++ ROYAL SOCIETY OF CANADA 
the parts which are vibrating from the parts which are in repose, by 
means of the sand which is driven from the former to collect on the 
latter. In these experiments of Chladni on plates, etc., the violin bow 
was used for the first time to produce the necessary vibrations. The 
bow had previously been used only for vibrating cords, the “ violon de 
fer”, and other musical instruments. Chladni made his discovery of 
sand figures in 1787, having been led thereto by Lichtenberg’s dis- 
covery of electric figures. 
The transversal nodal lines given by Chladni’s method in the case 
of rods vibrating longitudinally were readily explained. Not so, how- 
ever, the complicated nodal lines presented by vibrating plates, or the 
alternate lines which appear on the two sides of rods vibrating longi- 
tudinally, and which sometimes also appear on rods vibrating trans- 
versally. It was not until 1833 that an explanation of the former of 
these phenomena was offered by Wheatstone’s theory that the nodal 
lines were due to.the superposition of transversal vibrations, corre- 
sponding to sounds of the same pitch coexisting with respect to differ- 
ent directions in the plate. This theory was .confirmed experimentally 
in 1864 by Rudolph Keenig who constructed rectangular plates giving 
unison notes corresponding to different sets of nodal lines parallel to 
two adjacent sides of the plate. The theoretical figure results when 
the plate is vibrated so as to produce the coexisting unison notes. 
The alternate nodal lines given by vibrating rods were also ex- 
plained by the theory of the coexistence of two sounds near unison in 
the same vibrating rod. In this case, however, one sound corresponds 
to longitudinal and the other to transversal vibrations. This explana- — 
tion was first given by August Seebeck in 1849, whose theory was 
confirmed in 1859.by Terquem in a very important paper “Sur les 
vibrations longitudinales des verges libres aux deux extrémités.” . 
The Graphical Method.—In 1807, five years after the publication of M 
Chladni’s “Akustik,” appeared Dr. Thomas Young’s “Course of Lec- 
tures on Natural Philosophy and the Mechanical Arts,” in which we 
find the earliest description of the graphical method, including its. ap- 
plication to chronography. This description is as follows: 
“By means of this instrument we may measure, without dif- 
ficulty, the frequency of the vibrations of sounding bodies, by connect- 
ing them with a point which will describe an undulated path on the 
roller. These vibrations may also serve in a very simple manner for 
the measurement of the minutest intervals of time; for if a body, Of 
which ‘the vibrations are of a certain degree of trequency, be caused 
to vibrate during the revolution of an axis, and to mark its vibrations 
on a roller, the traces will serve as a correct index of the time occu- 
pied by any part of a revolution, and the motion of any other body 

