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In this (fourth) edition, some chapters have been considerably enlarged, viz. Mechanics ; Dynamics of Machinery; Friction ; Stress, Strain, and Elasticity; Hydraulic Motors and Machines; and Pumps. Several pages have also been added to many of the other chapters.

A most gratifying feature in connection with the publication of this book has been the number of complimentary letters received from all parts of the world, expressive of the help it has been to the writers; this opportunity is taken of thanking all correspondents both for their kind words and also for their trouble in pointing out errors and misprints. It is believed that the book is now fairly free from such imperfections, but the author will always be glad to have any pointed out that have escaped his notice, also to receive further suggestions. While remarking that the sale of the book has been very gratifying, he would particularly express his pleasure at its reception in the United States, where its success has been a matter of agreeable surprise.

The author would again express his indebtedness to all who kindly rendered him assistance with the earlier editions, notably Professor Hele-Shaw, F.R.S., Mr. A. H. Barker, B.Sc., Mr. Andrew Forbes, Mr. E. R. Verity, and Mr. J. W. Jukes. In preparing this edition, the author wishes to thank his old friend Mr. H. Rolfe for many suggestions and much help; also his assistant, Mr. R. H. Duncan, for the great care and pains he has taken in reading the proofs; and, lastly, the numerous correspondents (most of them personally unknown to him) who have sent in useful suggestions, but especially would he thank Professor Oliver B. Zimmerman, M.E., of the University of Wisconsin, for the "gearing" conception employed in the treatment of certain velocity problems in the chapter on “Mechanisms."

JOHN GOODMAN.

THE UNIVERSITY OF LEEDS,

August, 1904.

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MECHANICS APPLIED TO

ENGINEERING

CHAPTER I.

INTRODUCTORY.

The province of science is to ascertain truth from sources far and wide, to classify the observations made, and finally to embody the whole in some brief statement or formula. If some branches of truth have been left untouched or unclassified, the formula will only represent a part of the truth; such is the cause of discrepancies between theory and practice.

A scientific treatment of a subject is only possible when our statements with regard to the facts and observations are made in definite terms; hence, in an attempt to treat such a subject as Applied Mechanics from a scientific standpoint, we must at the outset have some means of making definite statements as to quantity. This we shall do by simply stating how many arbitrarily chosen units are required to make up the quantity in question.

We shall find that some of our units will be of a very complex character, but in every instance we shall be able to express them in terms of three fundamental units, viz. those of time, mass, and space. The complex units are usually termed “derived” units.

Units. Time (1). -Unless otherwise stated, we shall take one second as the unit of time, but sometimes we shall find it convenient to take minutes and hours. Mass (M).-Unit, one pound ; occasionally hundredweights and tons. I pound (lb.)

= 0·454 kilogramme.
1 kilogramme

= 2'2 lbs.
1 hundredweight (cwt.) 50-8 kilos.

1016 (tonneau or Millier).
1 tonneau or Millier = 0'984 ton.

I ton

B

Space (s).—Unit, one foot ; occasionally inches, yards, and miles.

Such terms as distance, length, breadth, width, thickness, are frequently used to denote space in various directions. I foot = 0*305 metre.

I sq. foot

= 0'0929 sq. metre. I metre = 3.28 feet.

I sq. metre = 10*764 sq. feet. I inch = 25.4 millimetres.

I sq. inch

= 6.541 sq. cms. i millimetre = 0·0394 inch.

i sq. mm. = 0'00155. sq. inch. I yard = 0'914 metre.

1 kilogramme = 2.2046 lbs. i metre = 1'094 yards. I mile

1 kilo. per sq.} = 14223 lbs. sq. inch. = 1609'3 metres. i kilometre = 1093.63 yards. 1 lb. sq. inch = 0'0703 kilo. sq. cm. = 0.621 mile.

I cubic inch = 16°387 c. cms.
I cubic foot = 0·0283 cubic metre.

Dimensions. The relation which exists between any given complex unit and the fundamental units is termed the dimensions of the unit. As an example, see p. 20, Chapter II.

Speed.-When a body changes its position relatively to surrounding objects, it is said to be in motion. The rate at which a body changes its position is termed the speed of the body.

Uniform Speed.-A body is said to have uniform speed when it traverses equal spaces in equal intervals of time. The

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body is said to have unit speed when it traverses unit space in unit time. Speed (in feet per second)

space traversed (feet)

time (seconds)

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