90 Proceedings of Royal Society of Edinburgh. [sess, 
2 r and r, we see that the breadth and the depth of the impression 
have the same ratio to each other as an abscissa to its ordinate in 
the above-mentioned ellipse. 
It is true that the supposition about the axis of the marker 
does not hold good in using the phonograph, as, in that case, it 
makes a certain angle, a, with the tangent ; but the only difference 
which this point occasions in the results is this, that they would 
have to be multiplied by the constant term cos a to obtain their 
real value, which, of course, is not necessary in the case of sound 
curves. Since the marker is constantly moving up and down on 
account of the vibration of the glass membrane, the value of the 
angle a changes every moment, but these changes are so minute 
(since the greatest depth of the impressions does not exceed 0*02 
mm.) that they may be neglected without any objection. 
Once for all, a list of the depths (d) was calculated by means of 
the formula (2), answering to every transverse diameter b which 
might be expected. 
For this purpose the diameter of the marker was cut out in a 
thin layer of paraffin on a glass plate, and was measured out by 
means of the same ocular micrometer which was to be used for 
measuring the transverse diameter of the impressions on the 
cylinder. The diameter of the recording marker proved to be 
lifty-six divisions of the ocular micrometer, or 1*0318 mm. Gener- 
ally the largest transverse diameter of the impressions did not 
exceed twenty divisions of the micrometer, which corresponds to a 
depth of 1*847 divisions, or 0*017 mm. 
Fig. 2 shows a photograph of the apparatus as I use it now for 
my researches. It is placed, when used, upon a firmly fixed table 
before a window with a northern exposure. The axis of the 
mandrill, G, on which the cylinder of the phonograph, H, is placed, 
carries a drum, P, the outside of which is divided into 360 equal 
parts. By means of a little pointer, W, you can read the divisions 
of the drum. The axis of the mandrill, G, carries also a cogged 
wheel, A, catching a pinion on the axis of a second drum, Q, 
which is equally divided into 360 parts, and may be read by means 
of a pointer, W\ The gearing of wheel and pinion is such that 
every division of the drum, Q, represents q of the circumference 
of the cylinder, H. 
