William Cain

May 14, 1847 (age 82)

Hillsboro, North Carolina, United States

From 1868 to 1874 and again from 1880 to 1882 Cain was engaged on railway location surveys, largely in North Carolina. During the interval, 1874-80, he was professor of mathematics and engineering in the Carolina Military Institute at Charlotte, North Carolina, and in 1882 he took a similar position in The Citadel, the Military College of South Carolina, at Charleston. He left in 1888 when he was elected professor and head of the department of mathematics and engineering at the University of North Carolina, a position he held until his retirement thirty-two years later. In 1918 he was chosen one of the original five "Kenan" professors. He wrote eight treatises on engineering and mathematical subjects, some of which passed through many editions. Most of them found wide acceptance among the engineering profession. The following six were popular compact handbooks: A Practical Theory of Voussoir Arches (1874); Maximum Stresses in Framed Bridges (1878); Voussoir Arches, Applied to Stone Bridges, Tunnels, Domes and Groined Arches (1879), republished in 1902 with the title Theory of Steel-Concrete Arches and of Vaulted Structures; Theory of Solid and Braced Elastic Arches (1879); Symbolic Algebra (1884); and Practical Designing of Retaining Walls (1888). His last two books were A Brief Course in the Calculus (1905) and Earth Pressure, Retaining Walls and Bins (1916). In addition to these treatises he contributed a multitude of papers to the technical and scientific press, a steady stream from 1874 until his retirement. Thereafter, until his death, discussions of articles in his field flowed continuously from his pen, and investigators constantly sought his counsel. Despite the fact that in the higher mathematics he was largely self-taught, his extraordinary intuitive grasp of the subject enabled him to analyze, from the standpoint of a theorist, a variety of engineering problems, such as the strength of masonry dams, pressures of earth against retaining walls, and the design of arches. Formulas which he developed were named for him, and engineers in the United States and abroad used his methods of analysis. Keeping in close touch with the work of foreign investigators, British, French, and Italian, Cain maintained a wide and forward outlook even during the decade following his retirement. He retained to the last his loyalty to the old South, and his bearing and manners were of the best Southern tradition. In his later years he became quite deaf. He was struck by an automobile as he was crossing the street in front of his house and died a few hours later. His portrait, by William Steene, hangs in Phillips Hall at the University.

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A brief course in the calculus

(This historic book may have numerous typos and missing te...)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1905 Excerpt: ... approaches as A / = o or---, is called the velocity of the point at the end of the time t. If the rate is uniform x/t = A x/A t is constant,. A x dx.: l1m =--A0A/ dt is constant and represents the rate here as well as in the case of variable motion. The velocity of the point P at any instant, is called the angular velocity of the supposed body at the instant. It is the velocity with which a point at a unit's distance from the axis moves for uniform rate or tends to move at any instant for non-uniform rate, and its value, in any case,. dx 1s dt Let us now discuss the case of motion presented by the crank, connecting rod and slide. In Fig. 37, CJP of length r, is the crank, Pthe. crank pin, PQ of length /, the connecting rod, and Q the slide (attached to the piston) which moves in the direction of the center C. The point P of course moves in a circle. When P is at A, Q is at D,:. AD = /. Let QD = s. Call 8 the angle A CP expressed in circular measure. We have,.-. J-r (1-cos 6) + I (x-y/x _ H. This formula is exact, but a little too complicated for practical use, so an approximation is resorted to. The term a is generally quite small, so that if we develop the radical expression to two terms only by the binomial formula giving, To get the velocity of the slide Q, we differentiate this with respect to t. ds It As we have just seen,--is the angular velocity or the velocity of a point on CP at a unit's distance from C. Call it 0) and assume it to be constant, so that P moves with the constant rate to r. The speed of Q by (2) is zero at 0 = o and 0 = ir or at the dead points A and B. The time-rate of change of the speed of Q is called its acceleration. Its value is, l(§)=H+7cH"2--(3) What are the accelerations of Q at 0 = o,-, ir? The forces acting on t...

Symbolic Algebra: Or the Algebra of Algebraic Numbers; Together (Classic Reprint)

(The object of the following essay is the discussion of ne...)

Practical Designing of Retaining Walls (Classic Reprint)

(Excerpt from Practical Designing of Retaining Walls The ...)

Earth Pressure: Retaining Walls and Bins

(This is a pre-1923 historical reproduction that was curat...)

A Practical Theory of Voussoir Arches (Classic Reprint)

(Excerpt from A Practical Theory of Voussoir Arches It is...)

Voussoir Arches Applied to Stone Bridges, Tunnels, Domes and Groined Arches (Classic Reprint)

(Excerpt from Voussoir Arches Applied to Stone Bridges, Tu...)

Maximum Stresses in Framed Bridges

(Leopold is delighted to publish this classic book as part...)

Theory of Solid and Braced Elastic Arches

(This book was originally published prior to 1923, and rep...)

William Cain

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Background

William Cain was born on May 14, 1847 in Hillsboro, North Carolina, United States; the son of Dr. William and Sarah Jane (Bailey) Cain. He was descended from William Cain, a merchant of Baltimore, who died in 1734.

Education

When only fourteen, having attended the Hillsboro Military Academy, William with other cadets drilled various bodies of Confederate troops. The Hillsboro Academy became the North Carolina Military and Polytechnic Institute and in 1866 Cain was graduated with the degree of A. M. He was its only graduate.

Career

From 1868 to 1874 and again from 1880 to 1882 Cain was engaged on railway location surveys, largely in North Carolina. During the interval, 1874-80, he was professor of mathematics and engineering in the Carolina Military Institute at Charlotte, North Carolina, and in 1882 he took a similar position in The Citadel, the Military College of South Carolina, at Charleston. He left in 1888 when he was elected professor and head of the department of mathematics and engineering at the University of North Carolina, a position he held until his retirement thirty-two years later. In 1918 he was chosen one of the original five "Kenan" professors.

He wrote eight treatises on engineering and mathematical subjects, some of which passed through many editions. Most of them found wide acceptance among the engineering profession. The following six were popular compact handbooks: A Practical Theory of Voussoir Arches (1874); Maximum Stresses in Framed Bridges (1878); Voussoir Arches, Applied to Stone Bridges, Tunnels, Domes and Groined Arches (1879), republished in 1902 with the title Theory of Steel-Concrete Arches and of Vaulted Structures; Theory of Solid and Braced Elastic Arches (1879); Symbolic Algebra (1884); and Practical Designing of Retaining Walls (1888). His last two books were A Brief Course in the Calculus (1905) and Earth Pressure, Retaining Walls and Bins (1916). In addition to these treatises he contributed a multitude of papers to the technical and scientific press, a steady stream from 1874 until his retirement. Thereafter, until his death, discussions of articles in his field flowed continuously from his pen, and investigators constantly sought his counsel. Despite the fact that in the higher mathematics he was largely self-taught, his extraordinary intuitive grasp of the subject enabled him to analyze, from the standpoint of a theorist, a variety of engineering problems, such as the strength of masonry dams, pressures of earth against retaining walls, and the design of arches. Formulas which he developed were named for him, and engineers in the United States and abroad used his methods of analysis.

Keeping in close touch with the work of foreign investigators, British, French, and Italian, Cain maintained a wide and forward outlook even during the decade following his retirement. He retained to the last his loyalty to the old South, and his bearing and manners were of the best Southern tradition.

In his later years he became quite deaf. He was struck by an automobile as he was crossing the street in front of his house and died a few hours later. His portrait, by William Steene, hangs in Phillips Hall at the University.

Achievements

He is known one of the pioneers in writing American civil engineering textbooks and researcher of a variety of engineering problems. In 1923 the American Society of Civil Engineers awarded him the J. James R. Croes Medal for his paper, "The Circular Arch Under Normal Loads".