Remarks:

I. This family consists of but one genus; one species is found in Europe; all others known occur in our fauna.

II, i. Rhynchites is cosmopolitan; Auletes occurs in Europe, and Eugnamptus in Asia. The latter is the most feebly developed of the family, and resembles in its distribution, Othnius and Ischalia of the Heteromera, and tribe Tachygonini (VI. iv, 17, mentioned below.

II, ii Pterocolus is an isolated form, having at present no relationships with other genera, though a feeble resemblance in form to the Ceutorhynchini (VI, iv, 18). If my method of interpretation be correct, there were older genera, by which Pterocolus and Tachygonus were affiliated.

III. Attelabus is cosmopolitan, and seems to be the highest development in the series Haplogastra.

IV. The Byrsopidæ are represented in all zoological regions, except Australia; but our genus, Thecesternus, represents an isolated group. From the great differences between individuals, which seem to have unstable specific characters, I am disposed to regard this group as an ancient survival, in the process of evoluting into something else. The variations in the length of the humeral processes of the elytra, and in the sculpture are scarcely explicable, unless we suppose that species formerly distinct are hybridizing. That an ancient type should suddenly effloresce in modern times to produce many species is hardly conceivable, and we should, therefore, be willing to admit, that in this instance the phenomenon is one of absorption, or integration rather than differentiation.

V, 1. Barynotus Schönherri occurs in Northern Europe, and is subarctic, and therefore quite capable of being found on both continents.

V, 3. Two species of Otiorhynchus are arctic, and common to both continents; three have been introduced with fruit trees. Mylacus occurs in Europe and Asia, and on our Pacific Coast; Trachyphlous in Europe, Asia, and in Eastern America.

V, 5. Tanymecus is supposed to be cosmopolitan, but has not yet been properly studied. Of the other genera in our fauna, Pandeleteins and Pachnæus extend to the Northern Tropics of America, and Hadromerus even to Brazil.

V, 6. Cyphus is largely represented in Tropical America, and is conjectured to occur in Asia (C. chrysis, Fabr). The other genera, so far as known. are North American, or extend only into the Northern Tropics.

V, 7. The only described genus of this tribe is Lachnopus, which extends from the Northern Tropics into our fauna. The other genera in our fauna are new, and their distribution is not yet known.

V, 8. One species of Phyllobius has been introduced from Europe into Canada. Scythropus occurs on both sides of the continent, in Europe, and also in Northern Africa.

V, 9. This tribe seems to be exclusively American, and one genus, Coleocerus, extends to the Southern Temperate Zone.

VI, i. Sitones is confined to the northern hemisphere; of the eight species in our fauna, five occur in Europe, and of these, but one, S. tibialis, can be supposed to have been introduced.

1

1877.]

[LeConte.

VI, ii. This sub-family is confined to the temperate and subarctic regions of the northern hemisphere; the genera are all different from those recognized on the other continent, though it is quite possible that some of them may be represented in Northern Asia.

VI, iii. Ithycerus is an entirely isolated form, having no relations to other genera, so far as known to me.

VI, iv, 1. One species of Phytonomus and two of Lepyrus are common to the subarctic regions of both continents. Listronotus and Macrops probably extend into tropical America, but a renewed study of the old genus Listroderes must be made before this can be definitely stated.

VI, iv, 2. This peculiar maritime fossorial tribe is represented by a different genus in Australia.

VI, iv, 3. Plinthus, Hylobius, and Pissodes, are confined to the northern hemisphere, but may be represented (teste Schönherr) in Brazil and Australia. Hilipus is largely represented in South America, but not on the other continent, unless H. orientalis Motsch, from Japan, should on proper examination prove to belong to the genus.

VI, iv, 4. The genera in this tribe are very indefinite, and the foreign species still require revision to bring out the facts in geographical distribution. Lixus, Cleonus, and Stephanocleonus, are the only examples I can mention at present of genera common to both continents.

VI, iv, 5. Procas picipes. two species of Grypidius and Tanysphyrus lemna, are common to the northern part of both continents, and have not been introduced. The only genus which extends to Tropical America is Phyllotrox.

VI, iv, 6. Trachodes is subarctic, and occurs on both continents. VI, iv, 7. Otidocephalus is peculiar to North and South America. VI, iv, 8. Magdalis is cosmopolitan, but most largely represented in Europe and North America.

VI. iv, 9 Anthonomus is cosmopolitan, or nearly so. Orchestes is confined to the northern hemisphere. The other genera in our fauna are new, and their distribution is consequently unknown.

VI, iv, 10. This tribe seems to be exclusively American, but both genera extend into the southern tropics.

VI, iv, 11. The tribe Tychiini has not been separated from Erirhinini sufficiently accurately to make any observations of value at present.

VI, iv, 12. I do not know if the species common to Europe and America have been introduced or not. The tribe, by the diminished number of joints in the funicle of the antennæ indicates a low grade, and the genera are widely diffused on the eastern continent, but do not occur in South America or Australia.

VI, iv, 13. This small tribe is represented on both continents; the species have not been studied with sufficient care to indicate the distribution of the genera.

VI, iv. 14. This tribe is American, and best represented in the tropics. VI, iv, 15. With the exception of Acalles, Cryptorhynchus, and Cœlo.

LeConte.]

Jan. 5,

sternus, which are supposed to be cosmopolitan, our genera are not found on the other continent. Those which have been previously described, mostly extend to the southern tropics of America, and of the eight new genera, nothing can yet be said. As a tribe the distribution is general.

VI, iv, 16. Copturus abounds in tropical America, and is feebly represented in tropical Asia. Piazurus is entirely American. As a tribe the distribution is general.

VI, iv. 17. Tachygonus is exclusively American; one species is Brazilian. The only representative in foreign parts is Dinorhopala Pascoe, in Burmah.

VI, iv, 18. With closer comparison the number of species common to Europe and the United States may probably be increased. There is but one, Ceutorhynchus rapa, which may have been introduced.

VI, iv, 19. Until a new study has been made of Baris, Centrinus, and allied genera, any remarks upon geographical distribution would be pre

mature.

VI, v. Balaninus, as recorded in the Munich Catalogue is cosmopolitan ; a better study of the foreign species is necessary, in order to know if they possess the essential character of the subfamily; the vertical movement of the mandibles.

VII, i. Our two genera extend into tropical America.

VII, ii. Cylas formicarius has probably been imported from Asia, though Convolvulus batata, upon which it depredates, is considered an American plant.

VIII, i, 1. Rhynchophorus is cosmopolitan, but confined to tropical and subtropical regions, being parasitic upon palm trees. Sphenophorus is cosmopolitan. Calandra has deen distributed in cereals until it is now difficult to determine whence the species have emigrated.

VIII, iii, 1. Dryophthorus seems to be cosmopolitan, the other genera are local, so far as known at present.

VIII, iii, 2. Cossonus and Mesites are common to both continents; Cau lophilus is found in Madera, and Himatium in India. Stenomimus occurs in Brazil, and Homaloxenus in San Domingo.

VIII, iii, 3. Stenoscelis is almost cosmopolitan; Rhyncolus is found throughout the northern hemisphere, and in Brazil; Phloophagus, Amaurorhinus, and Hexarthrum in the Atlantic Island and Europe; the last named also occurs in Japan.

IX, i. Platypus is cosmopolitan.

IX, ii, 1. Pityophthorus, Xyloterus, Xyleborus, Dryocotes, Cryphalus, and Tomicus, are common to both continents.

IX, ii, 2. Scolytus is widely diffused on both continents.

X, 1. Tropideres is the only genus occurring on the other continent.

X, 2. Anthribus and Brachytarsus are represented in Europe.

X, 3. Choragus also occurs in Europe. Aræocerus is cosmopolitan, and distributed in articles of commerce.

X, 4. Xenorchestes has been found only in Madeira.

XI. Apion is cosmopolitan.

1877.]

On Refraction Tables.

BY A. K. MANSFIELD, CORDOVA, S. A.

[Mansfield.

(Read before the American Philosophical Society, January 5, 1877.)

The operation of computing the difference between the true and the apparent zenith distances of stars, is usually performed by means of Bessel's refraction tables, which are calculated from his formula, namely:

This operation is usually logarithmic, and the refraction tables are therefore tables of logarithms. The computation may, however, be very much simplified, by the use of natural numbers in place of their logarithms, as will appear from the following:

In the above formula substitute R for d tang, and p for (BT)1„à. The

formula then becomes

R = R1p. . . . . .

.(1)

in which R, may be called the mean refraction, and is a factor depending almost entirely on the temperature and pressure of the atmosphere. For general purposes two tables may be made, one of mean refractions (R1), being the natural numbers corresponding to the table "d tan" of Bessel. and the other of corrections to the mean refraction. But since these corrections would be sometimes additive and sometimes subtractive, the latter table would be reduced to a smaller compass, if each observatory or place where the tables are adopted were to adapt them to the true mean refraction of that place. This may be done as follows:

Let Po be that value of ის which substituted in equation (1), would give true mean refraction for any particular place and let R be that mean refraction. Then

:

R1 is given by its log. in Bessel's first table "log. d tan," and a round value for log po near the above mentioned mean, may be chosen. From this formula a new table of mean refractions in natural numbers can easily be made.

Let be the correction to be applied to this mean refraction. Then

r = R — R1 = R1 (p − po) •

from which the table of corrections may be calculated.

*See Peter's "Astronomische Tafeln und Formeln."

..(3)

In making the table, comparatively few values need be computed, for, having these few values, the others may be supplied by interpolation. The following is a small portion of a table of these corrections, in what appears to be its most convenient form. It was computed from Bessel's tables, as given by Peter's.

Apparent zenith distance is here used as argument at the side. It may be replaced, however, by the corresponding declination, or the circle reading. Log. p is used as argument at the top, and -0.01000 is the assumed value of log. po When log. p lo. იი the correction is zero, therefore we have written the table of mean refractions in that column, thus combining both tables in one. This may be done when the arguments at the side are not chosen so far apart as to make the second differences of the mean refraction too great. In computing the tables from the above formulæ, the arithmetical complement of log. p must be used, when that log. as found from Bessel's tables, is negative. When log. p occurs in the line at the top of the table, the correction is negative, when in the line at the bottom, it is positive. To find the values of log. p for the lower line, corresponding to those of the upper line, call the natural number corresponding to any particular value in the upper line p1, and its corresponding value for the lower line 02. Then from formula (3), since r is minus in one case and plus in the other,

Before entering the table of corrections, log. B, log. T, and log. are taken as usual from Bessel's tables, are then added, and their sum is the argument log. p when the zenith distance is less than 450. When the zenith distance is 450 or more, a correction on account of the exponent is to be ap