20
2 Boarding School and University
ments of the propagation of light in relation to the motion of the Earth, an
attempt is made to show that ether is the medium in which light propagates.
However, Hoek died in 1873, at the young age of 39.
Because of Hoek’s lack of interest in practical astronomy, Kapteyn could
not have learned much from him. Moreover, he was no longer alive at the
time when Kapteyn was looking for a subject for a PhD thesis. After Hoek’s
death, Buys Ballot had temporarily taken on responsibility for astronomical
education again, but at the time was not interested in supervising a PhD in
astronomy. He has actually supervised only one PhD thesis on an astronomical
subject and that was in 1871 on the determination of the orbit of an asteroid.
Jean Oudemans returned to Utrecht as a professor of astronomy, but that was
in 1875, too late for Kapteyn, who already completed his dissertation in that
year under Grinwis.
2.3 Vibrating Flat Membranes
Kapteyn’s doctoral research was a sequel to that of his brother Willem (see
Fig. 2.5). The latter had, also under the supervision of Grinwis, researched the
theory of vibrating plates. This is the phenomenon, first studied exhaustively
by the German physicist Ernst Florens Friedrich Chladni (1756–1827), that
if you sprinkle a powder on a flat metal plate and then make it vibrate, for
example with the aid of a bow for a violin or so, you get to see a regular pattern.
This pattern shows where ‘nodes’ and ‘antinodes’ are in the vibrations, which
indicate where the vibration is greatest (the antinodes) and where absent (the
nodes). Compare this with a vibrating string: in the middle the vibration is
maximal and the ends of the string are stationary. In the first overtone the
tone is twice as high and the string vibrates like two half strings attached to
each other. Then halfway there is no vibration (a node) and at one and three
quarters the amplitude it is maximum. The theory of how that pattern is
determined by the shape and elastic properties of the plate had already been
studied by great scholars, such as Jacob (II) Bernoulli (1759–1789), JosephLouis Lagrange (1736–1813), Simeon Denis Poisson (1781–1840), Augustin
Louis Cauchy (1789–1857) and Gustav Robert Kirchhoff (1824-1887), but
also by the much less well-known French female mathematician Marie-Sophie
Germain (1776–1831).
Willem had not done much more than discuss the work of earlier researchers;
he concluded that Germain had started with a wrong assumption, but had
nevertheless derived the correct equation. He also discussed the experiments
2 Boarding School and University
ments of the propagation of light in relation to the motion of the Earth, an
attempt is made to show that ether is the medium in which light propagates.
However, Hoek died in 1873, at the young age of 39.
Because of Hoek’s lack of interest in practical astronomy, Kapteyn could
not have learned much from him. Moreover, he was no longer alive at the
time when Kapteyn was looking for a subject for a PhD thesis. After Hoek’s
death, Buys Ballot had temporarily taken on responsibility for astronomical
education again, but at the time was not interested in supervising a PhD in
astronomy. He has actually supervised only one PhD thesis on an astronomical
subject and that was in 1871 on the determination of the orbit of an asteroid.
Jean Oudemans returned to Utrecht as a professor of astronomy, but that was
in 1875, too late for Kapteyn, who already completed his dissertation in that
year under Grinwis.
2.3 Vibrating Flat Membranes
Kapteyn’s doctoral research was a sequel to that of his brother Willem (see
Fig. 2.5). The latter had, also under the supervision of Grinwis, researched the
theory of vibrating plates. This is the phenomenon, first studied exhaustively
by the German physicist Ernst Florens Friedrich Chladni (1756–1827), that
if you sprinkle a powder on a flat metal plate and then make it vibrate, for
example with the aid of a bow for a violin or so, you get to see a regular pattern.
This pattern shows where ‘nodes’ and ‘antinodes’ are in the vibrations, which
indicate where the vibration is greatest (the antinodes) and where absent (the
nodes). Compare this with a vibrating string: in the middle the vibration is
maximal and the ends of the string are stationary. In the first overtone the
tone is twice as high and the string vibrates like two half strings attached to
each other. Then halfway there is no vibration (a node) and at one and three
quarters the amplitude it is maximum. The theory of how that pattern is
determined by the shape and elastic properties of the plate had already been
studied by great scholars, such as Jacob (II) Bernoulli (1759–1789), JosephLouis Lagrange (1736–1813), Simeon Denis Poisson (1781–1840), Augustin
Louis Cauchy (1789–1857) and Gustav Robert Kirchhoff (1824-1887), but
also by the much less well-known French female mathematician Marie-Sophie
Germain (1776–1831).
Willem had not done much more than discuss the work of earlier researchers;
he concluded that Germain had started with a wrong assumption, but had
nevertheless derived the correct equation. He also discussed the experiments