Details
| ISBN-13: | 9780486481227 |
|---|---|
| Publisher: | Dover Publications |
| Publication date: | 08/18/2011 |
| Pages: | 320 |
| Product dimensions: | 5.30(w) x 8.40(h) x 1.00(d) |
Read an Excerpt
The Principles and Practice of Ornamental or Complex Turning
By John Jacob Holtzapffel
Dover Publications, Inc.
Copyright © 1973 Dover Publications, Inc.All rights reserved.
ISBN: 978-0-486-48122-7
CHAPTER 1
INTRODUCTION.
THE branch of the art to which this volume is devoted comprises two distinct varieties, one the decoration of surfaces and circular axial solids to which the work has been first reduced by plain turning, and the other the production of numerous compound solids and the subsequent ornamentation of their component superficies. Almost all the tools and appliances employed in ornamental turning fulfil both these purposes, for the former, the repetitions of the ornament they produce are superficial that they may not interfere with the contours previously determined and acquired by the work, for the latter, the tools excise portions of the material and often to a considerable depth to shape the compound solid, and then the same or other tools are used to decorate the various superficies so formed. In the latter class of work the lathe and its apparatus become a veritable shaping machine, inasmuch as the form to which the material is originally prepared is in part or entirely obliterated in the more or less complex solid eventually evolved from it.
The practice of ornamental turning so far as regards some kinds of surface patterns already possesses a respectable literature, ranging over many years, and generally monographs upon some particular piece of apparatus ; but the perhaps still more fascinating and certainly not less artistic work, the production and decoration of simple and compound solids, has hitherto remained comparatively untouched, and both classes of work will be pursued in the following pages.
The rise of ornamental turning does not appear to be more remote than the earlier half of the last century, a circumstance but natural in view of the primitive lathes until then employed. From the ruder appliances of earlier times, beauty in turned works whether in pottery or other materials depended solely upon elegance of outline, and the enrichment of the main form was nearly restricted to mouldings, bands of color and of incised circular lines. Such enrichments as in the ancient Greek vases although still plain turning are in the truest sense ornamental, and an attempt has been made to examine their motive in the previous volume, not only with regard to excellence in plain turning, but also for present reference ; for if the proportions of the main figure and the appropriate forms and positions of its mouldings are essential to success in plain turning, still more do they attract criticism when they are decorated by ornamental turning.
Many antique turned works may be met with in which a band or moulding has been subsequently reeded or carved by hand, and such a work, the nearest approach to ornamental turning, was probably that described by Virgil. Bucol. Ecl. III., v. 36, which as translated by Dryden runs:—
"Two bowls I have well turned of beechen wood:
Both by divine Alcimedon were made:
To neither of them yet the lip is laid.
The lids are ivy : grapes in clusters lurk
Beneath the carving of the curious work."
The undoubted early practice of the art of turning is unfortunately seldom and always obscurely referred to by the ancient writers, and the author is indebted to the deep reading of Colonel H. A. Ouvry, C. B. for the following particulars, the results of a careful research that he was good enough to undertake for these pages. In this interesting addition to the little that has been noted in the previous volumes upon this subject, Colonel Ouvry says:—
"It has been assumed on the authority of Pliny that Pheidias was the inventor of turning on the lathe ; but it must be taken into consideration that when a language such as the ancient Greek has been long dead, the meaning of many words, that is their exact meaning, becomes utterly lost. This happens to be the case in respect to the passage in Pliny on which the modern assumption rests that Pheidias was a turner on the lathe of both wood and ivory. The words [TEXT NOT REPRODUCIBLE IN ASCII] and [TEXT NOT REPRODUCIBLE IN ASCII], according to the celebrated antiquarian Heyne do not mean turning on the lathe. He says ' as to what is to be understood by the toreütick art is not so clear, especially in the passages in which Pliny treats of it, the common opinion that they signify the art of turning on the lathe has long been proved to be erroneous.' (Heyne, p. 127.)
"Vide Mémoire de l'Acad. des Inscriptions et Bell. Lett., tome ix., page 190. L'Abbé Gedoyn. 'Pline prétend que Phidias fut le premier qui trouva l'art de Tourneur avec gout, et que Polyclète acheva de la perfectionner. D'après le même critique ce jugement de Pline ne signifie autre chose, si non que les ouvrages de Polyclète avait quelque chose de plus recherchée, de plus élégante, de plus finie. Hancarville explique Toreûtique par le Tour auquel Phidias aurait donné une nouvelle forme, et que Polyclète aurait perfectionné.' I myself have no doubt that the Abbé was right and Hancarville was utterly mistaken.
"Vide Wieland über das Ideal der griechischen Kunst, on the words Toreutice and Torneutice.
"Don Vincenzo Reguero says 'toreutice fu l'arte del getto' (art of sculpture). On this question vide also Quatremère de Quincey, le Jupiter Olympien; vide again Anacreon, 17.
[TEXT NOT REPRODUCIBLE IN ASCII]
"Salmatius. Anacreon. Lipsiæ, 1793, points out that the word '[TEXT NOT REPRODUCIBLE IN ASCII],' plainly shows the error of those who ascribe the art of turning to Pheidias on the authority of Pliny.
"In India the native servants called my lathe 'chakra' which is a pure sanscrit word, [TEXT NOT REPRODUCIBLE IN ASCII], a wheel, and a turner was called [TEXT NOT REPRODUCIBLE IN ASCII], pronounced 'chakrajivanum,' one that lives by means of a wheel or lathe. In Persia the Arabic word [TEXT NOT REPRODUCIBLE IN ASCII], 'Kherad,' means a lathe, and [TEXT NOT REPRODUCIBLE IN ASCII], kherat-kerden, means to turn. The potter's wheel must have been the lathe in its infancy, and I have no doubt that the Romans had a simple lathe to turn platters, bedposts and the legs of chairs and couches, but nothing more than this, and that all the passages in ancient writers referring to decorated works which have been hitherto translated as 'turned on the lathe 'mean sculptured in alto-relievo. The passage in the Eclogue of Virgil upon which you asked my opinion, I take to mean that the cups were turned round as a first preparation, and afterwards acanthus flowers etc. were carved upon them, indeed as you suggest. Pheidias encrusted his cups with ivory and then carved them with the file and chisel. For the often-quoted passage in Pliny, vide Pliny, lib. xxxvi. cap. 8."
The three earliest known works that touch upon the practice of ornamental turning, those of Plumier, Teubers and Bergeron, and their very numerous illustrations, show the apparatus of that time to have been nearly confined to different modes of giving motion to the work while the tool remained stationary. Arresting the work from point to point by the division plate and index pending the application of a revolving tool to its edge or surface would appear to have been unknown except to the last named author, who refers at the termination of his work to some apparatus of this character as being the English system and to him novel. Both methods have been largely developed in this country and as will be seen are equally employed, both independently and in combination, thus affording the ornamental turner considerable choice of procedure and practically sufficient if not inexhaustible resources.
The clear arrangement of a description which has to travel over the voluminous details, necessary to even a moderate review of the apparatus and processes employed in ornamental turning has presented a task of no slight difficulty, not only as regards the comparative usefulness of distinct varieties, but from the circumstance that while every separate kind of tool or chuck is constructed for and fulfils in the first instance distinct and particular purposes, yet nearly every piece of apparatus will also partially if not absolutely perform some among the functions more conveniently appertaining to some other piece. The scheme adopted has been to place before the reader the forms of the more general cutting frames and chucks, proceeding from the more simple to the more comprehensive, with the aim to describe and illustrate so far as possible, types of all the results that may be attained with any used independently, and then to show the purposes and manipulation of the same apparatus used in combination. But the desire to render these descriptions thoroughly practical and to omit nothing that may be of real service to the amateur, has so unavoidably extended their length, that the author has found himself compelled to leave for the next volume the Geometric Chuck and the Rose Engine, apparatus in less general use, and the former of which has had an admirable exponent in Mr. T. S. Bazley, M.A.
Many necessary matters of detail are common to the use of all apparatus for, as also to the preparation of all works in ornamental turning, for convenience of reference, therefore, and to avoid repetitions these general details are collected in this preliminary chapter, leaving the more particular for subsequent notice as they arise. It has also appeared desirable to emphasize the descriptions of the distinct powers of every piece of apparatus by corresponding illustrations of their productions both of solid forms and of surface patterns ; and to prevent possible confusion these have been divided into two groups, the first, single pieces every one showing only one particular result.
These minor examples of solids it should be said do not greatly differ from the actual requirements for the construction of complete works, which latter from necessity or convenience are very generally composed or built up of similar separate pieces jointed to one another. This group however numerous is obviously insufficient even to indicate the wide field open to the amateur, while this volume would hardly serve its purpose without the addition of a second group, illustrations of a few complete works. The author is responsible for most of the designs of these specimens of either kind, all have been executed to appear in this work and with two objects, to explain the more convenient methods for the production of analogous works, and not less, to endeavour to show that the art of ornamental turning is by no means inconsistent with artistic results. More or less successful as these examples may be pronounced in this latter respect, unavoidable exigencies of space, as also with the woodcuts of the apparatus, preclude their presentment all of full size or to one scale, but this circumstance may be considered as of less moment as their general dimensions have been noted where necessary, while the fac-simile process employed has preserved absolute correctness of outline. Hence should any be deemed worthy of reproduction there will be no difficulty as to the enlargement or reduction of their measurements which may be taken directly from the plate ; mention may also be permitted that additional full sized illustrations have been prepared of most of the complete specimens for the convenience of those who may desire this further assistance.
In considering the merits of the plates it should also not be forgotten that considerable difficulties interfere with the successful illustration of all ornamentally turned works, either solid forms or surface patterns, any process for which purpose fails to render other than a faint conception of some marked elements in their real beauty; and this more especially as regards the absolute similarity of every distinct cut in any series, the equally exact disposition of the individual members of any group of ornament, and the brilliant play of light reflected by the polished facets and other forms cut by the tool. After some trials of various methods of engraving all of which failed to convey a satisfactory impression of the above particulars, the author determined upon the autotype process as more successful than any other in exhibiting a resemblance both as to the exactness and lustre of the ornamentation. Surface patterns cannot be better represented than by printing from the blocks upon which they have been cut in shallow lines ; this perfectly exhibits the truth of the intersections essential to the beauty of this class of ornament, and meets all requirements for measurements and explanations. On the other hand it should be remembered that all such illustrations produced from shallow lines, a necessity for printing, give no idea of the success and brilliancy of the actual work. As printed, the reticulations enclose numerous series of exactly similar and variously formed black spaces, the gradations and methodical arrangement of which it is that pleases. As executed upon the work, while all this variety and exact arrangement remains, the increased penetration of the tool converts all these black spaces into tiny or larger pyramidal and exquisitely polished facets, all lustrously reflecting light and correspondingly increasing the beauty of the work.
SECTION I.—THE GENERAL ADJUSTMENT OF THE WORK AND TOOLS. CONDITION AND REPARATION OF THE CUTTING TOOLS.
The first and natural conception of turned work is that of smooth and perfectly circular solids, and even those unacquainted with the lathe soon perceive that the work must have been in continuous revolution during the application of some cutting action by which the material was reduced to this regular form.
Works in ornamental turning have their superficies more or less decorated by incisions, perforations and projections grouped equidistantly or arranged in regular series, the members of every series individually exactly similar. These works again are by no means confined to the circular form as in plain turning, but include a considerable variety of complex ornamental solids, all of which in like manner exhibit absolute similarity both as to the separate component forms of any specimen, and in the decoration with which these are charged. In the former, the original circular form is attained by plain turning, and then the various distinct cuts the groupings of which supply the ornament, are made either with the work held fixed in certain definite and regular positions during the time that every separate cut in any series is placed upon it, or else the tool is stationary while the work acquires some rectilinear path or travels through a complete or partial rotation and usually upon other centers than that of its original axis.
The movements of the work and tools in the production of compound solids, forms that belong to the other division, are often not so apparent; but all such solids whether they branch from a central circular or rectangular nucleus, or those that are entirely contained by rectangular superficies may still be considered as originally circular pieces, from which the compound form is developed by far deeper cutting carried out under the same general conditions as those lately alluded to.
The cutting action may be divided into three principal methods. The work may be held at rest while the tool revolves and is advanced into simple contact with it, or during such contact is traversed along it; secondly, the work may traverse or may make a complete or partial rotation while the point of a fixed tool is advanced to it; and thirdly, the work may make its complete or partial revolution while a revolving tool is in simple contact with it or is traversed along it. Similar results may often be effected by one or other of these methods and this will be shown in every such case, not only as coming under the necessary description of the different apparatus, but also because this choice of procedure is very valuable inasmuch as one method usually presents greater facilities than another according to the particular form of the work and collateral conditions.
Under the first-named and perhaps most frequent system, the work carried in a chuck as in plain turning is arrested from point to point by means of the division plate and index at the moment it receives every distinct incision. The forms of these appliances have been fully described in the previous volume, but it may be mentioned here that the former consists of several concentric circles of equidistant holes usually drilled in the face of the mandrel pulley, but occasionally placed as in the Rose engine upon a broad band upon its edge. The numbers of the holes in the series of circles of the division plate admit of a great number of divisors, and the division plates for ornamental turning usually include circles of 360. 192. 144.120. 112. and 96. holes. All the direct divisions that may be obtained upon the work from these six circles have been given in a table, page 124, Vol. IV., and these are found amply sufficient for all purposes of ornamental turning; the second named 192. is however but twice the last 96, but this is now usually added for a purpose that will be referred to in a later chapter.
(Continues...)
Excerpted from The Principles and Practice of Ornamental or Complex Turning by John Jacob Holtzapffel. Copyright © 1973 Dover Publications, Inc.. Excerpted by permission of Dover Publications, Inc..
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.
Table of Contents
Preface
I. Introduction and Generalities
II.Conditional Expectations and Generalities
III. Projective and Direct Limits
IV. Martingales and Likelihood Ratios
V. Abstract Martingales and Applications
Bibliography
Index