Declaration was read publicly in the Observatory in the State House Yard. It is supposed that the Liberty Bell was rung on that occasion, but even of this there is no record. The name of the janitor of the State House at that time was Hurry. Yours truly,

Philadelphia, March 17, 1886. Now who is Geo. Lippard? Napoleon, O.

ARITHMETICAL SIGNS.

THOMPSON WESTCOTT.

W. W. WEaver.

Is 6÷2X3=1 or 9? and, in general, does the usage of mathematicians make the matter uniform, whichever way it may be?

Miamisburg, Ohio.

THOS. A. POLLOK.

There is, perhaps, not absolute uniformity, but the tendency is to perform the operations in the order in which the signs occur, making the result in the case given 9 and not 1. It would be easy to avoid all ambiguity by the use of the parenthesis.-ED.

QUERIES ANSWERED.

Q. 8, p. 492.—A contributes $300 for 3 months, $400 for 3 months, $500 for 3 months, $600 for 3 months. B, $1,000 for three months, $900 for 3 months, $800 for 3 months, $700 for 3 months; 3 ($300+ $400-$500+$600)=$5,400; 3($1,000+$900+$800+$700)=$10,200. $600+$700-$1,300. $1,300-$1,040 $260, loss. A loses

2%, or $90; B, 17, or $170. $600-$90-$510, A's share; $700$170 $530, B's share.

Mt. Union College.

P. S. BERG.

Same result and nearly same solution by R. A. LEISY, A. B. CARMAN, and A. W. BREYLEY. JOHN OVERHULTZ gets the same result by a different solution. JOHN G. gets a different result which we think is incorrect.

Q. 9, p. 492.-Let x+y and x-y be the numbers; by the conditions of the problem, x2-2: 16y::3 5, from which x2=y2+48y, 4xy=80, or x2- =400; equating the values of x2, clearing of fractions, 12 and transposing, 514+483-2000=(y+10) (513—21o+201—200)= o;y= 10 and x—2. xy12, and x-y-8.

No positive integral numbers will satisfy the conditions of the problem. For the word difference use sum, and the positive integral numbers, 12 and 8, will satisfy the conditions of the problem.

"In solving such problems, results will sometimes be obtained which do not apply to the question actually proposed. The reason appears to be that the algebraic mode of expression is more general than ordinary language, and thus the equation, which is a proper representation of the conditions of the problem, will also apply to other conditions. Experience will convince the student that he will

always be able to select the result which belongs to the problem he is solving, and that it will be sometimes possible, by suitable changes in the enunciation of the original problem, to form a new problem, corresponding to any result which was inapplicable to the original problem."-7odhunter's Algebra.

New Madison, O.

LON. C. WALKER.

Q. 1. p. 535.—The chief objections to the alphabetic method of teaching beginners to read are that it is not in accordance with sound educational principles, and is therefore laborious and irksome both to teacher and pupil; and it wastes time. Children can be taught to read in a better way, in less time, and with better educational results. The only reason I can conceive why any teachers continue to use it is that they do not know the better way. R. C. P.

Q. 2, p. 535.—To teach pupils how to study is an important part of the teacher's work; but it is not an easy part, and it is not easy to tell on paper how to do it. It is one of those things about which it is not possible to lay down absolute law. Individual pupils must be studied, as a physician studies each case he is called to treat. The previous oral instruction the pupil has received should be a preparation for the study of books. The way in which recitations are conducted will greatly affect the pupils' study. Perhaps a majority of pupils will need little more of help or direction in study than what they will get from well conducted recitations. But there will usually be a portion of the class requiring special attention. Sometimes it may be well for the teacher to study a lesson aloud in the presence of the class; and still there will be individual cases to be studied-individual difficulties to be found out and the remedy applied. Some will be found spending their force in memorizing the language of the lesson without thought; others will lack application and persistence and will need to be held down to the work. The subject lies near the heart of the teacher's work; no scheme or device can avail much, without the wisdom and personal power of a good teacher. L. B. S.

Q. 3, p. 535.-The best experience teaches concerning communication between pupils in study hours that all teachers cannot manage it in the same way,—indeed some cannot manage it at all; neither prohibition nor regulation avails for them. It requires a strong teacher to tolerate and regulate. One of the best schools the writer ever saw was one in which very little was said or done about whispering. The pupils had a good deal of liberty, the teacher making it a chief concern to see that every pupil had plenty of work to do, and that he did it as well as he was able. All things con

siderered, it is best for the average teacher to prohibit commnnication between pupils in study hours. I have given my opinion.

C. D.

Q. 4, p. 536.-The International Date Line is a line at which dates must be made later by one day when crossing it from east to west, and earlier by one day when crossing it from west to east. It is a very irregular line located mostly in the Pacific Ocean, and extends from pole to pole. Beginning at the North Pole, it passes Cape Lopatka and the Kurile, Japan, Jesso and Niphon Islands, and enters the China Sea. It then passes south just west of the Philippine Islands, but keeps east of Palawan Islands. This is its most western point, being 116° east longitude. It then takes a south-westerly course passing through the Soloo Islands. Thence it passes east nearly parallel with, but just north of the equator to a point 165° east longitude, just north of Schank Island; thence southeasterly through Navigator Islands to long. 268° west. Thence it turns South, keeping east of the Friendly, Tonga and Curtis Islands and west of the Society Islands, and thence south, crossing Chatham Island, to the South Pole. It is crooked because it is mostly located on the water, so as to prevent the conflicting of dates to the inhabitants living near the JOHN T. OMLor.

line.

Cassella, Ohio.

To the same effect are the answers of R. A. LEISY and P. S BERG. Do not most navigators now change time at the crossing of the 180th meridian, tending to obliterate the crooked line formerly in use?

The following, received after the foregoing went to the printer, puts the matter very clearly:

The International Date Line is an imaginary line passing through the Pacific Ocean from one pole to the other, and dividing those regions with respect to their settlement from the east or from the west. We may suppose that the day begins at this line; hence, when it is Sunday to the east, it will be Monday on the west. Imagine the sun to stand directly over this line. It will then be, let us say, Thursday noon. As the sun moves to the west, this noon point will be carried around the earth, and it will be Thursday noon in succession to Asia, Europe, the Atlantic Ocean, America, and the Pacific Ocean. But by the time the sun again approaches this line, it will have been almost a day since it was there before. It will, then, be Thursday noon until the sun reaches this line, when Friday noon will at once begin its trip around the world. Ships, therefore, crossing the Pacific Ocean from east to west are obliged to add a day to their calendar; those crossing from west to east must count one twice. Thus, if a ship is sailing

from Japan and reaches the International Date Line on Wednesday, the next day will be Wednesday also. If it is sailing from America and reaches the line on Friday, the next day will be Sunday (or the balance of the same day will be Saturday). For changing the days in this fashion, seamen commonly use the 180th meridian, instead of the line marked in the geographies. The International Date Line, as given on the maps, varies from the 180th meridian, because some places were not settled from the same side of the meridian. North of the equator, the International Date Line makes a great curve to the west of the Philippine Islands, because those islands were settled by the Spanish, who came from Mexico, and who, of course, brought with them the day to which they had always been accustomed. They did not understand why a change should be made in their day. For this reason it happens that the inhabitants of the Philippine Islands, in counting their time, are one day behind the time used in New Zealand, Australia, and other places that were settled from the west. Formerly, the Russians in Alaska were a day ahead of our time, because they had come around the world from the west, thereby gaining a day on the sun. A. B. CARMAN.

Dillie's Bottom, Ohio.

Q. 5, p. 536.—When the hour hand is at 7, the minnte hand is at 12; when situated in this way the hour hand is five minutes from six. Now if the hour hand remains stationary the minute hand must move 15 minutes to be within five minutes of four. The hour hand does not remain stationary, but moves and moves farther from seven, and the minute hand must stop short of fifteen minutes just the same distance that the hour hand moves farther from 7. If we represent the distance the hour hand moves by, then 24 will represent the distance the minute hand moves, and 26 will represent the distance both hands move, or 15 minutes. If 15 minutes, 2=131 minutes, the time past 7. D. G. BARNES.

Fairfield, O.

Mr. Barnes solves but one part of the problem. The other answer is readily obtained by taking of 25 minutes. P. S. BERG, R. A. LEISY and JOHN T. OMLER gave correct answers. The following is a good algebraic solution:

There are two conditions in this problem :

I. The minute hand has not yet reached 4.
Let x the time past seven.

Then 20-x-the distance of the minute hand from the figure 4, or the distance of the hour hand from the figure 6.

Then 20-x-the distance of the minute hand from the figure 4, or the distance of the hour hand from the figure 6.

I. At what point in a school course should a child begin to learn lessons from books? Is there any danger of carrying oral instruction too far?

2.

O. A. C.

In reading lessons, is it better to make corrections at once, or after the pupil has finished reading? Why?

C. T.

3. Is it unprofessional for an institute instructor to make direct application to an institute committee for employment?

R. W.

4. What are the fifteen decisive battles of the world?

F. O. R.

5. If will is used in the first person, or shall in the second or third, is the mode of the verb indicative or potential?

L. C. C.

6. I do not know who is in the garden. Parse "who."

L. C. C.

7. Vincent and Joy's Outline History of Greece says that the Olympic Games were celebrated every fifth year. Inasmuch as there were four years in each Olympiad, does it not follow that their statement is incorrect? A. B. CARMAN.

8. In what year did De Leon discover Florida ?

A. B. C.