14 REPORT—1868. 
sliding weight. But an alteration in the angle of the bent wire yields a more 
satisfactory result. When the wires are parallel and even in length, a combination 
of 1 to 1 is obtained, and the bead describes a circle passing into an oblique line ; 
but on opening the free limb to an angle of about 30°, the figure changes into 
the complex curve given by the ratio of 4 to 5. Opening the angle still further, 
the curve expressing the ratio of 3 to 4 is obtained; then at 45° 2 to 3; and at 
an angle of 75° the figure of eight comes out, expressing the ratio of 1 to 2. 
In fact, by varying the angle an entire series of combinations, more or less pertect, 
can be produced at will. 
Figure 1 shows the instrument. The wire is capable of being firmly fixed at 
any height in a support which is attached to a heavy stand, more convenient in 
use than a vice. 
Not only may this arrangment be used for exhibiting the combination of vibra- 
tions, but it also shows very prettily the formation of nodes and ventral segments. 
On the free arm an instructive change is seen to take place in the position 
of a node which is there formed. When the arms are equal and parallel, and a 
yatio of 1 to 1 obtained, the node is near the free extremity of the bent wire; as 
Fig. 1, Fig. 2. 
oe 
fo 
the wire is raised and the angle increases, the node rises nearer to the bend. It is 
also worth observing that, in any combination, the distance of the node from the 
free extremity of the wire, compared with its distance from the bend, is approxi- 
mately the same as the ratio of the interval depicted by the figure. 
Another arrangement for effecting the combination of rectanglar vibrations 
(shown in figure 2) has been adapted by Mr. Ladd from an instrument devised by 
Professor Helmholtz. 
Two flat pieces of steel are here welded at right angles to each other into a 
single rod. The upper part (a, fig. 2) is tapering, and on its summit is fixed a 
polished silver bead. The lower part (b) is capable of being firmly fixed in a sui- 
table support. According to the hgh at which 6 is clamped, so a corresponding 
portion is allowed to enter into vibration. A combination of the vibration of a 
with that of } can thus be obtained in any given ratio. Complete command of any 
figure can be had by marking its position on the lower strip of steel; and so nice 
an adjustment is possible, that an almost absolutely steady figure can be secured 
with a little care. 
The author proposes to call the instrument described in this paper a Tonophant. 
Haar. 
On Sources of Error in determinations of the Absorption of Heat by Liquids. 
By W. Frzrcuer Barrerr*, 
During the autumn of 1865 the author had observed that under certain condi- 
* Published ém eatenso in the Philosophical Magazine for September 1868. 
