attain a perfect whiteness till they are a year old. They visit Severn river first in the middle of May, on their journey northward, where they breed; return in the beginning of September, with their young, staying at Severn settlement about a fortnight each time. The Indian name is way-way, at Churchill river. Linnæus has not taken notice of this species.

Anas. 46. Canadensis. 198. 14.

Canada Goose. Faun. Am. Sept. 16.

Edw. 151. Catesby 1, 92, &c. Severn river, No 42.

The Canada geese are very plentiful at Hudson's Bay, great quantities of them are salted, but they have a fishy taste. The specimen sent over agrees perfectly with the descriptions and drawings. At Hudson's Bay this species is called the small grey goose. Besides this, and the preceding white goose, Mr. Graham, the gentleman who sent the account from Severn settlement, mentions 3 other species of wild geese to be met with at Hudson's Bay, he calls them, 1. The large grey goose. 2. The blue goose. 3. The laughing goose.

1

The first of these, the large grey goose, he says, is so common in England, that he thought it unnecessary to send specimens of it over. It is however presumed, that though Mr. Graham has shown himself a careful observer, and an indefatigable collector; yet, not being a naturalist, he could not enter into any minute examination about the species to which each goose belongs, nor from mere recollection know that his grey goose was actually to be met with in England. A natural history, by examination, often finds material differer ces, which would escape a person unacquainted with natural history. The wish, therefore, of seeing the specimens of these species of geese, must occur to every lover of that science. Mr. Graham says, the large geese are the only species that breed about Severn river. They frequent the plains and swamps along the coast. Their weight is 9 pounds.

The blue goose is as large as the white goose; and the laughing goose is of the size of the Canada or small grey goose. These last two species are verycommon along Hudson's Bay to the southward, but very rare to the northward of Severn river. The Indians have a peculiar method of killing all these species of geese, and also swans. As these birds fly regularly along the marshes, the Indians range themselves in a line across the marsh from the wood to high water mark, about musket shot from each other, so as to be sure of intercepting any geese which fly that way. Each person conceals himself, by putting round him some brush wood; they also make artificial geese of sticks and mud, placing them at a short distance from themselves, in order to decoy the real geese within shot: thus prepared, they sit down, and keep a good look out; and as soon as the flock approaches, they all lie down, imitating the call or note of geese, which these birds no sooner hear, and perceive the decoys, than they go straight down towards them; then the Indians rise on their knees, and discharge 1, 2, or 3 Y Y

VOL. XIII.

guns each, killing 2 or even 3 geese at each shot, for they are very expert. Mr. Graham says, he has seen a row of Indians, by calling round a flock of geese, keep them hovering among them, till every one of the geese was killed Every species of geese has its peculiar note or call, which must greatly increase the difficulty of enticing them.

Anas. 47. Edw. t. 100. N° 37 and 38.

Albeola. 199. 18. The Red Duck. Faun. Am. Sept. 17.
Sarcelle de la Louisiane. Brisson vI. t. 41, f. 1. Severn river,
Fishing Birds.

The descriptions and figures answer very well with the male, except that the 3 exterior feathers are not white on the outside, but all dusky. The female is not described by any one of the ornithologists; and therefore deserves to be noticed, to prevent future mistake. The whole bird is dusky, a few feathers on the forehead are rusty, and some about the ears of a dirty white; the breast is grey, the belly and speculum in the wings white; the bill and legs are black. They visit Severn settlement in June, build their nests in trees, and breed among the woods, and near ponds; the weight of the female is 1 pound, its length 14 inches, and its breadth 21.

Anas. 48. Clangula. 201. 23. 16. Severn river, N° 51.

Golden Eye. Br. Zool. Faun. Am. Sept.

These birds frequent lakes and ponds, and breed there: they eat fish and slime, and cannot rise off the dry land. The legs and irides are yellow; their weight is 2 pounds, and their measure 19 inches in length, and 2 feet in breadth. The specimen sent is the male.

Anas. 49. Perspicillata. 201. 25. Black Duck. Faun. Am. Sept. 16. Edw. 155. Churchill river, N° 14.

This species is exactly described, and well drawn by Edwards. The Indians call it she-ke-supartem. It ought to come into the first division of Linnæus's ducks, "rostro basi gibbo," as its bill is really very unequal at the base.

Anas. 50. Glacialis. 203. 30, and Hyenalis, 202. 29. Edw. t. 156. Swallow-tail. Br. Zool. Faun. Am. Sept. 17. Churchill river, N° 12.

At Churchill river the Indians call this species, har-har-vey; it corresponds with Edwards's description and drawing, pl. 156, but differs much from Linnæus's inexact description of the anas hymalis, to which he however quotes Edwards. On the whole, it is almost without a doubt that the bird represented by Edwards, plate 280, and Br. Zool. folio, plate a, 7, and quoted by Linnæus for his anas glacialis, is the male, and that the bird figured by Edwards t. 156, and quoted by Linnæus for the anas hyemalis, is the female, of one and the same species. Linnæus mentions a white body, in his anas hyemalis, which in Edw. tab. 156, and in the society's specimen, is all brown and dusky, except the belly, temples, a spot on the back of the head, and the sides of the rump, which are white.

Linnæus says, that the temples are black; in the specimen now sent over, and in Mr. Edwards's figure, which Linnæus quotes, they are white; the breast, back, and wings, are not black as he says, but rather brown and dusky. A further proof, that Linnæus's anas glacialis and hyemalis are the same, is that the feet in both t. 156 and 280 of Edwards are red, and the bill black, with an orange spot.

Anas. 51. Crecca. 204. 33. 17. Severn river, No 33, 34. This is a variety of the teal, for it wants the two white streaks above and below the eyes; the lower one indeed is faintly expressed in the male, which has also a lunated bar of white over each shoulder; this is not to be found in the European teal. This species is not very plentiful near Severn river; they live in the woods and plains near little ponds of water, and have from 5 to 7 young at a time. Anas. 52. Histrionica 204. 35. Harlequin Duck. Faun. Am. Sept. 16. Edw. t. 99. This bird had no number fixed to it; it agrees perfectly with Edwards's figure.

Varietas. Teal. Br. Zool. Faun. Am. Sept. Male and female.

Anas. 53. Boschas. 205. 40.

Severn river, No 39.

Mallard Drake. Faun. Am. Sept. Br. Zool.

It is called stock drake at Hudson's Bay, and corresponds in every respect with the European one, upon comparison.

21. Pelicanus, Pelican. 54. Onocrotalus 251. 1. A variety. York fort. This variety of the pelican, agrees in every particular with Linnæus's oriental pelecan (pelecanus onocrotalus orientalis), but has a peculiar tuft or fringe of fibres in the middle of the upper mandible, something nearer the apex than the base. This fuft has not been mentioned by any author, and is also wanting in Edwards's pelican, t. 92, with which the society's specimen corresponds in every other circumstance. The P. onocrotalus occidentalis, Linn. or Edw. t. 93 American pelican, is very different from it: the chief differences are the colour, which in our Hudson's Bay bird is white, but in Edwards's is of a greyish brown; and the size, which in the white bird is almost double of the brown one. The quill feathers are black, and the shafts of the larger ones white. The alula, or bastard wing, is black. The bill and legs are yellow.

*22. Colymbus, Diver, 55. Glacialis. 221. 5. Northern Diver. Br. Zool, Faun. Am. Sept. 16. Churchill river, N° 8. called a Loon there.

This bird is well described and drawn in the British Zoology, in folio.

**Grebe.

Am. Sept. 15.

56. Auritus, a. 222. 8. Edw. 145. Eared Grebe. Faun.
Severn river.
Severn river. N° 43.

This is exactly the bird drawn by Edwards, t. 145. The specimen sent over is a female. It differs much from our lesser crested grebe. Br. Zool. octavo I, p. 396, and Br. Zool, illustr. plate 77, fig. 2, and Ed. 96. fig. 2. However, in

both these works, it is considered only as a variety, or different in sex. Mr. Graham has the same opinion. It lives on fish, frequenting the lakes near the sea coast. It lays its eggs in water, and cannot rise off dry land. It is seen about the beginning of June, but migrates southward in autumn. It is called sekeep, by the natives. Its eyes are small, the irides red; it weighs 1 pound, and measures 1 foot in length, and one-third more in breadth.

23. Larus, Gull. 57. Parasiticus. 226. 10. Arctic Gull. Br. Zool. Faun. Am. Sept. 16. Edw. 148. 149. Churchill river, N° 15.

This species is called a man of war, at Hudson's Bay. It seems to be a female, by the dirty white colour of its plumage below; it agrees very well with Edwards's drawing, and that in the Br. Zool. illustr.

24. Sterna, tern. 58. Hirundo (variety), 227. 2. The greater tern. Br. Zool. Faun. Am. Sept.

The number belonging to this bird is lost, perhaps it is N° 17, from Churchill river, called a sort of gull, called egg-breakers, by the natives.' The feet are black; the tail is shorter and much less forked than that described and drawn in the Br. Zool. The outermost tail-feather also wants the black, which that in the British Zoology has, In other respects it is the same.

XXX. Geometrical Solutions of Three Celebrated Astronomical Problems. By the late Dr. Henry Pemberton, F.R. S. Communicated by Matthew Raper, Esq., F.R.S. p. 434.

Lemma.-To form a triangle with two given sides, that the rectangle under the sine of the angle contained by the two given sides, and the tangent of the angle opposite to the lesser of the given sides, shall be the greatest that can be.

Let the two given sides be equal to AB, and AC fig. 4, pl. 7: round the centre A, with the interval AC, describe the circle CDE, and produce BA to в; take BF a mean proportional between BE and BC, and erect the perpendicular FG, and complete the triangle AGB.

Here the sine of BAG is to the radius, as FG to AG; and the tangent of ABG to the radius, as FG to FB: therefore the rectangle under the sine of BAG and the tangent of ABG, is to the square of the radius, as the square of FG, or the rectangle EFC, to the rectangle under AG or AC and FB. But, EB being to BF as BF to BC, by conversion, EB is to EF as BF to FC, and also, by taking the difference of the antecedents and of the consequents, EF is to twice AF as BF to FC; and twice AFB is equal to EFC.

Now, let the triangle BAH be formed, where the angle BAH is greater than BAG. Here, the perpendicular HI being drawn, the rectangle under the sine of BAH and the tangent of ABH, will be to the square of the radius, as the rectangle EIC, to the rectangle under AC, IB. But IF is to FB as 2AFI to 2Afb, or

EFC; and 2AFI is greater than aƑ2 AI2; also AF2 Ar2 together with EFC, is equal to EIC; therefore by composition, the ratio of IB to BF is greater than that of EIC to EFC; and the ratio of AC X IB to AC X FB greater than that of EIC to EFC: also, by permutation, the ratio of AC X IB to EIC greater than the ratio of But the first of these ratios is the same with that of the square of the radius to the rectangle under the sine of BAH and the tangent of ABH; and the latter is the same with that of the square of the radius to the rectangle under the sine of BAG and the tangent of ABG; therefore the latter of these two rectangles is greater than the other.

AC X FB to EFC.

Again, let the triangle BAK be formed, with the angle BAK less than BAG, and the perpendicular KL be drawn. Then the rectangle under the sine of BAK and the tangent of ABK, is to the square of the radius, as the square of KL to the rectangle under AC, BL. Here, FL being to FB as 2AFL to 2AFB or EFC, and 2AFL less than AL-AF2, by conversion, the ratio of LB to FB will be greater than the ratio of ELC to EFC; therefore, as before, the rectangle under the sine of BAG and the tangent of ABG is greater than that under the sine of BAK and the tangent of ABK.

(

Corol. 1. BF is equal to the tangent of the circle from the point в; therefore BF is the tangent, and AB the secant, to the radius AC, of the angle, whose 'cosine is to the radius as AC to AB. Therefore AF is the tangent, to the same radius, of half the complement of that angle; and AF is also the cosine of the angle BAG to this radius.

Corol. 2. The sine of the angle composed of the complement of AGB, and twice the complement of ABG, is equal to 3 times the sine of the complement of AGB. Let fall the perpendicular AH, (fig. 5), cutting the circle in 1; continue GF to K, and draw AK. Then BF2 = EBC = GBL. Therefore GB: BF :: BF: BL, and the triangles GBF, FBL are similar. Consequently FL is perpendicular to GB, and parallel to AH; whence GH being equal to HL, GM is equal to MF, and мK equal to 3 times GM.

MK

Now the arc IK = 21C + GI; and the angle IAK = 21AC + GAI; also GM is to MK as the sine of the arc GI to the sine of the arc 1K, that is, as the sine of the angle GAI to the sine of the angle IAK. Therefore the sine of the angle IAK (= 21AC + GAI) is equal to 3 times the sine of the angle GAI; but GAI is the complement of AGB, and IAC the complement of ABG.

Corol. 3. If (fig. 6) any line BN be drawn to divide the angle ABG, and AN be joined, also Ao be drawn perpendicular to BN, and continued to the circle in P, the sine of the angle composed of NAP and 2PAC will be less than 3 times the sine of the angle NAP. Draw NQR perpendicular to AB, cutting AP in s; join AR, and draw at perpendicular to BN, and parallel to Ao; then BQ NBT. But Ba2 is greater than the rectangle EBC, that is, greater than the rectangle NBV,