- 
May 16, 1884.] 
teristic to permit of their being placed specifically. 
The formation represented belongs to the pliocene 
or later miocene, although its exact position is some- 
what uncertain. The tapir had been found in several 
states; and the mastodon was, of course, widely dis- 
tributed; but neither the rhinoceros nor the camel- 
like remains represented in the collection had before 
been found east of the Mississippi. Professor Heil- 
- prin regarded the discovery of importance as lending 
decided support to Professor Hilgard’s views regard- 
ing the former distribution of land in the region of 
the Gulf of Mexico, and the probable connection 
of Florida with Mexico. Similar fossils had, he 
believed, been found in the Mexican plains. The 
bed-rock near Archer, Fla., belongs to the oligocene 
formation. Mr. Joseph Willcox announced that 
he had again found in Florida, specimens of Num- 
mulites Willcoxi Heil., which had been regarded as of 
so much interest when collected by him a year ago. 
The examples now submitted for inspection had 
been obtained about fifteen miles north-east of the 
original locality on Cheeshowiska River, and about a 
hundred and fifty feet above the sea. Professor 
Heilprin commented on the importance of the dis- 
covery of the more elevated region just reported as 
indicating where the nummulitic formation could 
actually beseen. The other specimens were collected 
not more than two feet above tide-water, and were 
not, therefore, absolutely indicative of the position 
of the parent rock. From association with the Or- 
bitolites, we can state that the beds belong to the upper 
oligocene age. The genera Nummulina, Orbitoides, 
Heterostegina, Quinqueloculina, Triloculina, and 
perhaps Biloculina, together with Spirorbulina, were 
represented in the masses cf rock received from 
Mr. Willcox. The remains of fresh-water mollusks 
were associated with them, specimens of microscopic 
Paludina having been determined. This association 
of fresh-water with marine organisms might in- 
dicate the former emptying of a river into the sea, 
or the presence of fresh-water swamps in ancient 
Plorida. The elevation of the locality whence the 
fossils were obtained need not be regarded as com- 
plicating the problem; for it must be remembered 
that this in no way represents the original height of 
the formations. 
Philosophical society, Washington, 
March 29. — Dr. J. S. Billings spoke of the uncer- 
tainty of measurements of cranial capacity. The best 
results, without the division of the skull, are obtained 
by means of shot, which is poured in, and after- 
wards measured; but even these are poor. The 
same observer does not obtain closely approximate 
results from successive measurements of the same 
skull, and different observers obtain widely different 
results. He then exhibited a series of composite 
photographs of skulls, each photograph being derived 
from a series of adult male skulls of onerace. In the 
formation of each negative, the plate was exposed 
successively to from seven to eighteen skulls. —— 
Prof. G. Brown Goode spoke on fisheries exhibitions, 
describing especially the international exhibitions at 
SCIENCE. 
607 
Berlin (1880) and London (1883). Mr. M. H. Doo- 
little began a communication, which was completed 
at the following meeting. 
April 12. — Mr. M. H. Doolittle completed his com- 
munication on music and the chemical elements. 
The mathematical theory of music requires the satis- 
faction of the equation 27 = #¥ nearly, in which, for 
equal temperament, « = the number of equal inter- 
vals in the octave, and y = the number of these in- 
tervals that correspond to a nearly perfect fifth; and, 
for untempered music, «=the number of approxi- 
mately equal intervals in the octave, and y = the 
number corresponding to a perfect fifth. This equa- 
log3 
=e 
the Hehied of continued fractions, we obtain the 
succession of approximations, 2, 74, 74, 24, ete. For 
scales appropriate to major thirds, but disregarding 
fifths, we may substitute { for 3 in the above equa- 
tions, and obtain the approximations, 4, y:, $3, ete. 
For the chord having the vibration ratio T:4 we may 
obtain in like manner the approximations, +, 34, etc. 
The fraction 74, belonging to the first series, is the 
base of the chromatic scale, and, less directly, of the 
diatonic. The fractions # and 4, of the first and third 
series, probably represent all the five-toned scales of 
primitive music. Pentatonic, chromatic, and dia- 
tonic scales. have thus a mathematical basis, and are 
in a proper sense natural. There is reason to believe 
that simple mathematical principles underlie the 
phenomena of chemistry, and that the quantitative 
relations of the elements are expressible in the deriva- 
tives of small prime numbers. There is, therefore, 
no a priori absurdity in looking for a correspondence 
of musical and chemical ratios. If the keys of a piano 
be arranged with seven consecutive keys in a line, 
the next seven in the next line, and so on, the col- 
umns give successions of musical fifths. It has been 
shown, that when 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. If the piano-keys be arranged in lines 
of twelve, the columns give octaves; but nothing is 
developed from a similar arrangement of the chemi- 
cal elements. The general conclusion was reached, 
that there is no deep significance in the coincidence 
of the number seven in the diatonic scale and in the 
chemical groups. —— Mr. Henry Farquhar then re- 
viewed the theoretical discussion in Professor Tait’s 
article on mechanics, in the Encyclopaedia Britan- 
nica, dissenting from several of his positions. 
9 
tion gives 7 “nearly, = 474991 nearly; and, by 
NOTES AND NEWS. 
THE ‘circulars’ of Johns Hopkins university now 
appear so frequently, and with such varied and valu- 
able contents, that they may already be looked upon 
as among the most important contributions to learn- 
ing in our country. This is the more remarkable as 
no less than five important serial publications are 
issued under the auspices of the university, and in 
large measure are devoted to contributions from its 
