USA > Ohio > Annual report of the State Commissioner of Common Schools, to the Governor of the State of Ohio, 1892 > Part 17
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ANNUAL REPORT
TABLE XXX-INSTITUTE FUND.
Receipts
Expenditures.
Balance September 1st,
From examination fees.
Total.
Support of teachers' in-
stitutes.
Treasurer's fees.
Total.
Balance on hand Septem- ber 1st, 1892.
Adams
97 50
$ 153 50
$ 251 00
$ 168 10
$ 1 26
$ 169 36
$ 81 64
Allen
59 05
252 50
311 55
196 05
1 50
197 55
114 00
Ashland.
22 00
213 00
235 00
220 25
1 49
221 74
13 26
Ashtabula
125 55
219 50
345 05
343 95
343 95
1 10
Athens
168 39
241 00
409 39
409 39
409 39
Auglaize.
Belmont
293 94
299 00
592 94
365 40
3 47
368 87
224 07
Brown
408 63
248 50
657 13
150 00
1 99
151 99
505 14
Butler
438 13
314 00
752 13
300 00
2 51
302 51
449 62
Carroll
82 96
315 50
398 46
287 94
2 52
290 46
108 00
Champaign.
23 19
218 89
242 08
·218 61
1 76
220 37
21 17
Clark
70 72
163 40
234 12
223 90
1 31
225 21
8 91
Clermont
64 50
319 05
383 55
324 50
324 50
59 05
Clinton
107 81
222 00
329 81
241 24
1 78
243 02
86 79
Columbiana
185 67
232 91
418 58
266 00
1 68
267 68
150 90
Coshocton
71 70
231 00
302 70
193 68
1 85
195 53
107 17
Crawford
97 36
163 00
260 36
189 10
2 89
191 99
68 37
Cuyahoga
107 07
320 50
427 57
250 00
3 20
253 20
174 37
Darke
35 72
428 50
464 22
460 79
3 43
464 22
...
Defiance
35 18
151 50
186 68
135 25
1 30
136 55
50 13
Delaware
19 31
227 78
247 09
229 50
1 24
230 74
16 35
Erie ...
16 83
140 50
157 33
132 33
132 33
25 00
Fairfield
1 62
259 00
260 62
178 60
2 07
180 67
79 95
Fayette
35 48
169 00
204 48
198 90
1 74
200 64
3 84
Franklin
389 47
368 00
757 47
301 00
2 30
303 30
454 17
Fulton
68 66
202 50
271 16
229 00
1 62
230 62
40 54
Gallia
69 46
262 00
331 46
248 11
2 76
250 87
80 59
Geauga ..
211 19
211 19
209 64
1 55
211 19
Greene
202 38
196 00
398 38
200 00
1 75
201 75
196 63
Hamilton
198 61
375 50
574 11
391 42
391 42
182 69
Hancock
80 96
309 50
390 46
293 09
2 33
295 42
95 04
Hardin
28 23
295 82
324 05
305 72
2 21
307 93
16 12
Harrison
5 54
192 00
197 54
180 90
1 72
182 62
14 92
Henry
204 40
146 50
350 90
322 30
1 17
323 47
27 43
Highland
,131 63
218 50
350 13
215 60
1 75
217 35
132 78
Hocking
59 19
176 50
235 69
170 00
1 88
171 88
63 81
Holmes
73 19
188 50
261 69
296 25
1 50
297 75
36 06
Huron
101 21
269 50
370 71
274 00
274 00
96 71
Jackson
155 49
150 50
305 99
161 99
161 99
144 00
Jefferson
107 32
183 00
290 32
167 06
1 72
168 78
121 54
Knox
49 83
237 65
287 48
243 70
Lake
104 66
90 50
195 16
109 00
72
109 72
85 44
Lawrence
259 82
189 95
449 77
Licking ...
133 25
339 50
472 75
454 73
3 90
458 63
14 12
Logan.
12 93
247 00
259 93
257 95
1 98
259 93
Lorain
236 41
237 50
473 91
370 27
73
371 00
102 91
Lucas
20 65
258 00
278 65
243 25
4 09
247 34
31 31
Madison
28 76
169 50
198 26
177 13
177 13
21 13
Mahoning
339 75
339 75
337 04
2 71
339 75
Marion.
18 50
228 00
246 50
247 00
247 00
Medina.
29 91
305 50
335 41
335 33
335 33
08
Meigs
100 80
165 00
265 80
192 90
192 90
72 90
Mercer
86 83
182 50
269 33
158 25
92
159 17
110 16
Miami.
175 43
217 00
392 43
200 00
2 14
202 14
190 29
152 00
152 00
150 78
1 22
152 00
Guernsey.
123 00
123 00
88 81
1 19
90 00
33 00
Counties.
1891.
243 70
43 78
........
COMMISSIONER OF COMMON SCHOOLS.
TABLE XXX-INSTITUTE FUND-Conclude 1.
Receipts.
Expenditures.
Balance September 1st,
From examination fees.
Total.
Support of teachers' in-
stitute.
Treasurer's fees.
Total.
Balance on hand Septem- ber 1st, 1892.
Monroe
$ 96 61
$ 198 08
$ 294 69
143 03
$ 1 32
144 35
$.150 34
Montgomery
10 68
269 50
280 18
279 25
2 16
281 41
Morgan
102 29
364 00
466 29
381 05
1 30
382 35
83 94
Morrow
220 25
220 25
156 24
1 26
157 50
62 75
Muskingum
360 00
360 00
357 12
2 88
360 00
Noble
263 80
251 00
514 80
215 00
2 00
217 00
297 80
Ottawa
24 80
109 00
133 80
98 50
87
99 37
34 43
Paulding
14 50
180 00
194 50
166 50
1 13
167 63
26 87
Perry
1 46
183 00
184 46
110 35
1 46
111 81
72 65
Pickaway
12 62
188 00
200 62
199 12
1 50
200 62
Pike
129 91
129 91
231 50
231 50
:69 91
Portage
158 80
191 00
349 80
349 00
1 52
350 52
Preble.
6 68
186 00
192 68
189 66
3 02
192 68
Putnanı.
45 11
200 00
245 11
245 11
7 23
252 34
Richland
151 84
209 00
360 84
180 11
1 67
181 78
179 06
Ross
67 00
263 00
330 00
245 62
1 49
247 11
82 89
Sandusky.
354 72
351 72
309 63
2 30
311 93
42 79
Scioto
20 35
161 50
181 85
180 90
1 99
182 89
1 04
Sene ca
227 43
267 50
494 93
360 00
2 94
362 94
1 1 99
Shelby
47 12
178 50
225 62
153 48
1 44
154 92
70 70
Stark
1,170 48
689 30
1,859 78
330 00
6 60
336 60
1,523 18
Summit.
266 73
266 50
533 23
365 58
4 95
370 53
198 47
Tuscar .was
193 75
299 00
492 75
350 00
2 74
352 74
140 01
Union
41 66
199 50
241 16
153 48
1 59
155 07
86 09
Van Wert
51 71
182 50
234 21
180 11
1 09
181 20
53 01
Vinton
23 78
166 50
190 28
188 01
2 27
190 28
Warren ..
91 50
246 50
338 00
137 54
2 52
140 06
197 94
Washington
477 97
317 00
794 97
458 88
2 53
461 41
333 56
Wayne
25 37
299 50
324 87
300 00
2 40
302 40
22 47
Williams
24 30
238 00
262 30
244 55
1 20
245 75
16 55
Wood ..
59 81
276 50
336 31
317 20
2 21
319 41
16 90
Wyandot
19 84
180 00
199 84
103 50
1 45
104 95
94 89
Totals.
$9.527 82
$2,0997 15
$30,524 97
$20,895 72
$153 88
$21,049 60
$8,757 75
.
Trumbull.
128 00
441 00
569 00
189
Counties. ·
1891.
190
ANNUAL REPORT
· REPORT OF THE STATE BOARD OF SCHOOL EXAMINERS.
Two meetings of the Board for the examination of applicants for certificates were held during the year, one at Columbus, December 29th, 30th and 31st, 1891, and one at Cleveland, June 30th and July 1st and 2nd, 1892. At these meetings certificates were issued to the following named persons:
COLUBMBUS MEETING.
Examiners -- W. J. White, E. T. Nelson, Alston Ellis, J. W. Knott, E. A. Jones. HIGH SCHOOL, LIFE.
Edward F. Brewster.
Ralph M. Brown. E. B. Cox. C. W. Gilgen. ' Fletcher Hawk. J. E. McKean.
E. E. Richards. Frank Smith. E. M. Van Cleve. H. B. Williams. James E. Yarnell.
COMMON SCHOOL, LIFE.
Carey Boggess.
George P. Deshler.
B. F. Finkel.
U. M. Shappell.
C. M. Flowers.
Henry B. Smith.
J. W. Guthrie.
George W. Tooill.
George P. Harmount.
Mrs. Frank G. M. Van Slyck.
E. C. Hedrick.
G. W. Hoffman.
S. A. Muchmore. -
John W. Watson. W. M. Wikoff.
CLEVELAND MEETING.
Examiners-W. J. White, E. T. Nelson, J. W. Knott, E. A. Jones, J. C. Hartzler.
HIGH SCHOOL, LIFE.
J. C. Cooper, George P. Deshler, Clara G. Orton, Henry R. Warner.
COMMON SCHOOL, LIFE.
Millard F. Andrew. Jasper C. Barnes.
U. L. Monce. E. L. Moseiey.
Miss Anna M. Nutting. J. E. Ockerman.
E. E. Rayman. Geo. E. Ryan.
E. E. Smock.
W. P. Vandervoort.
Sylvester Wilkins.
R. B. Bennett. W. S. Cadman. Clifton D. Hubbell. Miss Louise John. J. L. Jordan. Samuel T. Logan. Edward Maag. J. V. McMillan.
Miss Clara G. Orton. Miss Olive Rush.
EXAMINATION QUESTIONS
USED BY THE STATE BOARD AT THE MEETINGS HELD AT CLEVELAND IN JULY AND AT COLUMBUS IN DECEMBER, 1892.
JULY MEETING.
-
ORTHOGRAPHY.
1. Of what does orthography treat? Give the derivation of the word. Of what does orthœpy treat ?
2. In English words, what determine the number of syllables? What is the organ of voice, and what are the organs of speech ?
3. What is a mute or close consonant? Give the list of them. What consonants are called liquids, and why? What consonants are called nasals, and why? What consonants are called sibilants, and why?
4. What are labials? Give the list of them. What are linguals? · Give the list of them.
5. Mark fully the pronunciation of vagary, hymeneal, and orthæpy. Name and make the best diacritical marks used by our best authors.
GRAMMAR.
"Art is the child of Nature; yes, Her darling child, in whom we trace The features of the mother's face, Her aspect and her attitude, All her majestic loveliness Chastened and softened and subdued
Into a more attractive grace, And with a human sense imbued. He is the greatest artist, then, Whether of pencil or of pen, Who follows nature."
192
ANNUAL REPORT.
1. Give the properties of each noun in the selection.
2: Name each word in the selection governed by the following rule of syntax; tell what part of speech each word is, and to what it belongs : "An adjective or a participle belongs to some noun or pronoun."
3. Parse the relative pronouns in the selection.
4. What should be the antecedent of a relative pronoun ? Illustrate.
5. Write a sentence containing a co-ordinate conjunction, immedi- ately followed by a relative clause.
UNITED STATES HISTORY.
1. Name five early discoverers; tell what each discovered, and un- der whose auspices the discoveries were made.
2. Give an account of three early settlements in the "New World," each under the auspices of a different nation.
3. Name five wars in which what is now the United States has been engaged; name a prominent battle of each war, and the opposing com- manders in each battle.
4. Name the territorial changes that took place at the close of the . French and Indian War.
5. Name five battles of the war of the Rebellion which occurred in Tennessee, and give the commanding general on each side in each battle.
6. What territory did the United States acquire by purchase, and from whom?
7. Give a method for teaching history.
GENERAL HISTORY.
1. Give in chronological order, with dates, the divisions into which general history is divided.
2. When and where lived what is known as the "historic race?" Give its subdivisions.
3. Name the authors you have read on Roman history. English history. Give a brief account of the founding of Rome.
4. Under what Roman ruler came the birth of Christ? Contrast the character of Constantine the Great and Nero. Describe the end of Nero's life.
5. Give in chronological order the duration and dates of the periods of Roman history. At what date was Greece incorporated into the Roman Empire?
1
193
COMMISSIONER OF COMMON SCHOOLS.
6. When and why was the Roman army withdrawn from the island of England? What resulted to the natives of the island?
7. Name some of the events between the time of Alfred the Great and the Norman conquest.
8. Relate the great events at Runnymede.
9. Give a brief account of the doings of Henry the Eighth and George the Third.
ENGLISH LITERATURE.
1. State what you regard as the beginning of the English language' and name some of the writers of that day.
2. When and under what circumstances came the revival of learn- ing in England?
3. By whom was the first entire English translation of the Bible made? Name some of his other literary work.
4. Give briefly the history of the "Elizabethan English."
5. Give the leading characteristics of three of the following Eng- lish authors: Chaucer, Spenser, Shakspeare, Bacon and Milton, and name their masterpieces respectively.
6. What English author's name is a synonym for "rhetorical ele- gance?" Quote from him.
7. When began American literature and who were among the first writers?
8. Name five of the leading modern American poets, and give your reasons for so classing them.
9. Outline your reading of American literature.
LATIN.
1. Translate: Progredior portu, classis et litora linquens, sollemnis cum forte dapes et tristia dona ante urbem in luco falsi Simoentis ad undam libabat cineri Andromache, Manisque vocobat Hectoreum ad tumulum, viridi quem caespite inanem et geminas, causam lacrimis, sacraverat, aras.
2. Parse italicised words.
2. Translate: Helvetii cum omnibus suis carris secuti impedi- menta in unum locum contulerunt; ipsi confertissimi acie, rejecto nostro equitatu, phalange facta, sub primam nostram aciem successerunt.
4. Parse: Secuti, impedimenta, confertissima, rejecto, phalange.
13 S. C. C. S.
194
ANNUAL REPORT.
5. Translate: Cæsar ad Lingonas litteras nuntiosque misit, ne cid frumanto neve alia juvarent; qui si juvissent, se eodem loco, quo Helvetios, habiturum. Ipse triduo intermisso cum omnibus copiis eos sequi coepit.
6. Where is habiturum found and upon what does it depend? What is the case and construction of Helvetios? What is the force of
. ui si juvissent? What is the object of habiturum?
RHETORIC.
1. Give a full definition of rhetoric and a simple outline of its divi- sions.
2. What general directions would you give a class of beginners in the study of rhetoric?
3. What is the value of the study of rhetoric, as compared with grammar, in the study of literature?
4. Define style, and show how the word came into use.
5. Define "periodic sentence" and "loose sentence," and give their advantages and their disadvantages.
6. Give such quotations as you my remember to illustrate the fol- lowing figures of speech: Metaphor, simile, irony, personification and hyperbole.
7-8. What are the essentials of an oration? An argument?
9-10. Give rhetorical analysis of the following: Now the bright morning star, day's harbinger,
Comes dancing from the East, and leads with her The flowery May, who from her green lap throws The yellow cowslip, and the pale primrose.
PHYSIOLOGY.
1. Describe the capillaries. How are they fitted to irrigate the tissues?
2. Describe the valves of the heart and their actions.
3. Why is the pulse lost in the capillaries?
4. Name the parts through which the air passes to the lungs.
5. Describe the several functions of the liver.
6. Explain the working of the different classes of joints.
7. What is a reflex action?
8. 'Name the different parts of the eye in their order and explain function of each.
195
COMMISSIONER OF COMMON SCHOOLS.
9. State the effect of alcohol: a, on heart; b, on circulation; c, on brain.
10. What instruction do you give in hygiene?
LOGIC.
1. What is Logic? Explain the use of the terms object and subject, objective and subjective, objectively and subjectively as applied to that about which the mind thinks. Distinguish between intuitive faculties and dis- cussive faculties.
2. When is a judgment said to be universal? Give an example. When is it said to be particular? Give an example.
3. What is a categorical judgment? Give an example. What is a hypothetical judgment? Hypothetical judgments are of what three classes? Give an example of each.
4. What is immediate inference? What is mediate inference? Give an example.
5. What is a syllogism? Give an example. In your syllogism, which is the major premise? The minor premise? The conclusion?
GEOGRAPHY.
1. Show by diagram the great circle of illumination on December 21.
2. What is the present condition of the earth's interior, and what are the effects of this condition? Give reasons.
3. Name and locate the predominant mountain system of each of the grand divisions, and the principal river system of each.
4. What are the leading wheat growing countries of the world?
5. Describe the leading forms of government of the world and give an example of each.
6. What nations own islands in the West Indies? Tell which belong to each.
7. On what bodies of water would you sail in going from Trieste to Chicago by water?
8. Name a characteristic animal of Australia. Of South America. Of India. Of Africa.
9. Of what is each of the following cities the capital: Tokio? Constantinople? Brussels? Copenhagen? Olympia?
10. Name the States that touch Lake Michigan and give the capital of each.
196
ANNUAL REPORT.
CIVIL GOVERNMENT.
1. What are the three branches of our national government? What are the functions of each? In what respects do two of these departments overlap each other with respect to their functions?
2. What is meant by the privilege of habeas corpus? What is meant by ex post facto laws? What is meant by "bills of attainder?"
3. What body has the right to impeach United States officers? What body tries the impeachments? How large a vote is necessary to convict in impeachments?
4. In what two ways may amendments to the Constitution be pro- posed? In what two ways may they be ratified? How many amend- ments have been ratified, and to what people do the last three apply?
5. What do you understand by "tariff for revenue only?" By "protective tariff?" What do you understand to be meant by the expres- sion: "The free and unlimited coinage of silver?"
POLITICAL ECONOMY.
1. Give a complete definition of political economy, and name the general divisions of the subject.
2. Give clear distinctions between value and utility, between money and currency, and explain what you regard as the base of wealth.
3. Assign reasons for or against the financial policy pursued by Congress during the Civil War.
4. Name some of the advantages and disadvantages of the division of labor.
5. What is meant by a mixed currency? What are its advantages? Disadvantages?
6. What must regulate an issue of paper currency to be safe? Give historic or other reasons?
7. What effect has education on the laboring classes?
8. At the close of the Civil War the national debt was $2,300,- 000,000. Give your theory of the best way, both as to time and manner, of paying off the debt.
9. Name the authors you have read on political economy, and give their characteristics.
GEOLOGY.
1. Name the leading writers on geology and give a list of their most important publications.
2. State in full the arguments in support of the theory of the earth's central fluidity.
197
COMMISSIONER OF COMMON SCHOOLS.
3. Show that metamorphic rocks were stratified, and not igneous.
4. Name the several formations found in Ohio; give their location and economic value.
5. Give a full account of the carboniferous formation in the United States; the distribution and extent of the several coal areas; describe the several varieties of coal; give some account of the methods of mining coal, and the value of yearly output.
ZOOLOGY.
1. Give some account of the life of Darwin; the name of his most important publication; the line of argument advanced.
2. What are the distinguishing characteristics of vertebrata; of articulata; of protozoa?
3. Explain instinct and habit as found in animals. .
4. What do you mean by the term fauna? Why should the fauna of Europe differ from that of Africa? Why should the fauna of the At- lantic coast differ from that of Ohio, Colorado, Texas and Utah?
5. Select some animal with which you are well acquainted:
(a) Give its zoological classification.
(6) Show in what respects it differs from other species or genera.
(c) Give an account of its development.
(d) State its distribution and habit.
(e) Is it a native or an introduced species? If introduced, when, by whom, or by what agency? Have its characters changed?
PSYCHOLOGY.
1. Define psychology as a science.
2. Give such an outline of the subject of psychology as you would elaborate before a class of beginners.
3. Distinguish between soul and spirit, and explain the relation- ships between the human spirit and the body.
4-5. What are sense-perceptions ? Acquired perceptions?
6-7. Is conscience a faculty ? If so, to which of the other faculties is it more nearly related ?
8-9. Into what classes do you divide the intuitions ?
10. State what you have done to acquaint yourself with the subject before you.
198
ANNUAL REPORT.
BOTANY.
1. Describe a typical flower, including a description of all the parts in their true order and their functions.
2. Describe a leaf; make drawings of its several parts.
3. Trace the development of a plant from the seed, naming the sev- eral stages.
4. Compare growth in exogens with that in endogens.
5. Give a careful description of underground stems.
6. Explain the flow of sap.
7. Explain the growth of roots.
8. Describe the process of fertilization in plants.
9. Describe in full a species from the genus Ranunculus.
10. Mention the character of the rosacea, the leguminosæ and the liliaceæ.
PHYSICS.
1. How would you illustrate to a class the properties of impenetra- bility and inertia ?
2. Find the length of a pendulum that will vibrate 5 times in 4 seconds.
3. Find the pressure on one side of a cistern 2 m. square and 4 m. high, filled with water. How would you illustrate to a class the upward pressure of liquids ?
4. Give two illustrations of each class of lever, and state the law of the pulley.
5. A ball weighing 970 grains, weighs in water 895 grains, in alco- hol 910 grains; find the specific gravity of the alcohol.
6. What apparatus would you suggest to illustrate the subject of , light?
7. Upon what principle does the process of distillation depend ? Define latent and specific heat.
8. A liter of air is measured at 0°c., and 760 mm .; what volume will it occupy at 740 mm., and 18°c .?
9. How does temperature affect the velocity of sound ? Upon what does pitch of sound depend? How can this be shown to a class ?
10. Define ampere, volt, and ohm. Explain fully electrification by induction.
CHEMISTRY.
1. How would you illustrate to a class the difference between a physical and a chemical change?
199
COMMISSIONER OF COMMON SCHOOLS.
2. What per cent. of nitric acid is nitrogen ?
3. Give the composition of air by volume and weight. How can it be shown that air is a mixture and not a chemical compound?
4. How would you prepare chlorine for experimental purposes ?
5. Indicate briefly the experiments you would make with carbon dioxide.
6. Describe the process of smelting iron ore, and explain the chem- ical changes.
7. How many liters of oxygen can be obtained from 10 grams of potassium chlorate when the barometer reads 750 mm., and the ther- mometer 25° ?
8. Represent the reaction in alcoholic fermentation.
9. What are bases ? What is a salt? What is meant by quantival- ues ?
10. Give the properties of sodium. Name its compounds, and give the formula for each.
ARITHMETIC.
1. A buys an article and sells it so as to gain 12} per cent. If he had bought it at 10 per cent. less, and sold it for $18 less, he would have gained $20. Find the cost of the article.
2. Divide 3 by 5 and explain as you would to a class.
3. (a) Reduce .68494 to a common fraction in its lowest terms.
(6) What part of .390625 is .05?
4. What per cent. of 10 pounds troy is 6 pounds avoirdupois?
5. A reservoir is 2.80 m. long, 1.50 m. wide, and 1.25 m. deep. Find how many liters it contains when full and to what height it would be necessary to raise it that it might contain 10 cbm.
6. How many per cent. above cost must a man mark his goods in order to take off 15 per cent., and still make a profit of 15 per cent? Give analysis.
7. On what per cent. of stock must an investment have been made from which $185.50 was derived yearly, and which, when sold out at 97, brought $5,141?
8. Find the interest due June 30, 1892, on a note dated March 30, 1887, for $1,800 with interest payable annually, at 6 per cent., when no interest has been paid.
9. A and B join capitals in the ratio of 7:11. At the end of 7 mos. A withdraws ¿ of his, and B } of his; after 11 months more they divide a profit of $10,092. What is the share of each?
10. A ball 3 inches in diameter weighs 4 lbs .; another ball of the same metal weighs 9 pounds. Find the diameter of the second ball to the nearest thousandths of an inch.
200
ANNUAL REPORT.
ALGEBRA.
1. Add
a b C
a-b b-c' c-d.
2. Multiply x4-18x24-80 x+++2x2-80
x4+18x2+-80 by
x4-2x2-80*
3. Simplify 3. 5 V 64a5 610 12 and 5 / 486a5m blon C.
4. A drover bought cattle for $1,350, and sold all but 20 for $1,000,
1 and gained $10 a head on those sold. How many did he buy?
5. x+y+z=12; x+y-z=2; x2+y2=z2; find the value of x, y and z.
GEOMETRY.
1. What is meant by an inscribed angle? How is it measured? Demonstrate.
2. Explain what is meant in geometry by similar, equivalent, and equal figures.
3. Prove that the side of a regular hexagon inscribed in a circle is equal to the radius of the circle. .
4. What is the difference between the perimeters of two lots of land, each containing an acre, if one is a square aud the other a circle?
5. Problem-To describe a circle in a given triangle.
6. How do you find the volume of a triangular pyramid? Explain geometrically.
7. Explain and illustrate the difference between a direct and in- direct demonstration.
8. Prove that the difference between the squares constructed upon two straight lines is equivalent to the rectangle of the sum and difference of these lines.
9. Deduce the rule for finding the convex surface of a cone.
10. State some of the advantages to be derived from the study of geometry.
TRIGONOMETRY.
1. What is the logarithm of a number? What is the base of a sys- tem of logarithms? In the common system, what base is used? If a number is an exact power of 10, what kind of a number is its logarithm?
2. What fundamental operations of arithmetic may be performed by using logarithms? Write the rule to perform each of these funda- mental operations by means of logarithms.
201
COMMISSIONER OF COMMON SCHOOLS.
3. Define sine, tangent, and secant. What is an acute-angled tri- angle? To what is the sine of an arc of 30° equal? Prove this. To what is the cosine of 30° equal? The tangent of 30°?
4. To what are the sine, cosine, and tangent of 45° respectively equal? Prove this.
5. In spherical trigonometry, what are Napier's circular parts? Write Napier's two rules for circular parts. When are two parts of a spherical of the same species?
ASTRONOMY.
1. Define the following terms: Azimuth, perigee, quadrature, aphelion, and radius vector.
2. Name the planets in order of their size, and give the number of satellites belonging to each.
0
3. How do you explain the inequality of our days and nights?
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