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13. C. saturninum, Ach. Th. rosulate, blackish-green, glaucous and subtomentose beneath, the lobes broad, oblong, rounded, waved, very entire ; apoth. scattered, somewhat plane, rufous, with a thin, entire margin. Ach. Syn. p. 320. Hook. Br. Fl. 2, p. 211. Exs. Schær.! Helv. 423.

Trunks and stones. New England. Arctic America, Rich. I have omitted several species of this genus, which require more observation.

II. LEPTOGIUM, Fr. Apothecia rounded, becoming discoid-open and scutelliform, somewhat pedicellate, with a proper exciple. Thallus gelatinous-membranaceous, subdiaphanous, texture cellulose.

1. L. Tremelloides, Fr. Thallus foliaceous, membranaceous, very thin and somewhat diaphanous, smooth on both sides, or powdery above, lead-colored ; lobes oblong, rounded, very entire ; apothecia scattered, elevated, plane, rufous-fuscous, with a paler margin. Fr. Fl. Scan. p. 293. Collema, Ach. Hook. Br. Fl. 2, p. 213.

Rocks and trunks, New England. New York, Torrey. Pennsylvania, Muhl.

2. L. lacerum, Fr. Th. foliaceous, membranaceous, very thin and somewhat diaphanous, glaucous-fuscescent, the lobes small, subimbricate, lacerate-laciniate, denticulate-ciliate ; apoth. (small) scattered, subsessile, somewhat concave, rufous, with a paler margin. Fr.! Fl. Scan. p. 293. Collema, Ach. Hook. Br. Fl. 2, p. 213.

On the earth, and rocks, among mosses. New England. New York, Halsey. Pennsylvania, Muhl.

3. L. Burgessii, Fr. Th. membranaceous, subimbricate, glaucousfuscescent, somewhat spongy and downy beneath, the lobes rounded, sinuate-laciniate, crisped and minutely lacerate-dentate at the margins ; apoth. depressed ; disk somewhat concave, fuscous, with an elevated, lacerate-dentate or foliose margin. Collema, Ach. Syn. p. 320. Hook. ! Br. Fl. 2, p. 211. Icon, E. Bot. t. 300.

Trunks. Mountains of New England.

Tribe II. EPHEBIDEÆ.

III. EPHEBE, Fr. Apothecia formed from the thallus, from concave becoming plane,

and at length convex, black, the margin evanescent. Thallus filamentous, not gelatinous.

E. pubescens, Fr. Thallus decumbent, softish, terete, black, the branches entangled, capillaceous; apothecia of the same color. Fr. Fl. Scan. p. 294. Cornicularia, Ach. B. fibrillosa, Ach. ; thallus obscurely fuscous, smoothish, very delicate, branched, somewhat hirsute with numerous, flexuous, branched, subclavate fibres. Cornicularia pubescens, var. fibrillosa, Ach. Syn. p. 302.

Rocks and stones; in alpine districts. Greenland, Dill. White Mountains. — B, North America, Ach.

a,

Professor Peirce communicated to the Academy Mr. Sears C. Walker's elliptic elements of Neptune.

T

e

48 21 2193

mean equinox, Jan. 1, 1847.
82 = 130 4 35.03.
i

1 46 59.54.
= 0.00857741.
M

21".55448. M = 328° 31' 56.36, mean noon, Greenwich, Jan. 1, 1847.

T = 164.6181 tropical years. “ The normal elliptic places of Neptune, derived from the discussion of 689 observations, European and American (including the two ancient observations of Lalande), were as follows:-. I. -- 1864 = May 9th, 1795, 215 45 7563 – 441 (0

30.28778). 134 Aug. 20th, 1846, 326 45 30.83

- 29.99256). III. 55 = Nov. 7th, 1846, 327 13 58.57

227.6 (r"

29.99256). IV.+

95 = April 6th, 1847, 328 8 0.67 + 163.8 (r!!! – 29.99236). V.+ 233 - Aug. 201h, 1847, 328 57 44.39 + ' 1.0 (7!!II – 29.99256).

“These elliptic places were derived from Neptune's places in the instantaneous orbit, by the subtraction of the effect of the perturbations of all the other planets, as communicated to Mr. Walker by Professor Peirce in November last. “ The expressions for the heliocentric coördinates are,

[9.9998769] r sin. (v + 138 21 52.13) m. eq. Jan. 1, 1847. y= [9.9662265) r sin. (v + 48 55 27.32). z = [9.5800962) r sin. (v + 45 2 37.90).

11.

1.2 (r!

“ Mr. Walker has applied to the elliptic values of v and r the perturbations 8 v and 8 r, which Professor Peirce communicated to him, and has compared the instantaneous values with the normal right ascensions and declinations, as follows :

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11

Obs. - Eph. Obs. - Eph. dr

A A. AD 1. + 37.60 + 0.01207 + 1.9 1.3. III. + ' 32.10 + 0.01608

2.9

1.2. IV. +' 31.29 + 0.01497 + 0.8 + 2.6. V. + 29.49 + 0.01493

0.0.

0.2 +

“ Mr. Walker has omitted the comparison of place II. because it is not the result of direct observation, like the rest.

A closer represen. tation might be obtained by least squares; but Mr. Walker prefers to wait for Mr. Peirce's new values of the perturbations."

Professor Peirce communicated his formulæ for the perturbations of Neptune's longitude and radius vector, resulting from his second approximation to the theory of Neptune. In his first approximation, Neptune's mean time of revolution was assumed to be just twice that of Uranus, and the eccentricity of Neptune's orbit was neglected. But the present approximation is based upon Mr. Walker's orbit, which has been presented to the Academy this evening, and includes all sensible terms as high as the cubes of the eccentricities.

“ The masses of the disturbing planets, and the elements of their orbits, which are adopted in this theory, are the same with those adopted by Leverrier, in his theories of Mercury and Uranus, with the exception of the mass of Uranus, which is taken from Lamont's determination by observations of the satellites.

“ The following notation is adopted in these formulæ : "t= the time in Julian years from Jan. 1, 1850.

“The mean longitude of each planet is denoted by the appropriate symbol of that planet.

“ The Longitude of the perihelion of each planet is denoted by a with the symbol of the planet subjacent.

“ The coefficient for correction of the mass of each planet is given in the usual form with the symbol of the planet subjacent.

" The formulæ are as follows:

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-TW) OF ARTS AND SCIENCES. “8v = the perturbation of Neptune's true longitude =

+ 178.37 sin. (¥ – )

8.63 sin. 2 ( - ) 1.70 sin. 3 (W-K) 0.54 sin. 4 (-Ę) 0.21 sin. 5(W – K) 0.09 sin. 6 ( Ħ -) 0.04 sin.: 7 (HI – ) 0.02 sin. 8 (HI

8- )
0.01 sin. 9 (H - )

0.01 sin. 10 († — «)
+ 1.93 sin. (v - - y)
105.20 sin. (2K - HI -Y)

0.09 sin. (2 - Ķ - Ty
+ 14.71 sin. (2 H

3 +16)

0.01 sin. (3 # — 2 — — y) +(1+uw)

0.39 'sin. (3 » – 4 Ķ + y)
0.09 sin. (4

5 try!
0.03 sin. (5 # – 6 — +ny)
0.01 sin. (6 — 7ķ + y)
0.004340 t cos. (Ę

(K -18)
0.23 sin, (HI - )
+ 1663.30 sin. (2 — — W)

0.16 sin. (2 — — —
58.87 sin. (2 # — 3ť tt

:) 0.03 sin. (3 # - 2 - 1) + 1.50 sin. (3 » – 4ľ + 9)

0.02 sin. (4 # — 3K -) +(1+x) + 0.28 sin. (4 nu — 5 to aw)

0.01 sin. (5 — 4Ļ )
0.10 sin. (5 # — 6 +)
0.01 sin. (6 # -5Ę — )
0.05 sin. (6 -7+)
0.03 sin. (7 # -8ť +8)
0.01 sin. (8 W -9+

9 a

HE 0.018461 t cos. (¥ -)

+

+

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3 ay)

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2

0.86 sin. (3Ę – – 2 ry)
0.86 sin. (-Ę)
0.01 sin. (4 § - H -

0.01 sin. (– ry)
t. 3

13.55 sin, (3Ę - W
13.73 sin. (¥– ķ + Ay)
0.14 sin. (4 — —

)
0.14 sin. ( + 217)

3.62 sin. (4 — 2 — 21) : +(1+r). +

+ 28.42 sin. (4 — — 2 - 18 - )

55.16 sin. (4ť — 2 — 29)
0.03 sin. (5 Ķ — 2 — 3ny)
0.03 sin. (2 ” — 3 — + y)
0.23 sin. (5 Ķ – 2 – 278 - T)
0.23 sin. (2 -3Ļ + y)
0.09 sin. (2 u — 2 — + y - y)
0.45 sin. (5 Ļ – 2 W – 17, - 217)
0.45 sin. (2 – 3ľ + 21y)

+1+++11+11++11+

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十十一十

+ +

+ (1+w)

0.06 sin. (6 Ļ – 3 » – 318)
0.28 sin. (3 — 5 — +218)
0.66 sin. (6 ķ – 3 – 2y —
2.16 sin. (3 ♡ — 5ľ + y +)
2.59 sin. (6 — — 3 — Ty

2

TW) 4.30 sin. (3 # - 5 Ķ +27) 2.72 sin. (6 § - 3 – 3 ) 0.85 sin. (2ť – +7 — 217) 0.56 sin. (– – 4W+) 0.66 sin. (2 Ķ - H - Try) 0.03 sin. (3 Ķ – 2 пу) 4.38 sin. (¥ – K) 0.13 sin. (2 \ - · HI 0.43 sin. (3 K - H - H ry) 0.43 sin. (¥ – Į + 1 0.24 sin. (2 Ķ - W - 2771 tay) 0.01 sin. (3 — — # — 2)

-)

1+++++

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