Polytechnic Association Proceedings. 775 



assists the vocalist in determining their harmonic relations. This 

 slight refoi-m only carries out what seems to have been the original 

 intention of the earl}-- masters. The Greeks applied to their tetra- 

 chords the syllables Ta, Te, The, The. Although their system 

 was early supplanted by the septave, no improvement in solmiza- 

 tion was made until, in the eleventh century, Guido Aretino desig- 

 nated the first six sounds by diflerent syllables. He was led to 

 heir use by noticing a marked relation between the ascending 

 sounds given to the first syllables of the following hymn to St. 



John: 



Ut queant laxis, 

 , Resonare flbris, 

 Mira gestorum, 

 Famuli tuorura, 

 Solve polluti, 

 Labii reatum, 

 Sancte Johannes. 



Regarding this discovery as a special revelation to him, he did 

 not venture to complete the scale, which w^as done long after his 

 time by adding si. The consonant ending of two of these syllables^ 

 was not favorable to prolonged vocal sound. Ut was afterwai-d 

 replaced by do. The I in sol, when followed by la did not seem 

 BO objectionable, and sol has held its place among syllables which 

 have been used in solmization for eight hundred years. GXiido's 

 scale commenced on G, and was sometimes designated by the 

 Greek name. Gamma, also by ut, from whence arose GammuC; thus 

 the discarded ut has found a permanent place in the name of the 

 scale. The change I propose is the substitution of To for do, and 

 of do for sol; thus To will always be found on the Tonic; mt on 

 the Mediant; and do on the Dominant; and To-mi-do will express 

 the common chord now known as the Jit'st, third, and Jifth. All 

 chords may be indicated by a combination of solfeggio syllables, 

 and numbers only used to designate the twelve grades of the spiral 

 which represent the twelve intervals of the tempered system. 



in. ON A NEW FORM OF WAVE APPARATUS. 

 By C. S. Lyman, of New Haven, Conn. 



The elass of waves which this piece of mechanism was designed 

 to Illustrate, is that whose type is the ordinary ocean wave in deep 

 water. The apparatus exhibits not only the wave profile with its 

 progressive motion, but also the motions taking place below the 

 surface, in the whole mass of liquid afiiected. Since the motions- 



