NATURE 
THURSDAY, JULY 17, 1902. 
MECHANICS OF ENGINEERING. 
The Mechanics of Engineering. By Prof. A. Jay 
DuBois, C.E., Ph.D., Yale University. Vol. i., Kine- 
matics, Statics, Kinetics, Statics of Rigid Bodies and of 
Elastic Solids. Pp. xxxiv + 634. Price 31s. 6d. 
Vol. ii. Stresses in Framed Structures and Designing. 
Pp. xxiii + 609. Price £2 2s. (New York: Wiley 
and Sons ; London: Chapman and Hall, Ltd., 1902.) 
HIS manual forms one of a number of publications 
which are being prepared by professors and instruc- 
tors of Yale University and issued in connection with 
the Bicentennial Anniversary. 
Dealing first with vol. i., the first 4oo pages of the 
book, about two-thirds of the whole, are devoted to what 
may be considered as the preliminary work of developing 
the principles of the mechanics of solids. In substance 
this part corresponds with the author’s treatise on the 
“Elementary Principles of Mechanics,” published in 
three volumes, entitled “ Kinematics,” “Statics” and 
“Kinetics.” The treatment is mainly analytical, graphical 
methods being reserved for the later chapters, in which 
the practical application of the principles is dealt with, 
and for the second volume. 
In the section dealing with the fundamental and 
derived units of measurement, the author rightly insists 
on the importance of constantly keeping in mind the 
dimensions of the various quantities, and of checking 
equations from time to time by inserting the dimensions 
and applying the principle of homogeneity. 
The old difficulty as to the use of the same word 
found to denote both mass and force is partially over- 
come by writing Ib. when mass is referred to, and pound 
when force is meant. There is thus a distinction to the 
eye if not tothe ear. This convention, however, is not 
adhered to in the latter parts of the work. 
In the development of the subject the reader is con- 
stantly reminded of the very useful fact that the various 
directed quantities which appear are vectors, and follow 
the vector law. But we think it would have tended to 
increased clearness of view if the author had brought 
into greater prominence the distinction between vectors 
the representative lines of which have different degrees 
of freedom, or, as they have been named, between 
unlocalised vectors, vectors localised in lines, and vectors 
which are localised at points. 
The authors fundamental definition of a vector as a 
directed quantity merely, with the frequent inference 
that any quantity which has magnitude and direction is 
a vector and therefore obeys the vector laws, is open to 
criticism. The reader will find that its application to the 
resolution and composition of angular displacements on 
pp. 58 to 60 is not very clear or convincing. Stated in 
this form it is liable to lead to slips like the one we 
“notice on p. 186 :— 
“Tf a rigid body has angular acceleration about an 
axis through its centre of mass, the resultant is a force 
couple in a plane at right angles to this axis. And con- 
versely,” &c. 
In the chapter on central forces the author touches on 
planetary motions and on harmonic motion. The latter 
NO. 1707, VOL. 66] 
265 
might with advantage be treated more fully in any sub- 
sequent edition, considered from the vector point of 
view, and with some reference to Fourier’s theorem. 
In treating of friction, only the simple approximate 
laws of solid friction are considered. Academic calcu- 
lations are made as to the action and efficiencies of 
machines like the wheel and axle, the different systems 
of pulleys, the screw, &c. Some useful lessons, not 
revealed in the treatise under review, would be learnt by 
any student who had the opportunity of putting the 
results of these calculations to the test by actual experi- 
ments in a laboratory. 
In the chapter on impact there are some practical 
observations on pile driving and onthe limiting pressures 
which may be put on pile and earth foundations. 
The section on the development of principles is 
brought to a close by a discussion of the action of the 
gyroscope and spinning top, and the statement of the 
equations of motion of a rigid body in their general form. 
In the part dealing with the practical applications of 
principles, the subject-matter treats mainly of questions 
specially interesting to the civil engineer. This is 
naturally to be expected, having regard to the position 
and qualifications of the author. 
There are two short chapters relating to framed struc- 
tures and bending moments, evidently curtailed in anti- 
cipation of vol. ii. Then follows an interesting discus- 
sion on masonry structures, dealing with earth and 
water pressures, and including the design of masonry 
dams and retaining walls. 
The closing section of the volume, comprising about 
150 pages, relates to the “Statics of Elastic Solids,” and 
deals with the design of such details as ties, riveted 
joints, pins and eye-bars, shafts, beams, springs and long 
columns ; and the first volume concludes with an ap- 
plication of the principle of least work to the swing 
bridge, the metal arch, the stone arch and the suspension 
bridge. 
The discussion of the theory of elasticity is meagre 
and disappointing. The various formule are established 
without giving the reader any clear insight with regard 
to the assumptions made and to the consequent limitations 
to the practical applications of the formula that are ob- 
tained. Consequently there is a tendency to interpret 
the results of the calculations as if they had the same 
certainty as demonstrations in geometry, and sometimes 
the proof given is quite illusory. For instance, the inves- 
tigations on pp. 509 to 511 on the strengths of shafts 
need thorough revision. The work of St. Venant in 
regard to the torsion of shafts of other than circular sec- 
if 
tion is entirely ignored. The formula ‘- +, applicable 
to circular shafts only, is taken as if it were true for all 
forms of section, and is actually applied to square and 
rectangular shafts. As another example of misleading 
theory, we think the working of example 3, p. 491, 
relating to a plate girder, should be entirely recast. 
In other portions of the subject the author is more 
happy. He applies the method of strain energy and 
the principle of least work to framed metal arches, in a 
manner readily lending itself to cases of travelling loads. 
He also investigates temperature stresses in the two- 
hinged and the continuous arch. We think he is right 
N 
