28 PHILOSOPHICAL SOCIETY OF WASHINGTON. 
have in any case involved the prime number seven. It would be 
interesting to know what scale best represents the songs of wild 
birds. 
There is much reason to believe that simple mathematical princi- 
ples underlie the phenomena of chemistry. It is not, a priori, 
absurd to suppose that matter in some way conforms to the prop- 
erties of the primes 2, 3, and 5; in which case such derivative 
numbers might be expected prominently to appear as prominently 
: : : ay Silents 
occur in the science of music. The fraction 75 might reasonably 
be expected. 
If all the keys of a piano should be arranged seven consecutive 
keys in a line, the next seven in the next line, and so on, the columns 
give successions of fifths. It has been shown that if the chemical 
elements are arranged in the order of their atomic weights in lines 
of seven, the columns contain elements remarkably similar to each 
other. We seem to have a chemical scale remarkably analogous 
to the ordinary musical scale. If the piano keys be arranged in 
lines of twelve, the columns give octaves; but nothing is devel- 
oped from a similar arrangement of the chemical elements, whence 
it may be inferred that the observed analogies are accidental, and 
have no true logical basis. 
If the intervals of the chemical scale could be supposed to cor- 
respond to the seven intervals of the diatonic scale, the non-appear- 
ance of the twelve-fold relation would be accounted for; but, while 
the diatonic scale may have some claim to be called natural, it is 
not directly established by algebraic investigation of the relations 
of prime numbers. Until the discovery of chemical flats and 
sharps, there will be insufficient reason to regard the present chem- 
ical scale as diatonic. 
Mr. Leravour illustrated the connection between tone and 
wave-length by means of a logarithmic spiral of base 2, the har- 
monic notes having radii vectores equal to multiples of the principal 
note. 
Mr. Exvxriorr said he had learned from Mr. Poole that he had 
endeavored, in his euharmonic organ, to produce perfect chords in 
all keys without temperament. | 
Mr. KumMMELL remarked that in modern music the,intervals of 
the major and minor thirds are the most important, because with- 
