winds; contrary-the far wider term-is employed rather of the course or character of events, as running counter to one's expectations or designs, though we sometimes speak of contrary winds; opposite rather belongs to that which is widely unlike." Inimical and hostile belong strictly to personal character and feeling, the latter being the stronger term of the two. Allude, v., to make indirect reference to, to hint at.

Syn. to refer, hint, suggest, intimate, insin

uate.

Ant. specify, demonstrate, declare.

Syn. dis.: "To allude is indirect; refer is direct and positive." If we quote an author, for instance, not by name, but by description, style, or subject-matter, we allude to him; but if we point, specifically and plainly, to something he has said or written, we refer to him. The fault of reference is not obscurity, but inexactness; the fault of allusion is often its vagueness and indefiniteness; we say a wrong or inaccurate reference, a vague or obscure allusion. Hint, in the main, has to do with matters of knowledge; suggest, with matters of conduct. We receive a hint of danger, a suggestion how to avoid it.

Amend, v., to correct a fault or error, to improve, to make or grow better. Syn. correct, reform, emend, mend, rectify, improve, better.

Ânt.: spoil, corrupt, vitiate, mar.

Syn. dis. Amend, emend, and mend are really the same word, their common root being menda, Lat., for a blemish. In ordinary usage, amend means to better morally, while emend means to remove faults, chiefly literary blemishes. To correct is to bring into conformity with moral or artificial rule; to reform is to correct in a more continuous and lasting manner. To rectify means to set right or straight what formerly was wrong or false. "We amend our moral conduct, correct errors, reform our way of life, rectify mistakes, emend the readings of an author, improve our mind, mend or better our condition."

Animate, v., to give life to, inspire, inspirit, invigorate.

Syn.: cheer, enliven, inspire, embolden, exhilarate.

Ant. dishearten, depress, discourage. Syn. dis. Animate and inspire imply the communication of the vital or mental spark; enliven, cheer, and exhilarate signify action on the mind or body. The lower influence is expressed by the word animate, as "the soul animates the body;" the higher, more energetic, and finer faculties are said to be imparted by inspiration, as, to be inspired with a sublime courage or devotion. To enliven respects the mind; cheer relates to the heart; exhilarate regards the spirits, both animal and mental; they all denote an action on the frame by the communication of pleasurable emotions.

Apparent, adj., that may be easily seen, obvious, plain.

Syn.: clear, visible, manifest, evident, plain, seeming.

Ant.: dubious, hidden, inapparent, unobservable, real.

Syn. dis.: Apparent, as a scientific term, means seeming, as opposed to real; here we

deal with it in the sense of being clear, visible, in opposition to concealed or dubious. In the general sense, the synonyms of apparent agree in expressing various degrees in the capability of seeing; visible is the only one used purely in a physical sense; clear, plain, obvious, as well as apparent, are used physically and morally; evident and manifest solely in a moral acceptation. Obvious is applied to what we cannot help understanding; evident denotes what is easily recognizable as a fact or truth; manifest (lit. "struck by the hand") is that which is palpably plain, and exhibits itself without question.

Assent, n., act of admitting or agreeing to, consent, accord.

Syn.: consent, approbation, concurrence, agreement.

Ant.: dissent, disavowal, repudiation.

Syn. dis.: "Assent respects the judgment; consent respects the will. We assent to what we admit to be true; we consent to what we allow to be done. Some men give their hasty assent to propositions which they do not fully understand; and their hasty consent to measures which are very injudicious. Approbation is a species of assent; concurrence of consent." To approve is not merely to assent to a thing, but to signify that it has the support of our reason and judgment. Concurrence is generally used only of numbers, not of single individuals. Assent, v., to admit as true, to yield to, to agree to.

Syn.: to accede, acquiesce, concur, comply, accord.

Syn. dis.: "To assent is purely mental, and denotes a concurrence with approval as an act of the judgment; to acquiesce is to concur with what is said or done by another; to consent is to agree to act according to the will of another." Avocation, n., Lit., a calling off, a direction of the attention; a calling away from any business or work in which one is chiefly engaged.

Syn.: calling (by common but incorrect usage), employment, business, occupation.

Syn. dis. This word is often and wrongly confounded with vocation, which means one's steadily-pursued profession, business, or calling in life. One's avocations are the things that interrupt or call away from business or pursuit, the objects that occupy one incidentally. "The term avocation is properly used of the minor affairs of life, less prominent and engrossing than business, or such calls as are beside a man's duty or occupation in life." One's vocation may be to teach; one's avocations may be anything in which one finds relief from the drudgery and routine of teaching.

Beg, v., to ask earnestly, to solicit, to supplicate, to desire.

Syn. beseech, solicit, expect, supplicate, crave, implore, request, entreat, adjure.

:

Ant. insist, exact, extort, require, demand. Syn. dis. "To beg marks the wish; to desire, the will and determination. Beg is the act of an inferior; desire that of a superior. We beg a thing as a favor, we desire it as a right. To beg indicates a state of want; to beseech, entreat, and solicit, a state of urgent necessity; supplicate and implore, a state of abject distress; crave, the lowest state of physical want. One begs

Benignity, n., kind-heartedness, loving-kindness, graciousness.

"The king was desirous to establish peace rather by benignity than by the shedding of blood."

Syn. benevolence, humanity, kindness, tenderness.

Ant. harshness, malignity, churlishness.

Syn. dis. "Benevolence and benignity lie in the will; humanity lies in the heart; kindness and tenderness in the affections; benevolence indicates a general good-will to all mankind; benignity, a particular good-will flowing out of certain relations; humanity is a general tone of feeling; kindness and tenderness are particular modes of feeling. Benignity is always associated with power and accompanied with condescension; benevolence, in its fullest sense, is the sum of moral excellence."

Bent, "., disposition towards something, tendency, proclivity.

Syn. bias, inclination, prepossession, proneness, predilection.

Ant. indisposition, aversion, prejudice.

Syn. dis. These various terms denote a predisposing and preponderating influence on the mind. "Bent is applied to the will, affections, and powers in general; bias solely to the judgment; inclination and prepossession to the state of the feelings. The bent includes the general state of the mind, and the object on which it fixes a regard; bias, the particular influential power which sways the judging faculty. Inclination is a faint kind of bent; prepossession is a weak species of bias."

Between, prep., in the middle, from one to an

other.

"How long halt ye between two opinions?"—I. Kings xviii, 21.

Syn. betwixt, intermediate, intervening, and (wrongly) among.

Syn. dis. "In strict accuracy, between is used only of two. When there are more than two the proper term to use is among; but this distinction is not always, as it should be, observed. Between (from twain) is used in reference to two things, parties or persons; among, in reference to a greater number, as: There was a perfect understanding between the two leaders of the people, though there was great dissension among the rioters. Betwixt and intermediate signify between two objects; intervening signifies coming between; the former is applicable to space and time, the latter either to time or circumstances."

Blame, v., to find fault with, to express disapproval of.

Syn. reprove, reproach, upbraid, censure, condemn.

Ant. acquit, exculpate, exonerate, praise. Syn. dis. The expression of one's disapprobation of a person, or of that which he has done, is the common idea in the significance of these terms; but to blame expresses less than to reprove. We simply charge with a fault in

blaming; but in reproving severity is mixed with the charge. Reproach expresses more than either; it is to blame harshly. To blame and reprove are the acts of a superior; to reproach, upbraid, that of an equal; to censure and condemn leave the relative condition of the agent and the sufferer undefined. Blame, reproach, upbraid, and condemn may be applied to ourselves; reproof and censure are applied to others. We blame ourselves for acts of imprudence; our consciences reproach us for our weakness, and upbraid or condemn us for our sins."

Brace, n. (etymol.), a pair, referring principally to the two arms [F. bras; O. F. the arm, strength]. Syn. couple, pair. Syn. dis.: "Couple or pair are said of persons or things. When used for persons, the word couple has relation to the marriage tie; the word pair to the association of the moral union. * * When used for things, couple is promiscuously employed in familiar discourse for any two things joined together; brace is used by sportsmen for birds which are shot and supposed to be coupled. Brace signifies things locked together, after the manner of the folded arms, which on that account are confined to the number of two. Brace is sometimes employed of men, but then contemptuously." The term couple should never be employed for two, brace, or pair unless when referring to persons or things joined or linked together.

Calamity, n., a great misfortune or cause of misery, either public or private, but more frequently the former.

Syn.: disaster, misfortune, mischance, mishap, visitation.

Ant. blessing, boon, God-send.

:

Syn. dis. A calamity seldom arises from the direct agency of man; like visitation, it is a term sometimes used to denote providential infliction or retribution. In its general sense, it is a great misfortune or disaster; a misfortune is a great mischance or mishap. "The devastation of a country by hurricanes or earthquakes, or the desolation of its inhabitants by famine or plague, are great calamities; the overturning of a carriage, or the fracture of a limb, are disas ters; losses in trade are misfortunes; any minor misadventure is a mischance or a mishap." Calculate, v., to arrive at a result by an arithmetical operation of any kind; to compute, to reckon, to estimate.

:

Syn. compute, reckon, count, enumerate. Syn. dis. To calculate is the generic term; the rest are specific; computation and reckoning are branches of calculation, or an application of those operations to the objects of which a result is sought. To calculate comprehends arithmetical operations in general, or particular applications of the science of numbers, in order to obtain a certain knowledge; to compute is to form a numerical estimate, though it is applicable to magnitude. Count is etymologically another form of compute, but its signification is nearer to that of reckon: it is to reckon one by one, to add up the individual items. Estimate is to compute more generally, as to estimate the average or probable market value of goods, distance, and the like, in a rough manner. Enumerate is to tell the number by expressing the items, and is a process of speech rather than of arithmetic."

A

MAN rows a boat at the rate of five miles an hour against a river current of three miles an hour. How long will it take him to reach a point on the river bank four miles above his starting point?

He moves up-stream five miles every hour, and, at the same time, he moves three miles in the opposite direction. His movement with respect to the river bank is, therefore, but two miles an hour, up-stream, as we find by deducting from the five miles gained every hour the three miles lost. He will, therefore, reach the point in two hours, as he would do if there were no current in the river and he rowed at the rate of two miles an hour.

The Composition In solving this problem of Velocities we have performed an operation known in mechanics as the composition" of movements or of velocities. We have combined two velocities which have different directions and have obtained the resultant,' as it is called; that is to say, the single velocity, which is equivalent to the two existing simultaneously. In the case supposed there might have been a third movement to be taken into account. A strong wind would have moved the boat in one direction or another and would thus have affected its velocity with reference to the river bank. Indeed, the movements of a body are sometimes very complex; it may be moving in several directions at the same time; yet in all such cases the result is that it moves practically in some single, definite direction and with a definite velocity. How to determine this resultant velocity under. various circumstances, is the question we are now to consider.

they are in the same direction, to find the resultant we have only to add them together and take their sums. Thus, if this man were to row down-stream at the rate of five miles an hour, while the river flowed three miles an hour, he would, in effect, move at the rate of eight miles an hour with reference to the river bank. It is equally clear that when they are in opposite directions, as when this man rowed up-stream, we must take their difference for the resultant.

But suppose that the two velocities to be combined are neither in the same nor in opposite directions, but make an angle with each other? We will examine a case of this kind. A river flows from west to east at the rate of three and a half miles an hour, or 300 feet a minute. A man starts to row a boat directly across it, from its southern to its northern bank, rowing at the rate of 600 feet a minute. The problem is to find in what direction and with what velocity he moves in consequence of having these two independent movements; or we will make the problem a little more definite and will ask in what direction and how far from his starting point he will be at the end of five minutes?

We can solve this problem the more readily with the help of a diagram. Draw upon a sheet of paper, in a horizontal direction, a line of any convenient length, say three inches, to represent the direction and velocity of the current. Mark the left hand end of this line A, the right hand B. Consider A as representing the point at which the man starts; B indicates the point 300 feet east of A, to which he would be carried in one minute, if he allowed his boat merely to drift with the current. Now, according to the supposition he is not drifting, but is rowing northward. Erect at A a perpendicular line six inches long, to represent the course of the boat and its velocity, 600 feet a minute. Mark the upper end of this line C. C indicates the point at which the man would be after rowing one minute if there were no current in the river; but actually, while he has been rowing this distance of 600 feet the whole surface of the river has

moved eastward 300 feet, so that he will now be, not at C, but at a point 300 feet east of C. Indicate this fact by drawing from C, to the right, a horizontal line three inches in length, and mark the end of this line D. D indicates the point at which the man is at the expiration of one minute, as a result of the two simultaneous movements. The line CD is equal to and parallel with the line AB. A line drawn from B to D will be equal to and parallel with AC. Our diagram is, therefore, a parallelogram. Draw a line Draw a line diagonally from A, the point at which the man started, to D, the point at which he now is. This line, clearly, represents the direction in which he would have to row and the distance he must traverse to reach the point D from A, moving in a straight line, if there were no current in the river.

Furthermore—and here is the important point-it represents the line along which he actually has moved, since for every foot, every inch, which he moved northward in rowing he was carried eastward by the steady current a distance one half as great, so that at every instant during the minute he was at some point on this line. He arrived at the point D in one minute after leaving A. The line AD therefore represents the resultant of the two velocities represented by the lines AB and AC, respectively. As long as he continues to row under these circumstances he will move in the direc

same way, would still have been a parallelogram, and the diagonal drawn from A to D would still have represented the resultant of the two velocities. Thus, suppose that the boat had been rowed with the same velocity in a northeast direction. In this case we should have drawn the line AC of the same length as before, but sloping to the right at an angle of 45 degrees to the horizontal, to indicate a northeast direction. CD would still have been drawn horizontal, and therefore parallel with AB, and BD would still be parallel with AC. only effect of the change would have been to make the diagonal longer than before. That is, the resultant velocity would have proved to be greater than before. Had the boat been rowed toward the northwest, a similar construction would have brought out a resultant velocity smaller than in the first case.

Rule

From the study of this lowing simple rule for compounding two problem we get the fol

velocities and obtaining their resultant :

Represent the two velocities by two straight line being drawn from a point (A), at lines of lengths proportional to them, each which the motion is conceived to begin, in the direction of the velocity, which it represents. Construct a parallelogram by combining with these lines two others of the same lengths. The diagonal drawn from the vertex of the angle at A to that of the

find where he will be at the end of five minutes. Either we can prolong this line on our diagram to five times its length and measure the distance thus found, remembering that the diagram is drawn to a scale of one hundred feet to the inch, or we can measure the line AD and thus get the resultant velocity in feet, which we can then multiply by five. Or, if we wish to be more exact, we can calculate the length of the line AD geometrically. It will be found that the resultant velocity is, in this case, 670 feet a minute, nearly.

tion and the velocity of the resultant motion. Composition of When more than two veSeveral Velocities locities are to be compounded, begin by representing them by lines of lengths proportional to them, all drawn from the same point (A), each in the direction of the velocity which it represents. Compound any two of them by the method just given. Then compound the resultant obtained with a third, and if there is still another, compound the second resultant with this, and so on, until all of the lines have been used-have been made the sides of parallelograms. The last resultant is the resultant of all of the velocities taken together. Thus: Suppose that in our problem of the man and boat we had had to take account of a southeast wind blowing with a force sufficiently great to move the boat steadily toward the northwest at the rate of one hundred feet a minute. We

should represent this velocity by a line one inch in length drawn from A at an angle of forty-five degrees to the horizontal, sloping upward to the left, to represent a northwest direction. Then, having obtained the resultant AD as before, we should construct a second parallelogram, taking AD for one side and the inch line just drawn for another side. The diagonal drawn from A to the angle opposite it in this second parallelogram would represent the resultant of the three velocities. The extremity of this new diagonal and not the point marked D, would now indicate the position of the man at the end of the minute, as a result of the rowing, the current and the wind combined.

Polygon of Velocities

Our problem in this case was to find the position of the man at the end of one minute as a result of his having motion in three directions at the same time. A moment's thought will show that he would reach the same point if he moved to the same distances in the same directions at different times. Thus, let him move east 300 feet, then north 600 feet, then northwest PROBLEMS

HE following problems may be solved by drawing diagrams to scale and measuring as accurately as possible the distances to be found. The answers to be given next month, will be those obtained by calculation. See how close you can come to these

answers.

I. Find the resultant of two velocities, one of 50, the other of 80 feet a minute, a, when they are in the same direction, b, when they are in contrary directions, c, when they are at right angles with each other, d, when they make with each other an angle of 45 degrees, or one half of a right angle.

2. Find the resultant of the four following velocities: North, 40 feet a minute; northwest, 50 feet a minute, CURVILINEAR MOTION

N all of the cases thus far considered the movements have been in straight lines; the velocities have been uniform. The composition of two velocities, of which one is uniform, while

100 feet, and he will arrive at precisely the same point as though he had moved to these distances in these directions at one and the same time. This consideration gives us a second method of solving a problem of this kind. Beginning at a point A draw a line AB in the direction of one of the velocities and of a length which will represent that velocity on some convenient scale. From B draw a second line, BC, of a proper length and in the proper direction to represent a second velocity. In the same way represent a third by a line CD, and so on, until all the velocities have thus been consecutively represented by lines proportional to them in length and drawn in the proper directions, the lines joining one another. The end of the last line thus laid down will indicate the point to which the moving body would be carried in the given time if the movements were simultaneous. A line drawn from this point to the starting point, A, will, therefore, represent the resultant of the velocities. The irregular figure thus drawn is called a "polygon of velocities." The side last drawn, to complete the polygon, represents the resultant.

southwest, 20 feet a minute; south, 80 feet a minute. Solve by both methods.

3. Decompose a velocity of 100 feet a second into two component velocities of which one is twice the other. What are the two velocities?

4. A ship is sailing in a northeast direction at the rate of fourteen miles an hour. How fast is this ship moving due east; how fast due north?

5. A railway train is running past a station at the rate of 30 miles an hour 45 feet a second. A mail bag is thrown from it with the velocity of 15 feet a second, in a direction at right angles with the track. In what direction and with what velocity will the bag be moving when it strikes the platform of the station in what direction will it slide on the platform?

the other is accelerated, always results in a curvilinear motion. A familiar case is that of projectiles. A stone thrown from the hand, a ball shot from a gun, a jet of water issuing horizontally from a spigot, always describes a curved path. The