426 Mr. Charles Tomlinsons Expei'iments 



vessel with a handle, as well as on a glass goblet or disk 

 furnished with a damper, where the lower fundamental 

 tone can be produced, and where the upper. Thus, suppose 

 a cylindrical china cup with a handle be chosen. The 

 vessel may be about half filled with coloured water, and 

 the point of the rim exactly opposite to the handle, and at 

 90°, on each side of the handle will yield the lower funda- 

 mental tone, and four fans will be seen upon the surface of 

 the water, the fan which proceeds from the quadrant which 

 contains the handle being smaller in size, and more feeble 

 in action than the other three fans. At the two points 45° 

 on each side of the handle, and at two other points 45° on 

 each side of the point diametrically opposite to the handle, 

 the upper fundamental tone is produced, the handle and the 

 three points, whence the lower fundamental tone was ob- 

 tained, now forming the nodes in the upper fundamental 

 tone, when it will be observed, that the four fans are all 

 equal, because there are four vibrating arcs in action un- 

 impeded by lip or handle ; whereas, with the lower funda- 

 mental tone unimpeded action pertains to three only of the 

 vibrating arcs, the fourth containing the lip or handle. 



With the same vessel two secondary tones of the first 

 kind may be produced. Each one of these divides the 

 vessel into six vibrating sectors. To produce the lower 

 secondary tone, the handle must, as before, be included in 

 a vibrating sector, and from the handle a radius of the 

 circle described by the rim of the cup will divide the peri- 

 phery into six equal parts, so that if one leg of a pair of 

 compasses rest on the point at the handle, and the space 

 between the two legs be equal to a radius, the second leg 

 will extend to a centre of vibration, from which the lower 

 secondary tone can be produced, and so on all round. The 

 upper secondary tone due also to sex-nodal division will be 

 found at the two points situate 30° on each side of the 

 handle, and at four other points from these, the length of 

 a radius being between any two points. 



131. I have employed the term points in order to give a 

 precision to my meaning, but it must not be understood 

 literally, because as a vibrating sector always includes 90° 

 for the fundamental tone in any circular vessel with a lip 

 or a iiandle ; and 60° for the first secondary tone, the bow 



