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OBSERVATIONS ON THE ASTEROIDS. A call for a complete list of the Asteroids has waited for nearly a year.

The discovery of these planetoids have been numerous in later years.

The subscript figures immediately following the discoverers' names indicate the number each discovered successively. The number discovered in each decade are as follows :

1801 to 1850 inclusive (first fifty years) 13
1851 to 1860
1861 to 1870

50
1871 to 1880

107 1881 to 1887

52

49

Total,

271 Dr. Palisa, of Europe, leads in the list — he having discovered 60; while Dr. Peters, of America, follows, as second in the list, with 47; these two together having discovered more than one-third of the 271.

Of the 271 Asteroids thus far known, 77 were discovered by American astronomers, and 196 by European astronomers.

No. 47 (Melete) was first named Pseudo-Daphne ("falseDaphne) by its discoverer, Goldschmidt, because when he discovered No. 41 (Daphne), he soon after lost it; and in searching for it later, he discovered No. 47 (Melete) and in turn lost this also, and not until August 27, 1861, did he re-discover Melete or "Pseudo-Daphne."

Nos. 49 and 50 (Doris and Pales) were called the “ twin planets,” because Goldschmidt discovered them at the same time, Sept. 19, 1857.

No. 59 (Elpis) was first called “Olympia,” but afterwards named Elpis.

No. 65 (Cybele) was first called "Maximiliana," but of late years it has been called Cybele.

The Nine Muses have been immortalized by their names : No. 18. Melpomene, Hind.. No. 33. Polyhymnia, Chacornacz. No. 22. Calliope, Hind: No. 62. Erato, No. 23. Thalia, Hindy. No. 81. Terpsichore, Tempel No. 27. Euterpe, Hind: No. 84. Clio,

Luther No. 30. Urania, Hind:

Prof. Hind evidently intended to continue with the names of the last three Muses had not No. 30 (Urania) been his 8th and last dis

Forster,

covery of an Asteroid. Hence the names were completed as given.

The names of the Three Graces appear: No. 23 (Thalia), No. 31, (Euphrosyne), and No. 48 (Aglaïa). While the names of only two of the Three Fates appear: No. 97 (Clôthô), and No. 120 (Lachesis); the other Fate is Atropos.

Several countries have been immortalized : No. 53 (Europa), No. 97 (Asia), No. 136 (Austria), No. 232 (Russia), and 241 (Germania).

FIRST MENTION OF Ice-CREAM. The first mention of ice-cream that is found in our history is in the account of the festivities following Washington's first inauguration as president, in the city of New York, in 1789. Among the ices used on that occasion was ice-cream, which is said to have been prepared, or at least suggested, by Dolly Adams, then the brightest star in social and diplomatic circles. The new confection made quite a sensation at that time, and probably helped to increase Dolly Adams's popularity.-Pittsburgh Dispatch.

THE MOTIVE POWER OF THE WORLD. Four fifths of the engines now working in the world have been constructed during the last twentyfive years. France owns 47,590 stationary or locomotive boilers, 7,000 locomotives, and 1,850 boilers of boats ; Germany has 10,000 locomotives, 59,000 boilers, and 1,700 ships' boilers ; Austria has 12,000 boilers, and 2,800 locomotives.

The force equivalent to the working power steam engines represent: in the United States, 7,500,000-horse power; in England, 7,000,000horse power; in France, 3,000,000-horse power ; in Austria, 1,500,000horse power; and in Germany, 4,500,000-horse power. In these figures the motive power of the locomotives is not included, whose number in all the world amounts to 105,000, representing a total of 3,000,ooo borse power. Adding this amount to the other powers, we obtain a grand total of 46,000,000-horse power.

A steam horse power is equal to three actual horses' power; and a living horse is equal to seven men. The steam engines of the world represent, therefore, approximately the work of 1,000,000,000 men, or more then double the working population of the earth, whose total population amounts to 1,455,923,000 inhabitants. Steam has accordingly trebled man's working power, enabling him to economize his physical strength, while attending to his intellectual development. — London Times.

MAIDEN—ATHENS. (Vol. IV, p. 442.) Apropos I send you a pro lific word-Athensto go with the word “ Maiden." The sentence was formed many years ago.

“ Nat. Heath's Seth has ten hens ; he set a hen at the east sea; she ate ants as she sat 'neath the ants' nest; he then set a hat, a neat net, 'neath the nest; the hens then ate the ants at the sea."

SETH HEATH.

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QUESTIONS.

. 1. Lord Francis Bacon is quoted as saying that “small-pox and ague are minor evils compared with the plague.” Where in his works does he say it?

E. B., Washington, D. C. Is the decimal coinage a “Yankee notion ” ? Canada introduced it from the United States in 1858. Where did the United States get it, and when ?

Thos. BENGOUGH, Toronto, Can. 3. Where, when, and how originated the "three days of grace promissory notes and bills of draft?

Thos. BENGOUGH. Can any one inform me who was Dick, and what was the peculiarity of his hat-band, in the saying, “ Odd as Dick's hat-band.”

DJAFAR. any of

your readers inform me as to the authorship of the following lines? They have been much used to soothe the restless, seeking sleep.

DJAFAR.
“ Sleep sweetly in this quiet room,
O thou, who'er thou art,
And let no mournful yesterdays
Disturb thy peaceful heart.
Nor let tomorrow scare thy rest,
With dreams of coning ill;
Thy Maker is thy changeless friend,
His love surrounds thee still.
Forget thyself and all the world,
Put out each glaring light;
The stars are watching overhead,

Sleep sweetly, thou, good night !" 6. Why are “sixty-three gallons " called a hogshead (hog's head)?

A. L. G., Manchester, N. H. 7. The “New Astronomy," by P. E. Trastour, M. D., Page 60, says " that whitish glimmer of irregular form which makes the turn of our heavens, is known by the name of milky way, and more generally by the popular name of Saint James' Way.” Why so called, and what Saint James is referred to ?

CHARLES Cabot. 8. Which of the two apostles named James was the auther of the Epistle that bears that name, James, brother of John, son of Zebedee ; or James, son of Alpheus ?

ANDREW SMITH. 9. What was the real names by which Jesus (the Christ) was called by the Hebrews, the Greeks, and the Romans ? for we are told that Pilate wrote the title “in Hebrew, and Greek, and Latin."(John xix, 20).

ANDREW SMITH. In the constellation Orion are three stare generally known as the Belt of Orion ”; also, known by the name of the Three Kings. What three kings are alluded to?

ANDREW SMITH. 11. Why does fanning a person in a hot day cool the person? Also, why does blowing into hot tea or coffee cool it ?

W. B. Who is the author of this quotation : “In the house of mourning lay the casket robbed of its adorning."

J. FRANCIS RUGGLES, Bronson, Mich.

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12.

Simultaneous Equations.

By B. F. BURLESON, Oneida Castle, N. Y.

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In such equations the unknown quantities are similarly involved. The method given for the elimination and resolution of such equations is imperfectly treated in our text-books as regards its adaptability to the resolution of a great class of problems in algebra, geometry, and trigonometry. We beg permission to show in a fuller manner its application and usefulness.

It is well known that if s= the sum of any number of quantities, m= the sum of their products taken two and two, n= the sum of their products taken three and three, p= the sum of their products taken four and four, r = the sum of their products taken five and five, etc., etc.; then the quantities themselves will be the roots of the general equation,

Xm-sXm-i+mXm-2-n Xm-3+pXm-4 We will now give some formulæ involving the utility of this principle. We take it for granted that the reader is acquainted with the notation of the triangle, now almost universally adopted by mathematicians. In the books s = the semi-perimeter of the triangle; we put it equal to the whole of the perimeter, which we consider more systematic. No other changes in notation have been made.

1. a2+62+c=52—2m. 2. a3+3+co=93 — 38m+3n. 3. a'+64+c=s4—482m +48n+2m2. 4. a5+55+c=55—58m+584n-+-58m2-5mn. 5. a6 +86 +c=56 -684m+6son+98 m2—128mn+3n2— 2m3. 6. a?+37+c=si_785m+784n+1483m2—21s2m+7812—78m3

+7m2n. 7. a8+68+8=38 — 856m +885n+2084m2—32somn+12s2n2

-16sPm3 +24sman-Smn2+2m4. 8.

a2+62+c2+d=(1) 9, 23 +63 +63+d3=(2) 10. a4+24+04+24584-482m +48n+2m2-4p. 11.

25+15+c5+d=55583m +582n +58m2_5mn—58p. 12. a2+62+62+d2+2=(1)=(8). 13, 23+23+03+03+3=(2)=(9).

14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27.

. 28. 29. 30. 31. 32. 33.

a4+24+04+04+4=(10).
a5+15+c5+do+e5=s5—583m +5sn+58m2_5mn—5sp +5r.
a2b2+a2c2+62c2=m2—2sn.
ab3+a%c3+63c3=m3—3smn +3n2.
a464+a4c4+64c4=m4—4sman+4mn+2sn?.
a2b-_-6c+a c+ab2+bc2+ac=sm--3n.
k=1/(4:?m—54–8sn).
t=[an auxiliary quantity] = V(4sm—4—8sn).
R=n:t. (23). r=t: 2s.
R, [the radius of the nine-point circle]=n+2t.
R+R+=(+2+3ns): 2st.
RR+R,r+Rr=(3nt2+2nos)=-4st?.
RR=n?:- 4st.
ra+r.tr.=(4sm—93)2t.
rotrare+rir=182.
rarist.
PA+P+P=mt:-2n.
P 2+PP+P2=t(m2—2sn) :-4n2.
P.P.+P.Pc+PP=(493---95-88?n) --4n.
P.P.P=1:-8n.
m+m+m=(32-6m): 4.
m, mi tmgm. tmm =(9m2—18sn):-16.
m+m+m2=(984—3682m+36n+18m2):-16.
m.mm.=(-496+2484m—30s_m2—4m3—36son+72smn.

-27n3):8.
Ule=(4s4mna—son2—853n3) = V(s2m2—2smn+n2).
Sin A+ SinB+SinC=st-2n.
CosA+Cos B+CosC=(2sn+t)- 2sn.
Sin A SinB Sin C=t3-:-8n?.
Cos A CosB CosC=(8312-8snt—213):16sn?.
Cost A Cos. B Cos?C=3t-:-8n.
Sin! A SinB Sinc=t?:-8sn.
Sino_A+Sina{B+Sina?C=(4sn—(2) -- 4sn.
Cos? A+ Cosa B+ Cos? C=(8sn+t2) --4sn.
Sin? A+ SinoB+Sin?C=(3442—8snt—+4):8s-na.
Cos? A+ CosaB+ Cos?C=(8592—93t+8snt +213) --8sna.
Sin2 A+Sin2B+Sin2C=t3--2n?.
Cos2 A+ Cos2B+Cos2C=(8snt+213 — S3t2—48n"); 4sno.

35. 36. 37.

38.
39.
40.
41.

43.

45. 46. 47. 48. 49. 50.

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