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Kuldip S. Rattan + Nathan W. Klingbeil

Introductory
Mathematics for
Engineering Applications
 Preface

This book is intended to provide first-year engineering students with a comprehen-

sive introduction to the application of mathematics in engineering. This includes
math topics ranging from precalculus and trigonometry through calculus and dif-
ferential equations, with all topics set in the context of an engineering applica-
tion. Specific math topics include linear and quadratic equations, trigonometry, 2-D
vectors, complex numbers, sinusoids and harmonic signals, systems of equations and
matrices, derivatives, integrals, and differential equations. However, these topics are
covered only to the extent that they are actually used in core first- and second-year
engineering courses, including physics, statics, dynamics, strength of materials, and
electric circuits, with occasional applications from upper-division courses. Additional
motivation is provided by a wide range of worked examples and homework problems
representing a variety of popular engineering disciplines.
While this book provides a comprehensive introduction to both the math
topics and their engineering applications, it provides comprehensive coverage of
neither. As such, it is not intended to be a replacement for any traditional math
or engineering textbook. It is more like an advertisement or movie trailer. Indeed,
everything covered in this book will be covered again in either an engineering or
mathematics classroom. This gives the instructor an enormous amount of freedom
− the freedom to integrate math and physics by immersion. The freedom to lever-
age student intuition, and to introduce new physical contexts for math without the
constraint of prerequisite knowledge. The freedom to let the physics help explain
the math and the math to help explain the physics. The freedom to teach math to
engineers the way it really ought to be taught − within a context, and for a reason.
Ideally, this book would serve as the primary text for a first-year engineering
mathematics course, which would replace traditional math prerequisite requirements
for core sophomore-level engineering courses. This would allow students to advance
through the first two years of their chosen degree programs without first complet-
ing the required calculus sequence. Such is the approach adopted by Wright State
University and a growing number of institutions across the country, which are now
enjoying significant increases not only in engineering student retention but also in
engineering student performance in their first required calculus course.
Alternatively, this book would make an ideal reference for any freshman
engineering program. Its organization is highly compartmentalized, which allows
instructors to pick and choose which math topics and engineering applications to
cover. Thus, any institution wishing to increase engineering student preparation and

vi
 Preface vii

motivation for the required calculus sequence could easily integrate selected topics
into an existing freshman engineering course without having to find room in the
curriculum for additional credit hours. Finally, this book would provide an outstand-
ing resource for nontraditional students returning to school from the workplace, for
students who are undecided or are considering a switch to engineering from another
major, for math and science teachers or education majors seeking physical contexts
for their students, or for upper-level high school students who are thinking about
studying engineering in college. For all of these students, this book represents a one-
stop shop for how math is really used in engineering.
 Acknowledgement

The authors would like to thank all those who have contributed to the development
of this text. This includes their outstanding staff of TA’s, who have not only pro-
vided numerous suggestions and revisions, but also played a critical role in the success
of the first-year engineering math program at Wright State University. The authors
would also like to thank their many colleagues and collaborators who have joined in
their nationwide quest to change the way math is taught to engineers. Special thanks
goes to Jennifer Serres, Werner Klingbeil and Scott Molitor, who have contributed
a variety of worked examples and homework problems from their own engineering
disciplines. Thanks also to Josh Deaton, who has provided detailed solutions to all
end-of-chapter problems. Finally, the authors would like to thank their wives and
families, whose unending patience and support have made this effort possible.

This material is based upon work supported by the National Science Founda-
tion under Grant Numbers EEC-0343214, DUE-0618571, DUE-0622466 and DUE-
0817332. Any opinions, findings, and conclusions or recommendations expressed in
this material are those of the authors and do not necessarily reflect the views of the
National Science Foundation.

viii
 Straight Lines in CHAPTER
1
Engineering

In this chapter, the applications of straight lines in engineering are introduced. It is

assumed that the students are already familiar with this topic from their high school
algebra course. This chapter will show, with examples, why this topic is so impor-
tant for engineers. For example, the velocity of a vehicle while braking, the voltage-
current relationship in a resistive circuit, and the relationship between force and
displacement in a preloaded spring can all be represented by straight lines. In this
chapter, the equations of these lines will be obtained using both the slope-intercept
and the point-slope forms.

1.1 VEHICLE DURING BRAKING

The velocity of a vehicle during braking is measured at two distinct points in time, as
indicated in Fig. 1.1.

t, s v(t), m/s
1.5 9.75
2.5 5.85

Figure 1.1 A vehicle while braking.

The velocity satisfies the equation

v(t) = at + vo (1.1)
where vo is the initial velocity in m/s and a is the acceleration in m/s2 .
(a) Find the equation of the line v(t) and determine both the initial velocity vo and
the acceleration a.
(b) Sketch the graph of the line v(t) and clearly label the initial velocity, the acceler-
ation, and the total stopping time on the graph.
The equation of the velocity given by equation (1.1) is in the slope-intercept form
y = mx + b, where y = v(t), m = a, x = t, and b = vo . The slope m is given by
𝚫y y2 − y1
m= = .
𝚫x x2 − x1

1
2 Chapter 1 Straight Lines in Engineering

Therefore, the slope m = a can be calculated using the data in Fig. 1.1 as
v2 − v1 5.85 − 9.75
a= = = −3.9 m/s2 .
t2 − t1 2.5 − 1.5
The velocity of the vehicle can now be written in the slope-intercept form as
v(t) = −3.9 t + vo .
The y-intercept b = vo can be determined using either one of the data points. Using
the data point (t, v) = (1.5, 9.75) gives
9.75 = −3.9 (1.5) + vo .
Solving for vo gives
vo = 15.6 m/s.
The y-intercept b = vo can also be determined using the other data point (t, v) =
(2.5, 5.85), yielding
5.85 = −3.9 (2.5) + vo .
Solving for vo gives
vo = 15.6 m/s.
The velocity of the vehicle can now be written as
v(t) = −3.9 t + 15.6 m/s.
The total stopping time (time required to reach v(t) = 0) can be found by equating
v(t) = 0, which gives
0 = −3.9 t + 15.6.
Solving for t, the stopping time is found to be t = 4.0 s. Figure 1.2 shows the velocity of
the vehicle after braking. Note that the stopping time t = 4.0 s and the initial velocity

Velocity, m/s

15.6 Initial velocity, v0

(y -intercept)

1
a 3.90 m/s2

Stopping time
(x -intercept)

0
t, s
0 4.0

Figure 1.2 Velocity of the vehicle after braking.

 1.2 Voltage-Current Relationship in a Resistive Circuit 3

vo = 15.6 m/s are the x- and y-intercepts of the line, respectively. Also, note that the
slope of the line m = −3.90 m/s2 is the acceleration of the vehicle during braking.

1.2 VOLTAGE-CURRENT RELATIONSHIP

IN A RESISTIVE CIRCUIT
For the resistive circuit shown in Fig. 1.3, the relationship between the applied voltage
Vs and the current I flowing through the circuit can be obtained using Kirchhoff’s
voltage law (KVL) and Ohm’s law. For a closed-loop in an electric circuit, KVL states
that the sum of the voltage rises is equal to the sum of the voltage drops, i.e.,
∑ ∑
Kirchhoff’s voltage law: ⇒ Voltage rise = Voltage drop.

I
R VR
Vs , V I, A
VS
10.0 0.1
V 20.0 1.1

Figure 1.3 Voltage and current in a resistive circuit.

Applying KVL to the circuit of Fig. 1.3 gives

Vs = VR + V. (1.2)
Ohm’s law states that the voltage drop across a resistor VR in volts (V) is equal to the
current I in amperes (A) flowing through the resistor multiplied by the resistance R
in ohms (Ω), i.e.,
VR = I R. (1.3)
Substituting equation (1.3) into equation (1.2) gives a linear relationship between the
applied voltage Vs and the current I as
Vs = I R + V. (1.4)
The objective is to find the value of R and V when the current flowing through the
circuit is known for two different voltage values given in Fig. 1.3.
The voltage-current relationship given by equation (1.4) is the equation of a
straight line in the slope-intercept form y = mx + b, where y = Vs , x = I, m = R, and
b = V. The slope m is given by
Δ y Δ Vs
m=R= = .
Δx ΔI
Using the data in Fig. 1.3, the slope R can be found as
20 − 10
R= = 10 Ω.
1.1 − 0.1
4 Chapter 1 Straight Lines in Engineering

Therefore, the source voltage can be written in slope-intercept form as

Vs = 10 I + b.
The y-intercept b = V can be determined using either one of the data points. Using
the data point (Vs , I) = (10, 0.1) gives
10 = 10 (0.1) + V.
Solving for V gives
V = 9 V.
The y-intercept V can also be found by finding the equation of the straight line using
the point-slope form of the straight line (y − y1 ) = m(x − x1 ) as
Vs − 10 = 10(I − 0.1) ⇒ Vs = 10 I − 1.0 + 10.
Therefore, the voltage-current relationship is given by
Vs = 10 I + 9. (1.5)
Comparing equations (1.4) and (1.5), the values of R and V are given by
R = 10 Ω, V = 9 V.
Figure 1.4 shows the graph of the source voltage Vs versus the current I. Note that
the slope of the line m = 10 is the resistance R in Ω and the y-intercept b = 9 is the
voltage V in volts.
The values of R and V can also be determined by switching the interpretation
of x and y (the independent and dependent variables). From the voltage-current
relationship Vs = I R + V, the current I can be written as a function of Vs as
1 V
I= Vs − . (1.6)
R R
This is an equation of a straight line y = m x + b, where x is the applied voltage Vs ,
y is the current I, m = R1 is the slope, and b = − V
R
is the y-intercept. The slope and

VS , V

20

10 R
1

10
V 9V

0 I, A
0 0.1 1.1

Figure 1.4 Voltage-current relationship for the data given in Fig. 1.3.
 1.2 Voltage-Current Relationship in a Resistive Circuit 5

y-intercept can be found from the data given in Fig. 1.3 using the slope-intercept
method as
Δy ΔI
m= = .
Δ x Δ Vs
Using the data in Fig. 1.3, the slope m can be found as
1.1 − 0.1
m= = 0.1.
20 − 10
Therefore, the current I can be written in slope-intercept form as
I = 0.1 Vs + b.
The y-intercept b can be determined using either one of the data points. Using the
data point (Vs , I) = (10, 0.1) gives
0.1 = 0.1 (10) + b.
Solving for b gives
b = −0.9.
Therefore, the equation of the straight line can be written in the slope-intercept form
as
I = 0.1 Vs − 0.9. (1.7)
Comparing equations (1.6) and (1.7) gives
1
= 0.1 ⇒ R = 10 Ω
R
and
V
− = −0.9 ⇒ V = 0.9 (10) = 9 V.
R
Figure 1.5 is the graph of the straight line I = 0.1Vs − 0.9. Note that the y-intercept
V 1
is − = − 0.9 A and the slope is = 0.1.
R R
I, A

1.1

0.1

0.1 1
0 VS ,V
0 10 20

y-intercept

0.9

Figure 1.5 Straight line with I as independent variable for the data given in Fig. 1.3.
6 Chapter 1 Straight Lines in Engineering

1.3 FORCE-DISPLACEMENT IN A PRELOADED

TENSION SPRING
The force-displacement relationship for a spring with a preload fo is given by

f = k y + fo , (1.8)

where f is the force in Newtons (N), y is the displacement in meters (m), and k is the
spring constant in N/m.

y f, N y, m
f 1 0.1
k 5 0.9

Figure 1.6 Force-displacement in a preloaded spring.

The objective is to find the spring constant k and the preload fo , if the values of the
force and displacement are as given in Fig. 1.6.

Method 1 Treating the displacement y as an independent variable, the force-

displacement relationship f = k y + fo is the equation of a straight line y = mx + b,
where the independent variable x is the displacement y, the dependent variable y is
the force f , the slope m is the spring constant k, and the y-intercept is the preload fo .
The slope m can be calculated using the data given in Fig. 1.6 as
5−1 4
m= = = 5.
0.9 − 0.1 0.8
The equation of the force-displacement equation in the slope-intercept form can
therefore be written as

f = 5y + b.

The y-intercept b can be found using one of the data points. Using the data point
(f , y) = (5, 0.9) gives

5 = 5 (0.9) + b.

Solving for b gives

b = 0.5 N.

Therefore, the equation of the straight line can be written in slope-intercept form as

f = 5y + 0.5. (1.9)

Comparing equations (1.8) and (1.9) gives

k = 5N∕m, fo = 0.5N.
 1.3 Force-Displacement in a Preloaded Tension Spring 7

Method 2 Now treating the force f as an independent variable, the force-

1 f
displacement relationship f = ky + fo can be written as y = f − o . This relation-
k k
ship is the equation of a straight line y = mx + b, where the independent variable
x is the force f , the dependent variable y is the displacement y, the slope m is the
1
reciprocal of the spring constant , and the y-intercept is the negated preload
k
f
divided by the spring constant − o . The slope m can be calculated using the data
k
given in Fig. 1.6 as

0.9 − 0.1 0.8

m= = = 0.2.
5−1 4

The equation of the displacement y as a function of force f can therefore be written

in slope-intercept form as

y = 0.2f + b.

The y-intercept b can be found using one of the data points. Using the data point
(y, f ) = (0.9, 5) gives

0.9 = 0.2 (5) + b.

Solving for b gives

b = −0.1.

Therefore, the equation of the straight line can be written in the slope-intercept form
as

y = 0.2f − 0.1. (1.10)

1 f
Comparing equation (1.10) with the expression y = f − o gives
k k

1
= 0.2 ⇒ k = 5 N/m
k

and
fo
− = −0.1 ⇒ fo = 0.1 (5) = 0.5 N.
k
Therefore, the force-displacement relationship for a preloaded spring given in
Fig. 1.6 is given by

f = 5y + 0.5.
8 Chapter 1 Straight Lines in Engineering

1.4 FURTHER EXAMPLES OF LINES IN ENGINEERING

Example The velocity of a vehicle follows the trajectory shown in Fig. 1.7. The vehicle starts
1-1 at rest (zero velocity) and reaches a maximum velocity of 10 m/s in 2 s. It then
cruises at a constant velocity of 10 m/s for 2 s before coming to rest at 6 s. Write the
equation of the function v(t); in other words, write the expression of v(t) for times
between 0 and 2 s, between 2 and 4 s, between 4 and 6 s, and greater than 6 s.

v(t), m/s

10

t, s
0 2 4 6

Figure 1.7 Velocity profile of a vehicle.

Solution The velocity profile of the vehicle shown in Fig. 1.7 is a piecewise linear function
with three different equations. The first linear function is a straight line passing
through the origin starting at time 0 sec and ending at time equal to 2 s. The second
linear function is a straight line with zero slope (cruise velocity of 10 m/s) starting
at 2 s and ending at 4 s. Finally, the third piece of the trajectory is a straight line
starting at 4 s and ending at 6 s. The equation of the piecewise linear function can
be written as
(a) 0 ≤ t ≤ 2:

v(t) = mt + b
10 − 0
where b = 0 and m = = 5. Therefore,
2−0
v(t) = 5t m/s.
(b) 2 ≤ t ≤ 4:

v = 10 m/s.
(c) 4 ≤ t ≤ 6:

v(t) = mt + b,
0 − 10
where m = = −5 and the value of b can be calculated using the data
6−4
point (t, v(t)) = (6, 0) as

0 = −5 (6) + b ⇒ b = 0 + 30 = 30.
 1.4 Further Examples of Lines in Engineering 9

The value of b can also be calculated using the point-slope formula for the
straight line

v − v1 = m(t − t1 ),
where v1 = 0 and t1 = 6. Thus,

v − 0 = −5(t − 6).

Therefore,

v(t) = −5(t − 6).

or

v(t) = −5t + 30 m/s.

(d) t > 6:
v(t) = 0 m/s.

Example The velocity of a vehicle is given in Fig. 1.8.

1-2
(a) Determine the equation of v(t) for
(i) 0 ≤ t ≤ 3 s
(ii) 3 ≤ t ≤ 6 s
(iii) 6 ≤ t ≤ 9 s
(iv) t ≥ 9
(b) Knowing that the acceleration of the vehicle is the slope of velocity, plot the
acceleration of the vehicle.

v(t), m/s

24

12

t, s
0 3 6 9

Figure 1.8 Velocity profile of a vehicle.

10 Chapter 1 Straight Lines in Engineering

Solution (a) The velocity of the vehicle for different intervals can be calculated as
(i) 0 ≤ t ≤ 3 s:
v(t) = mt + b,
12 − 24
where m = = −4 m/s2 and b = 24 m/s. Therefore,
3−0
v(t) = −4t + 24 m/s.
(ii) 3 ≤ t ≤ 6 s:
v(t) = 12 m/s.
(iii) 6 ≤ t ≤ 9 s:
v(t) = mt + b,
0 − 12
where m = = −4 m/s2 and b can be calculated in slope-intercept
9−6
form using point (t, v(t)) = (9, 0) as
0 = −4(9) + b.
Therefore, b = 36 m/s and
v(t) = −4t + 36 m/s.
(iv) t > 9 s:
v(t) = 0 m/s.
(b) Since the acceleration of the vehicle is the slope of the velocity in each interval,
the acceleration a in m/s2 is given by
⎧−4; 0≤t≤3s
⎪
⎪ 0; 3≤t≤6s
a=⎨
⎪−4; 6≤t≤9s
⎪ 0; t>9s
⎩
The plot of the acceleration is shown in Fig. 1.9.

Acceleration, m/s2

t, s
0 3 6 9

Figure 1.9 Acceleration profile of the vehicle in Fig. 1.8.

 1.4 Further Examples of Lines in Engineering 11

Example In a bolted connector shown in Fig. 1.10, the force in the bolt Fb is related to the
1-3 external load P as
Fb = C P + Fi ,
where C is the joint constant and Fi is the preload in the bolt.
(a) Determine the joint constant C and the preload Fi given the data in Fig. 1.10.
(b) Plot the bolt force Fb as a function of the external load P, and label C and Fi
on the graph.

P (l(b) Fb (l(b)
400 500
800 600

Figure 1.10 External force applied to a bolted connection.

Solution (a) The force-load relationship Fb = CP + Fi is the equation of a straight line,

y = mx + b. The slope m is the joint constant C, which can be calculated as
ΔFb 600 − 500 100 lb
C= = = = 0.25.
ΔP 800 − 400 400 lb
Therefore,
Fb (P) = 0.25 P + Fi . (1.11)
Now, the y-intercept Fi can be calculated by substituting one of the data points
into equation (1.11). Substituting the second data point (Fb , P) = (600, 800)
gives
600 = 0.25 × 800 + Fi .
Solving for Fi yields
Fi = 600 − 200 = 400 lb.
Therefore, Fb = 0.25 P + 400 is the equation of the straight line, where
C = 0.25 and Fi = 400 lb. Note that the joint constant C is dimensionless!
(b) The plot of the force Fb in the bolt as a function of the external load P is shown
in Fig. 1.11.
12 Chapter 1 Straight Lines in Engineering

Fb (lb)

600 (800, 600)

(400, 500) C
500 1

Fi 400

P (lb)
0 400 800

Figure 1.11 Plot of the bolt force Fb as a function of the external load P.

Example For the electric circuit shown in Fig. 1.12, the relationship between the voltage V
1-4 and the applied current I is given by V = (I + Io )R. Find the values of R and I0 if
the voltage across the resistor V is known for the two different values of the current
I as shown in Fig. 1.12.

I, amp V, volt
I R Io V 0.1 1.2
0.2 2.2

Figure 1.12 Circuit for Example 1-4.

Solution The voltage-current relationship V = R I + R Io is the equation of a straight line

y = mx + b, where the slope m = R can be found from the data given in Fig. 1.12 as
ΔV 2.2 − 1.2 1 volt
R= = = = 10 Ω.
ΔI 0.2 − 0.1 0.1 amp
Therefore,
V = 10(I) + 10 I0 . (1.12)
The y-intercept b = 10 I0 can be found by substituting the second data point
(2.2, 0.2) in equation (1.12) as
2.2 = 100 × 0.2 + 10 I0 .
Solving for I0 gives
10 I0 = 2.2 − 2 = 0.2,
 1.4 Further Examples of Lines in Engineering 13

which gives
I0 = 0.02 A.
Therefore, V = 10 I + 0.2; and R = 10 Ω and I0 = 0.02 A.

Example The output voltage vo of the operational ( amplifier

) (Op–Amp)
( )circuit shown in
1-5 100 100
Fig. 1.13 satisfies the relationship vo = − vin + 1 + vb , where R in
R R
kΩ is the unknown resistance and vb is the unknown voltage. Fig. 1.13 gives the
values of the output voltage for two different values of the input voltage.
(a) Determine the value of R and vb .
(b) Plot the output voltage vo as a function of the input voltage vin . On the plot,
clearly indicate the value of the output voltage when the input voltage is zero
(y-intercept) and the value of the input voltage when the output voltage is zero
(x-intercept).

100 kΩ

R kΩ vin , V vo , V
5 5
10 −5
vin vo
vb OP−AMP

Figure 1.13 An Op–Amp circuit as a summing amplifier.

( ( ) )
100 100
Solution (a) The input-output relationship vo = − vin + 1 + vb is the equa-
R R
100
tion of a straight line, y = mx + b, where the slope m = − can be found
R
from the data given in Fig. 1.13 as
100 Δvo −5 − 5 −10
− = = = = −2.
R Δvin 10 − 5 5
Solving for R gives R = 50 Ω. Therefore,
( ) ( )
100 100
v0 = − vin + 1 + vb
50 50
= −2 vin + 3 vb . (1.13)
The y-intercept b = 3 vb can be found by substituting the first data point
(v0 , vin ) = (5, 5) in equation (1.13) as
5 = −2 × 5 + 3 vb .
14 Chapter 1 Straight Lines in Engineering

Solving for vb yields

3 vb = 5 + 10 = 15,
which gives vb = 5 V. Therefore, vo = −2 vin + 15, R = 50 Ω, and vb = 5 V. The
x-intercept can be found by substituting vo = 0 in the equation vo = −2 vin + 15
and finding the value of vin as
0 = −2 vin + 15,
which gives vin = 7.5 V. Therefore, the x-intercept occurs at Vin = 7.5 V.
(b) The plot of the output voltage of the Op–Amp as a function of the input voltage
if vb = 5 V is shown in Fig. 1.14.

vo, V
y−intercept b 3, vb 15 V
15

5 100
m 2
R
vin, V
0 5 10
5
x−intercept 7.5 V

Figure 1.14 An Op–Amp circuit as a summing amplifier.

Example An actuator used in a prosthetic arm (Fig. 1.15) can produce a different amount of
1-6 force by changing the voltage of the power supply. The force and voltage satisfy the
linear relation F = kV, where V is the voltage applied and F is the force produced
by the prosthetic arm. The maximum force the arm can produce is F = 44.5 N when
supplied with V = 12 volts.
(a) Find the force produced by the actuator when supplied with V = 7.3 volts.
(b) What voltage is needed to achieve a force of F = 6.0 N?
(c) Using the results of parts (a) and (b), sketch the graph of F as a function of
voltage V. Use the appropriate scales and clearly label the slope and the results
of parts (a) and (b) on your graph.

Figure 1.15 Prosthetic arm.

 1.4 Further Examples of Lines in Engineering 15

Solution (a) The input-output relationship F = k V is the equation of a straight line y = m x,

where the slope m = k can be found from the given data as
44.5
k= = 3.71 N/V.
12
Therefore, the equation of the straight line representing the actuator force F
as a function of applied voltage V is given by

F = 3.71 V. (1.14)

Thus, the force produced by the actuator when supplied with 7.3 volts is found
by substituting V = 7.3 in equation (1.14) as

F = 3.71 × 7.3
= 27.08 N.
(b) The voltage needed to achieve a force of 6.0 N can be found by substituting
F = 6.0 N in equation (1.14) as
6.0 = 3.71 V
6.0
V=
3.71
= 1.62 volts. (1.15)
(c) The plot of force F as a function of voltage V can now be drawn as shown in
Fig. 1.16.

F, N

44.5

27.1 m k 3.71

6.0
V, volt
0 1.62 7.3 12

Figure 1.16 Plot of the actuator force verses the applied voltage.
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 This mystical error is distinctly characterized in the first chapter of
this gospel, and is there met by the direct assertions, that in Jesus
Christ, the Word, and the God, was not only life, but that the life
itself was the light of men;――and that John the Baptist “was not
the Light, but was only sent to bear witness of the Light;” and
again, with all the tautological earnestness of an old man, the aged
writer repeats the assertion that “this was the true Light, which
enlightens every man that comes into the world.” Against these
same sectaries, the greater part of the first chapter is directed
distinctly, and the whole tendency of the work throughout, is in a
marked manner opposed to their views. With them too, John had
had a local connection, by his residence in Ephesus, where, as it is
distinctly specified in the Acts of the Apostles, Paul had found the
peculiar disciples of John the Baptist long before, on his first visit to
that city; and had successfully preached to some of them, the
religion of Christ, which before was a strange and new thing to them.
The whole tendency and scope of this gospel, indeed, as directed
against these two prominent classes of heretics, both Gnostics and
Sabians, are fully and distinctly summed up in the conclusion of the
twentieth chapter;――“These things are written, that ye might
believe that Jesus is the Christ, the Son of God, and that in
believing on him, ye might have life through his name.”

As to the place where this gospel was written, there is a very

decided difference of opinion among high authorities, both ancient
and modern,――some affirming it to have been composed in
Patmos, during his exile, and others in Ephesus, before or after his
banishment. The best authority, however, seems to decide in favor of
Ephesus, as the place; and this view seems to be most generally
adopted in modern times. Even those who suppose it to have been
written in Patmos, however, grant that it was first given to the
Christian world in Ephesus,――the weight of early authority being
very decided on this latter point. This distinction between the place of
composition and the place of publication, is certainly very reasonable
on some accounts, and is supported by ancient authorities of
dubious date; but there are important objections to the idea of the
composition of both this and the Apocalypse, in the same place,
during about one year, which was the period of his exile. There seem
to be many things in the style of the gospel which would show it to
be a work written at a different period, and under different
circumstances from the Apocalypse; and some Biblical critics, of
high standing, have thought that the gospel bore marks in its style,
which characterized it as a production of a much older man than the
author of the energetic, and almost furious denunciations of the
Apocalypse, must have been. In this case, where ancient authority is
so little decisive, it is but fair to leave the point to be determined by
evidence thus connected with the date, and drawn from the internal
character of the composition itself,――a sort of evidence, on which
the latest moderns are far more capable of deciding than the most
ancient, and the sagest of the Fathers. The date itself is of course
inseparably connected with the determination of the place, and like
that, must be pronounced very uncertain. The greatest probability
about both these points is, that it was written at Ephesus, after his
return from Patmos; for the idea of its being produced before his
banishment, during his first residence in Asia, has long ago been
exploded; nor is there any late writer of authority on these points,
who pretends to support this unfounded notion.

his first epistle.

All that has been said on the character and the objects of the
gospel, may be exactly applied to this very similar production. So
completely does it resemble John’s gospel, in style, language,
doctrines and tendencies, that even a superficial reader might be
ready to pronounce, on a common examination, that they were
written in the same circumstances and with the same object. This
has been the conclusion at which the most learned critics have
arrived, after a full investigation of the peculiarities of both,
throughout; and the standard opinion now is, that they were both
written at the same time and for the same persons. Some reasons
have been given by high critical authority, for supposing that they
were both written at Patmos, and sent together to Ephesus,――the
epistle serving as a preface, dedication, and accompaniment of the
gospel, to those for whom it was intended, and commending the
prominent points in it to their particular attention. This beautiful and
satisfactory view of the object and occasion of the epistle, may
certainly be adopted with great propriety and justice; but in regard to
the places of its composition and direction, a different view is much
more probable, as well as more consistent with the notion, already
presented above, of the date and place of the gospel. It is very
reasonable to suppose that the epistle was written some years after
John’s return to Ephesus,――that it was intended, (along with the
gospel, for the churches of Asia generally, to whom John hoped to
make an apostolic pastoral visit, shortly,) to confirm them in the faith,
as he announces in the conclusion. There is not a single
circumstance in gospel or epistle, which should lead any one to
believe that they were directed to Ephesus in particular. On the
contrary, the total absence of anything like a personal or local
direction to the epistle, shows the justice of its common title, that it is
a “general epistle,” a circular, in short, to all the churches under his
special apostolic supervision,――for whose particular dangers,
errors and necessities, he had written the gospel just sent forth, and
to whom he now minutely commended that work, in the very opening
words of his letter, referring as palpably and undeniably to his
gospel, as any words can express. “Of that which ‘was from the
beginning, of the Word,’ which I have heard, which I have seen with
my eyes, which I have looked upon, which my hands have
handled,――of the Word of Life” &c.; particularizing with all the
minute verbosity of old age, his exact knowledge of the facts which
he gives in his gospel, assuring them thus of the accuracy of his
descriptions. The question concerns his reputation for fidelity as a
historian; and it is easy to see therefore, why he should labor thus to
impress on his readers his important personal advantages for
knowing exactly all the facts he treats of, and all the doctrines which
he gives at such length in the discourses of Christ. Again and again
he says, “I write,” and “I have written,” recapitulating the sum of the
doctrines which he has designed to inculcate; and he particularizes
still farther that he has written to all classes and ages, from the
oldest to the youngest, intending his gospel for the benefit of all. “I
have written to you, fathers,”――“unto you, young men,”――“unto
you, little children,” &c. What else can this imply, than a dedication of
the work concerning “the WORD,” to all stations and ages,――to the
whole of the Christian communities, to whom he commits and
recommends his writings;――as he writes “to the
fathers――because they know him who was from the
beginning,”――in the same way “to the young men, because they
are constant, and the Word of God dwells in them,” and “that the
doctrine they have received may remain unchangeable in them,” and
“on account of those who would seduce them.” He recapitulates
all the leading doctrines of his gospel,――the Messiahship, and the
Divinity of Jesus,――his Unity, and identity with the divine
abstractions of the Gnostic theology. Here too, he inculcates and
renewedly urges the great feeling of Christian brotherly love, which
so decidedly characterizes the discourses of Jesus, as reported in
his gospel. So perfect was the connection of origin and design,
between the gospel and this accompanying letter, that they were
anciently placed together, the epistle immediately following the
gospel; as is indubitably proved by certain marks in ancient
manuscripts.

It was mentioned, in connection with a former part of John’s life, that this epistle is
quoted by Augustin and others, under the title of the epistle to the Parthians. It seems very
probable that this may have been also addressed to those churches in the east, about
Babylon, which had certainly suffered much under the attacks of these same mystical
heretics. It is explained, however, by some, that this was an accidental corruption in the
copying of the Greek.――The second epistle was quoted by Clemens Alexandrinus, under
the title of “the epistle to the virgins,” προς παρθενους, which, as some of the modern critics
say, must have been accidentally changed to παρθους, by dropping some of the syllables,
and afterwards transferred to the first (!) as more appropriate;――a perfectly unauthorized
conjecture, and directly in the face of all rules of criticism.

the second and third epistles.

These are both evidently private letters from John to two of his
intimate personal friends, of whose circumstances nothing whatever
being known, except what is therein contained, the notice of these
brief writings must necessarily be brief also. They are both honorably
referred to, as entertainers of the servants of Jesus Christ as they
travel from place to place, and seem to have been residents in some
of the Asian cities within John’s apostolic circuit, and probably
received him kindly and reverently into their houses on his tours of
duty; and them he was about to visit again shortly. The second
epistle is directed to a Christian female, who, being designated by
the very honorable title of “lady,” was evidently a person of rank; and
from the remark towards the conclusion, about the proper objects of
her hospitality, it is plain that she must have been also a person of
some property. Mention is made of her children as also objects of
warm affection to the aged apostle; and as no other member of her
family is noticed, it is reasonable to conclude that she was a widow.
The contents of this short letter are a mere transcript, almost
verbatim, of some important points in the first, inculcating Christian
love, and watchfulness against deceivers;――(no doubt the
Gnostical heretics,――the Cerinthians and Nicolaitans.) He
apologizes for the shortness of the letter, by saying that he hopes
shortly to visit her; and ends by communicating the affectionate
greetings of her sister’s children, then residents in Ephesus, or
whatever city was then the home of John. The third epistle is
directed to Gaius, (that is, Caius, a Roman name,) whose hospitality
is commemorated with great particularity and gratitude in behalf of
Christian strangers, probably preachers, traveling in his region.
Another person, named Diotrephes, (a Greek by name, and probably
one of the partizans of Cerinthus,) is mentioned as maintaining a
very different character, who, so far from receiving the ministers of
the gospel sent by the apostle, had even excluded from Christian
fellowship those who did exercise this hospitality to the messengers
of the apostle. John speaks threateningly of him, and closes with the
same apology for the shortness of the letter, as in the former. There
are several persons, named Gaius, or Caius, mentioned in apostolic
history; but there is no reason to suppose that any of them was
identified with this man.

For these lucid views of the objects of all these epistles, I am mainly indebted to Hug’s
Introduction, to whom belongs the merit of expressing them in this distinctness, though
others before him have not been far from apprehending their simple force. Michaelis, for
instance, is very satisfactory, and much more full on some points. In respect to the place
whence they were written, Hug appears to be wholly in the wrong, in referring them to
Patmos, just before John’s return. Not the least glimmer of a reason appears, why all the
writings of John should be huddled together in his exile. I can make nothing whatever of the
learned commentator’s reason about the deficiency of “pen, ink and paper,” (mentioned in
Epistle ii. 12, and iii. 13.) as showing that John must still have been in “that miserable
place,” Patmos. The idea seems to require a great perversion of simple words, which do not
seem to be capable of any other sense than that adopted in the above account.

the traditions of his life in ephesus.

To this period of his life, are referred those stories of his miracles
and actions, with which the ancient fictitious apostolic narratives are
so crowded,――John being the subject of more ancient traditions
than any other apostle. Some of those are so respectable and
reasonable in their character, as to deserve a place here, although
none of them are of such antiquity as to deserve any confidence, on
points where fiction has often been so busy. The first which follows,
is altogether the most ancient of all apostolic stories, which are not in
the New Testament; and even if it is a work of fiction, it has such
merits as a mere tale, that it would be injustice to the readers of this
book, not to give them the whole story, from the most ancient and
best authorized record.

It is related that John, after returning from banishment, was often

called to the neighboring churches to organize them, or to heal
divisions, and to ordain elders. On one occasion, after ordaining a
bishop, he committed to his particular care and instruction a fine
young man, whom he saw in the congregation, charging the bishop,
before the whole church, to be faithful to him. The bishop accordingly
took the young man into his house, watched over him, and instructed
him, and at length baptized him. After this, viewing the young man as
a confirmed Christian, the bishop relaxed his watchfulness, and
allowed the youth greater liberties. He soon got into bad company, in
which his talents made him conspicuous, and proceeding from one
step to another, he finally became the leader of a band of robbers. In
this state of things, John came to visit the church, and presently
called upon the bishop to bring forward his charge. The bishop
replied that he was dead,――dead to God;――and was now in the
mountains, a captain of banditti. John ordered a horse to be brought
immediately to the church door, and a guide to attend him; and
mounting, he rode full speed in search of the gang. He soon fell in
with some of them, who seized him, to be carried to their head
quarters. John told them that this was just what he wanted, for he
came on purpose to see their captain. As they drew near, the captain
stood ready to receive them; but on seeing John, he drew back, and
began to make off. John pursued with all the speed his aged limbs
would permit, crying out, “My son, why do you run from your own
father, who is unarmed and aged? Pity me, my son, and do not fear.
There is yet hope of your life. I will intercede for you; and, if
necessary, will cheerfully suffer death for you, as the Lord did for us.
Stop,――believe what I say; Christ hath sent me.” The young man
stopped, looked on the ground, and then throwing down his arms,
came trembling, and with sobs and tears, begged for pardon. The
apostle assured him of the forgiveness of Christ; and conducting him
back to the church, there fasted and prayed with him, and at length
procured his absolution.

Another story, far less probable, is related in the ancient

martyrologies, and by the counterfeit Abdias. Craton, a philosopher,
to make a display of contempt for riches, had persuaded two wealthy
young men, his followers, to invest all their property in two very
costly pearls; and then, in the presence of a multitude, to break
them, and pound them to dust. John happening to pass by, at the
close of the transaction, censured this destruction of property, which
might better have been given in alms to the poor. Craton told him, if
he thought so, he might miraculously restore the dust to solid pearls
again, and have them for charitable purposes. The apostle gathered
up the particles, and holding them in his hand, prayed fervently, that
they might become solid pearls, and when the people said “Amen,” it
took place. By this miracle, Craton, and all his followers, were
converted to Christianity; and the two young men took back the
pearls, sold them, and then distributed the avails in charity.
Influenced by this example, two other young men of distinction,
Atticus and Eugenius, sold their estates, and distributed the avails
among the poor. For a time, they followed the apostle, and
possessed the power of working miracles. But, one day, being at
Pergamus, and seeing some well-dressed young men, glittering in
their costly array, they began to regret that they had sold all their
property, and deprived themselves of the means of making a figure
in the world. John read in their countenances and behavior the state
of their minds; and after drawing from them an avowal of their regret,
he bid them bring him each a bundle of straight rods, and a parcel of
smooth stones from the sea shore. They did so,――and the apostle,
after converting the rods into gold, and the stones into pearls, bid
them take them, and sell them, and redeem their alienated estates, if
they chose. At the same time, he plainly warned them, that the
consequence would be the eternal loss of their souls. While he
continued his long and pungent discourse, a funeral procession
came along. John now prayed, and raised the dead man to life. The
resuscitated person began to describe the invisible world, and so
graphically painted to Atticus and Eugenius the greatness of their
loss, that they were melted into contrition. The apostle ordered them
to do penance thirty days,――till the golden rods should become
wood, and the pearls become stones. They did so, and were
afterwards very distinguished saints.

Another story, of about equal merit, is told by the same authority.

While John continued his successful ministry at Ephesus, the
idolaters there, in a tumult, dragged him to the temple of Diana, and
insisted on his sacrificing to the idol. He warned all to come out of
the temple, and then, by prayer, caused it to fall to the ground, and
become a heap of ruins. Then, addressing the pagans on the spot,
he converted twelve thousand of them in one day. But Aristodemus,
the pagan high priest, could not be convinced, till John had drunken
poison without harm, by which two malefactors were killed instantly,
and also raised the malefactors to life. This resuscitation he
rendered the more convincing to Aristodemus, by making him the
instrument of it. The apostle pulled off his tunic, and gave it to
Aristodemus. “And what is this for?” said the high priest. “To cure you
of your infidelity,” was the reply. “But how is your tunic to cure me of
infidelity?” “Go,” said the apostle, “and spread it upon the dead
bodies, and say: ‘The apostle of our Lord Jesus Christ hath sent me
to resuscitate you, in his name, that all may know, that life and death
are the servants of Jesus Christ, my Lord.’” By this miracle the high
priest was fully convinced; and afterwards convinced the proconsul.
Both of them were baptized,――and persecution, from that time,
ceased. They also built the church dedicated to St. John, at
Ephesus.

For this series of fables I am indebted again to the kindness of Dr. Murdock, in whose
manuscript lectures they are so well translated from the original romances, as to make it
unnecessary for me to repeat the labor of making a new version from the Latin. The sight of
the results of abler efforts directly before me, offers a temptation to exonerate myself from a
tedious and unsatisfactory effort, which is too great to be resisted, while researches into
historical truth have a much more urgent claim for time and exertion.

The only one of all these fables that occurs in the writings of the Fathers, is the first,
which may be pronounced a tolerably respectable and ancient story. It is narrated by
Clemens Alexandrinus, (about A. D. 200.) The story is copied from Clemens Alexandrinus
by Eusebius, from whom we receive it, the original work of Clemens being now lost.
Chrysostom also gives an abridgement of the tale. (I. Paraenes ad Theodosius) Anastasius
Sinaita, Simeon Metaphrastes, Nicephorus Callistus, the Pseudo-Abdias, and the whole
herd of monkish liars, give the story almost verbatim from Clemens; for it is so full in his
account as to need no embellishment to make it a good story. Indeed its completeness in all
these interesting details, is one of the most suspicious circumstances about it; in short, it is
almost too good a story to be true. Those who wish to see all the evidence for and against
its authenticity, may find it thoroughly examined in Lampe’s Prolegomena to a Johannine
Theology (I. v. 4‒10.) It is, on the whole, the best authorized of all the stories about the
apostles, which are given by the Fathers, and may reasonably be considered to have been
true in the essential parts, though the minute details of the conversations, &c., are probably
embellishments worked in by Clemens Alexandrinus, or his informants.

The rest of these stories are, most unquestionably, all unmitigated falsehoods; nor does
any body pretend to find the slightest authority for a solitary particular of them. They are
found no where but in the novels of the Pseudo-Abdias, and the martyrologies. (Abdiae
Babyloniae episcopi et Apostolorum discipuli de Historia, lib. V., St. John.)

his death.

Respecting the close of his life, all antiquity is agreed that it was
not terminated by martyrdom, nor by any violent death whatever, but
by a calm and peaceful departure in the course of nature, at a very
great age. The precise number of years to which he attained can not
be known, because no writer who lived within five hundred years of
his time has pretended to specify his exact age. It is merely
mentioned on very respectable ancient authority, that he survived to
the beginning of the reign of Trajan. This noblest of the successors
of Julius, began his splendid reign in A. D. 98, according to the most
approved chronology; so that if John did not outlive even the first
year of Trajan, his death is brought very near the close of the first
century; and from what has been reasonably conjectured about his
age, compared with that of his Lord, it may be supposed that he
attained upwards of eighty years,――a supposition which agrees
well enough with the statement of some of the Fathers, that he died
worn out with old age.

Jerome has a great deal to say also, about the age of John at the time when he was
called, arguing that he must have been a mere boy at the time, because tradition asserts
that he lived till the reign of Trajan. Lampe very justly objects, however, that this proof
amounts to nothing, if we accept another common tradition, that he lived to the age of 100
years; which, if we count back a century from the reign of Trajan, would require him to have
attained mature age at the time of the call. Neither tradition however, is worth much. Our old
friend Baronius, too, comes in to enlighten the investigation of John’s age, by what he
considers indubitable evidence. He says that John was in his twenty-second year when he
was called, and passing three years with Christ, must have been twenty-five years old at the
time of the crucifixion; “because,” says the sagacious Baronius, “he was then initiated into
the priesthood.” An assertion which Lampe with indignant surprise stigmatizes as showing
“remarkable boldness,” (insignis audacia,) because it contains two very gross
errors,――first in pretending that John was ever made a priest, (sacerdos,) and secondly in
confounding the age required of the Levites with that of the priests when initiated. For
Baronius’s argument resting wholly on the very strange and unfounded notion, that John
was made a priest, is furthermore supported on the idea that the prescribed age for entering
the priesthood was twenty-five years; but in reality, the age thus required was thirty years,
so that if the other part of this idle story was true, this would be enough to overthrow the
conclusion. Lampe also alludes to the absurd idea of the painters, in representing John as a
young man, even while writing his gospel; while in reality all writers agree that that work was
written by him in his old age. This idea of his perpetual youth, once led into a blunder some
foolish Benedictine monks, who found in Constantinople an antique agate intaglio,
representing a young man with a cornucopia, and an eagle, and with a figure of victory
placing a crown on his head. This struck their monkish fancies at once, as an
unquestionable portrait of John, sent to their hands by a miraculous preservation.
Examination however, has shown it to be a representation of the apotheosis of Germanicus.

But even here, the monkish inventors have found room for new
fables; and though the great weight of all ancient testimony deprives
them of the opportunity to enter into the horrible details of a bloody
and agonizing death, they can not refuse themselves the pleasure of
some tedious absurdities, about the manner of his death and burial,
which are barely worth a partial sketch, to show how determined the
apostolic novelists are to follow their heroes to the very last, with the
glories of a fancifully miraculous departure.

The circumstances of his death are described in the

martyrologies, and by Abdias, in this manner. He had a vision
acquainting him with his approaching exit, five days before it
happened. On a Lord’s-day morning, he went to the great church at
Ephesus, bearing his name, and there performed public worship as
usual, at day-break. About the middle of the forenoon, he ordered a
deacon, and some grave diggers, with their tools, to accompany him
to the burying ground. He then set them to digging his grave, while
he, after ordering the multitude to depart, spent the time in prayer.
He once looked into the grave, and bid them dig it deeper. When it
was finished, he took off his outer garment, and spread it in the
grave. Then, standing over it, he made a speech to those present,
(which is not worth repeating,) then gave thanks to God for the
arrival of the time of his release,――and placing himself in the grave,
and wrapping himself up, he instantly expired. The grave was filled
up; and afterwards miracles took place at it, and a kind of manna
issued from it, which possessed great virtues.

There is no need, however, of such fables, to crown with the false

honors of a vain prodigy, the calmly glorious end of the “Last of the
Apostles.” It is enough for the Christian to know, that, with the long,
bright course of almost a century behind him, and with the mighty
works of his later years around him, John closed the solemn
apostolic drama, bearing with him in his late departure the last light
of inspiration, and the last personal “testimony of Jesus, which is the
spirit of prophecy.” Blessed in his works thus following him, he died
in the Lord, and now rests from his labors on the breast of that loved
friend, who cherished so tenderly the youthful Son of
Thunder;――on the bosom of his Redeemer and his Lord,――
“The bosom of his Father and his God.”
 PHILIP.
In all the three gospel lists, this apostle is placed fifth in order, the
variations in the arrangements of the preceding making no difference
in his position. In the first chapter of Acts, however, a different
arrangement is made of his name, as will be hereafter mentioned.
The mere mention of his name on the list, is all the notice taken of
him by either of the three first evangelists, and it is only in the gospel
of John, that the slightest additional circumstance can be learned
about him. From this authority it is ascertained that he was of
Bethsaida, the city of Andrew and Peter, and probably also the home
or frequent visiting-place of the sons of Zebedee, by the younger of
whom he is so particularly commemorated. Immediately after the
narration of the introduction of Andrew, John and Peter, to Jesus, in
the first chapter of this gospel, it is said that Jesus next proceeded
from Bethabara into Galilee, and there finds Philip; but the particular
place is not mentioned, though Bethsaida being immediately after
mentioned as his home, very probably was the place of the meeting.
Andrew and Peter, on their return home, had doubtless had no small
talk among their acquaintances, about the wonderful person
announced as the Messiah, to whom they had been introduced, and
had thus satisfied themselves that he was really the divine character
he was said to be. Philip too, must have heard of him in this way,
before he saw him; so that when Jesus met him, he was prepared at
once to receive the call which Jesus immediately gave
him,――“Follow me.” From the circumstance that he was the first
person who was summoned by Jesus, in this particular formula of
invitation to the discipleship, some writers have, not without reason,
claimed for Philip the name and honors of the Protoclete, or “first-
called;” though Andrew has commonly been considered as best
entitled to this dignity, from his being the first mentioned by name, as
actually becoming acquainted with Jesus. Philip was so devoutly
engaged, at once, in the cause of his new Master, that he, like
Andrew, immediately sought out others to share the blessings of the
discipleship; and soon after meeting one of his friends, Nathanael,
he expressed the ardor of his faith in his new teacher, by the words
in which he invited him to join in this honorable fellowship,――“We
have found him of whom Moses, in the law, and all the prophets did
write,――Jesus of Nazareth, the son of Joseph.” The result of this
application will be related in the life of the person most immediately
concerned. After this, no notice whatever is taken of Philip except
where incidental remarks made by him in the conversations of
Jesus, are recorded by John. Thus, at the feeding of the five
thousand, upon Jesus’s asking whether they had the means of
procuring food for the multitude, Philip answered, that “two hundred
pence would not buy enough for them, that every one might take a
little,”――thus showing himself not at all prepared by his previous
faith in Jesus, for the great miracle which was about to happen;
though Jesus had asked the question, as John says, with the actual
design of trying the extent of his confidence in him. He is afterwards
mentioned in the last conversations of Jesus, as saying to him,
“Show us the Father, and it sufficeth us,”――here too, betraying also
a most unfortunate deficiency, both of faith and knowledge, and
implying also a vain desire to gratify his eyes with still more
miraculous displays of the divine power of his Master; though, even
in this respect, he probably was no worse off than all the rest of the
disciples, before the resurrection of Jesus.

Protoclete.――Hammond claims this peculiar honor for Philip, with great zeal. (See
his notes on John i. 43.)

Of his apostleship not one word is recorded in the New Testament,

for he is no where mentioned in the Acts, except as being one of the
apostles assembled in the upper chamber after the ascension; nor
do the epistles contain the slightest allusion to him. Some of the
most ancient authorities among the Fathers, however, are distinct in
their mention of some circumstances of his later life; but all these
accounts are involved in total discredit, by the fact that they make
him identical with Philip the deacon, whose active and zealous
labors in Samaria, and along the coast of Palestine, from Gaza,
through Ashdod to Caesarea, his home, are minutely related in the
Acts, and have been already alluded to, in that part of the life of
Peter which is connected with these incidents. It has always been
supposed, with much reason, in modern times, that the offices of an
apostle and a deacon were so totally distinct and different, that they
could never both be borne by one and the same person; but the
Fathers, even the very ancient ones, seem to have had not the
slightest idea of any such incompatibility; and therefore uniformly
speak of Philip the apostle, as the same person with Philip, one of
the seven deacons, who is mentioned by Luke, in the Acts of the
Apostles, as having lived at Caesarea, in Palestine, with his
daughters, who were virgins and prophetesses. Testimony more
distinct than this, can no where be found, among all the Fathers, on
any point whatever; and very little that is more ancient. Yet how does
it accord with the notions of those who revere these very Fathers as
almost immaculate in truth, and in all intellectual, as well as moral
excellence? What is the evidence of these boasted Fathers worth,
on any point in controversy about apostolic church government, or
doctrine, or criticism, if the modern notion of the incompatibility of the
two offices of apostle and deacon is correct?

The testimony of the Fathers on this point, is simply this. Eusebius (Church History, III.
31,) quotes Polycrates, bishop of Ephesus, who, in his letter to Victor, bishop of Rome,
(written A. D. 195, or 196,) makes mention of Philip in these exact words: “Philip, who was
one of the twelve apostles, died in Hierapolis;” (in Phrygia;) “and so did two of his
daughters, who had grown old in virginity. And another of his daughters, after having
passed her life under the influence of the Holy Spirit, was buried at Ephesus.” This certainly
is a most perfect identification of Philip the apostle with Philip the deacon; for it is this latter
person who is particularly mentioned in Acts, xxi. 8, 9, as “having four daughters who did
prophesy.” He is there especially designated as “Philip the evangelist, one of the seven,”
while Polycrates expressly declares, that this same person “was one of the twelve.”
Eusebius also, in the preceding chapter, quotes Clemens Alexandrinus as mentioning Philip
among those apostles who were married, because he is mentioned as having had
daughters; and Clemens even adds that these were afterwards married, which directly
contradicts the previous statement of Polycrates, that three of them died virgins, in old age.
Yet Eusebius quotes all this stuff, with approbation.
 Papias, (A. D. 140,) bishop of Hierapolis, the very place of the death and burial of Philip,
is represented by Eusebius as having been well acquainted with the daughters of Philip,
mentioned in Acts, as the virgin prophetesses. Papias says that he himself “heard these
ladies say that their father once raised a dead person to life, in their time.” But it deserves
notice, that Papias, the very best authority on this subject, is no where quoted as calling this
Philip “an apostle;” though Eusebius, on his own authority, gives this name to the Philip of
whom Papias speaks. It is therefore reasonable to conclude, that this blunder, betraying
such a want of familiarity with the New Testament history, originated after the time of
Papias, whose intimate acquaintance with Philip’s family would have enabled him to say, at
once, that this was the deacon, and not the apostle; though it is not probable that he was
any less deplorably ignorant of the scriptures than most of the Fathers were.

Now what can be said of the testimony of the Fathers on points where they can not refer,
either to their own personal observation, or to informants who have seen and heard what
they testify? The only way in which they can be shielded from the reproach of a gross
blunder and a disgraceful ignorance of the New Testament, is, that they were right in
identifying these two Philips, and that modern theologians are wrong in making the
distinction. On this dilemma I will not pretend to decide; for though so little reverence for the
judgment and information of the Fathers has been shown in this book, there does seem to
me to be some reason for hesitation on this point, where the Fathers ought to have been as
well informed as any body. They must have known surely, whether, according to the notions
of those primitive ages of Christianity, there was any incompatibility between the apostleship
and the deaconship! If their testimony is worth anything on such points, it ought to weigh so
much on this, as to cause a doubt whether they are not right, and the moderns wrong.
However, barely suggesting this query, without attempting a decision, as Luther says, “I will
afford to other and higher spirits, occasion to reflect.”

This is all the satisfaction that the brief records of the inspired or
uninspired historians of Christianity can give the inquirer, on the life
of this apostle;――so unequal were the labors of the first ministers of
Christ, and their claims for notice. Philip, no doubt, served the
purpose for which he was called, faithfully; but in these brief
sketches, there are no traces of any genius of a high character, that
could distinguish him above the thousands that are forgotten, but
whose labors, like those of the minutest animals in a mole-hill,
contribute an indispensable portion to the completion of the mass, in
whose mighty structure all their individual efforts are swallowed up
forever.

And though the ancient Polycrates may have blundered

grievously, in respect to the apostle’s personal identity, his hope of
the glorious resurrection of those whom he supposed to have died in
Asia will doubtless be equally well rewarded, if, to the amazement of
the Fathers, the apostle Philip should rise at last from the dust of
Babylon, or the ashes of Jerusalem, while his namesake, the
evangelist, shall burst from his tomb in Hierapolis. “For,” as
Polycrates truly says, “in Asia, some great lights have gone down,
which shall rise again on that day of the Lord’s approach, when he
shall come from the heavens in glory, and shall raise up all his
saints;――Philip, one of the twelve apostles, who sleeps at
Hierapolis, with his venerable virgin daughters,――John, who lay in
the bosom of the Lord, and who is laid at Ephesus,――Polycarp, at
Smyrna,――Thraseas, at Eumenia,――Sagaris, at
Laodicea,――Papirius and Melito, at Sardis――all await the
visitation of the Lord from the heavens, in which he shall raise them
from the dead.”

NATHANAEL, BAR-THOLOMEW.
his name and call.

In respect to this apostle, there occurs a primary question about

his name, which is given so differently in different sacred authorities,
as to induce a strong suspicion that the two names refer to two
totally distinct persons. The reasons for applying the two words,
Nathanael and Bartholomew, to the same person, are the
circumstances,――that none of the three first evangelists mention
any person named Nathanael, and that John never mentions the
name Bartholomew,――that Bartholomew and Nathanael are each
mentioned on these different authorities, among the chosen disciples
of Jesus,――that Bartholomew is mentioned by the three first
evangelists, on all the lists, directly after Philip, who is by John
represented as his intimate friend,――and that Bartholomew is not
an individual name, but a word showing parentage merely,――the
first syllable being often prefixed to Syriac names, for this purpose;
and Bar-Tholomew means the “son of Tholomew,” or “Tholomai;” just
as Bar-Jonah means the “son of Jonah;” nor was the former any
more in reality the personal, individual name of Nathanael, than the
latter was of Peter; but some circumstance may have occurred to
make it, in this instance, often take the place of the true individual
name.

A few very brief notices are given of this apostle by John, who
alone alludes to him, otherwise than by a bare mention on the list. It
is mentioned in his gospel that Nathanael was of Cana, in Galilee, a
town which stood about half-way between lake Gennesaret and the
Mediterranean sea; but the circumstances of his call seem to show
that he was then with Philip, probably at or near Bethsaida. Philip,
after being summoned by Jesus to the discipleship, immediately
sought to bring his friend Nathanael into an enjoyment of the honors
of a personal intercourse with Jesus, and invited him to become a
follower of the Messiah, foretold by Moses and the prophets, who
had now appeared, as Jesus of Nazareth, the son of Joseph. On
hearing of that mean place, as the home of the promised King of
Israel, Nathanael, with great scorn, replied, in inquiry, “Can any good
thing come out of Nazareth?” To this sneering question, Philip
answered by the simple proposition, “Come and see;”――wisely
judging that no argument could answer his friend’s prejudice so well
as an actual observation of the character and aspect of the
Nazarene himself. Nathanael, accordingly, persuaded by the
earnestness of his friend, came along with him, perhaps, partly to
gratify him, but, no doubt, with his curiosity somewhat moved to
know what could have thus brought Philip into this devout regard for
a citizen of that dirty little town; and he therefore readily
accompanied him to see what sort of prophet could come out of
Nazareth.

The words with which Jesus greeted Nathanael, even before he

had been personally introduced, or was prepared for any salutation,
are the most exalted testimonial of his character that could be
conceived, and show at once his very eminent qualifications for the
high honors of the apostleship. When Jesus saw Nathanael coming
to him, he said, “Behold a true son of Israel, in whom is no
guile!”――manifesting at once a confidential and intimate knowledge
of his whole character, in thus pronouncing with such ready decision,
this high and uncommon tribute of praise upon him, as soon as he
appeared before him. Nathanael, quite surprised at this remarkable
compliment from one whom he had never seen until that moment,
and whom he supposed to be equally ignorant of him, replied with
the inquiry, “Whence knowest thou me?” Jesus answered, “Before
Philip called thee, when thou wast under the fig-tree, I saw thee.”
The fig-trees of Palestine, presenting a wide, leafy cover, and a
delightful shade, were often used in the warm season as places of
retirement, either in company, for conversation, or in solitude, for
meditation and prayer, as is shown in numerous passages of the
Rabbinical writings; and it was, doubtless, in one of these
occupations that Nathanael was engaged, removed, as he
supposed, from all observation, at the time to which Jesus referred.
But the eye that could pierce the stormy shades of night on the
boisterous waves of Galilee, and that could search the hearts of all
men, could also penetrate the thick, leafy veil of the fig-tree, and
observe the most secret actions of this guileless Israelite, when he
supposed the whole world to be shut out, and gave himself to the
undisguised enjoyment of his thoughts, feelings, and actions, without
restraint. Nathanael, struck with sudden but absolute conviction, at
this amazing display of knowledge, gave up all his proud scruples
against the despised Nazarene, and adoringly exclaimed, “Rabbi!
thou art the Son of God,――thou art the King of Israel.” Jesus,
recognizing with pleasure the ready faith of this pure-minded
disciple, replied, “Because I said unto thee, ‘I saw thee under the fig-
tree,’――believest thou? Thou shalt see yet greater things than
these.” Then turning to Philip as well as to Nathanael, he says to
them both, “I solemnly assure you, hereafter ye shall see heaven
open, and the angels of God ascending and descending upon the
Son of Man.”

On the day but one after this occurrence, as John records, Jesus
was in Cana of Galilee, the residence of Nathanael, and was present
at a wedding which took place there. From the circumstance that the
mother of Jesus was there also, it would seem likely that it was the
marriage of some of their family friends; otherwise the conjecture
might seem allowable, that the presence of Jesus and his disciples
on this occasion, was in some way connected with the introduction of
Nathanael to Jesus; and that this new disciple may have been some
way concerned in this interesting event. The manner in which the
occurrence is announced,――it being next specified, that two days
after the occurrences recorded in the end of the first chapter, Jesus
was present at a marriage in Cana of Galilee,――would seem to
imply very fairly, that Jesus had been in some other place
immediately before; and it is probable therefore, that he
accompanied Nathanael home from Bethsaida, or whatever place
was the scene of his calling to the discipleship, along with Philip. The
terms of the statement are not, however, absolutely incompatible
with the idea of this first introduction of these two disciples to Jesus,
in Cana itself, which may have been the part of Galilee into which
Jesus is said to have gone forth, after leaving Bethabara; although,
the reasons above given make it probable that Bethsaida was the
scene. After this first incident, no mention whatever is made of
Nathanael, either under his proper name, or his paternal appellation,
except that when the twelve were sent forth in pairs, he was sent
with his friend Philip, that those who had been summoned to the
work together, might now go forth laboring together in this high
commission. One solitary incident is also commemorated by John, in
which this apostle was concerned, namely, the meeting on the lake
of Gennesaret, after the resurrection, where his name is mentioned
among those who went out on the fishing excursion with Peter. His
friend Philip is not there mentioned, but may have been one of the
“two disciples,” who are included without their names being given.
From this trifling circumstance, some have concluded that Nathanael
was a fisherman by trade, as well as the other four who are
mentioned with him; and certainly the conjecture is reasonable, and
not improbable, except from the circumstance, that his residence
was at Cana, which is commonly understood to have been an inland
town, and too far from the water, for any of its inhabitants to follow