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them to make out their application. If I find that they are very poor writers-not only in their penmanship, but in their general way of making out the papersthey are deficient, they are not capable of 'becoming very good firemen, and I tell them so at once, and generally they will leave the roundhouse. With very few exceptions, when they come to make out their papers, while their writing may not be what would be called fine penmanship, it is good writing, and everything looks as though they knew their business, and I give them an opportunity. But if I find, after a few weeks or months have passed,

work that we have had in previous years, they have not had a collision, have never had a wheel off the track from their own carelessness.

But this spoils my wipers; they are all crazy to get out, and for that reason I am very greatly hampered for men to wipe the engines. But as far as promotion is concerned, when I can find out the traits of character of a man I can tell whether he is going to make a successful fireman or not. Sometimes a man's disposition is such that he is an unpleasant man to do business with. You can not get along with such men. You will find that just

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Fig. 15. FREIGHT TRANSPORTATION AFTER THE YUKON IS FROZEN

they do not know anything about an engine, when you tell them to go and wipe a driving box they go and wipe off the drawhead on the back of the tender, I tell them they will not do. Some of the men that I have employed during the six years I have been in Minneapolis, have become excellent engineers.

I have been compelled, on account of the scarcity of men, within the last four or five weeks, to take the firemen that are down thirty-seven numbers below the last one that has been examined, and put them out running engines, and I would state, as I stated to our superintendent a few days ago, that these young men have shown a better record than the old engineers, and while we have had triple the

as necessary a qualification as anything else in making good engineers or firemen. And I think there is a great value in the suggestion that one gentleman has made here tonight concerning the application of phrenology in the selection of applicants for the position of fireman.

MR. FOQUE: Before this discussion is closed, I wish to endorse Mr. Lynch's remarks, and add that it is my firm belief that the principal thing is to measure a man's head. I do not think it makes much difference whether we promote a fireman from the position of wiper or machinist-helper or machinist apprentice. It is not altogether the ability of a man to get out of a scrape that makes him valuable. Some men are apparently born

to keep out of trouble, while others are continually having little annoying things happen. The former are much to be preferred to those who are all the time having little troubles, but who show a nice ability to fix them up afterwards.

MR. BIRSE: I would like to ask some of the members if they have ever had any experience with making firemen out of brakemen. That was advocated with us, but it has not been very successful. We had a few that went to the position of

fireman and have turned out to be very good men. I think we can get very good firemen from the ranks of the brakemen if they have got a good education. I would like to hear from some of the members on that question.

MR. LYNCH: It is a common practice nowadays for firemen to look for a job braking. The engines are so large and the brakeman's work is so light that they prefer braking to firing.-Northwest Railway Club.

Smokeless Firing

By Ed. E. Sheasgreen

Th' ol' man lighted his dudeen
An' squeezed it in his gums between
Then cussed an' raved at his machine-
Th' pointer was a laggin'.
His lilacs stood out from his chin;
His greasy face got black as sin;
While his poor fire boy's hide got thin
Twixt shovelin' an' twixt naggin'.

"See here, you chump, look at th' steam!" Howled poor old dad in fearful mien. "Put on th' blower! "T does surely seem You don't know how to fire!" "Well, now ol' boy, jest hol' yer rail, Yer slippin' bad; She sure won't fail With smoke that's white." Thus whispered Dale

Too dead to shout with ire.

"I'm firin' her jest as our T. E. Explained it when he last saw me; I'll bet an X no smoke you see

No matter 'bout th' steamin'! Why it's no trick ter keep 'em hot. Jest put one scoop full on a spot Where grates 're showin' up a lot

Yo' kinder ketch m' meanin'?

"An' then yo' twist yer scoop aroun,
An' if the pop should start ter soun',
Why then jest drop a damper down-
Oh, say, it's sich a frolic!

No matter if we have one car,

Er three miles long the freight trains are, Jest fire th' same-it's as easy, sar, 'S to laugh when full o' colic.

"Why from our present new G. M.,
Down to our honorable ol' M. M.,
With clerks an' artists followin' 'em,
They all know how to do it.

An' even those who boss the schools,
An' mail freak questions from their
stools,

All say that we're a pack o' fools

An' don't know how to do it.

"Perfessers who have never been Jest once inside the cab; an' men In stores, an' even kids 'll len'

Their help about th' bizness. An' I suppose some demons, too, That watch while we're a smokin'

through,

'Re thinkin' they'd know how to do

'Re chuck full o' this quizness.

"An' some o' you who tossed th' wood
Back in th' days o' Robin Hood
Yo' think yo' know jest how we should
Burn coal without it smokin'.

I have ne'er yet th' bosses seen,
Er clerks, er artists in between,
Ner you, ol' whiskers, cussin' mean,
Once do these laps-no jokin'!
"You make me weary, every one!
If firin' a cruiser 's sich holy fun,
With trains o' twenty hundred ton,

Why don't you all go firin',
An' not be tellin' how to do?
"Twould help th' temper o' those like you,
An' help these tonnage freighters

through

For a bosship through yer 'spirin'."

Again th' ol' man lights his pipe;
The fire boy hits th' door a swipe,

Th' smoke rolls out now black an' ripe-
Th' pop begins to simmer;

While far across th' starry sky,
All through th' night, th' clouds fly,
Until at last, "On Time," their eye

Sees terminal light aglimmer,

in Arithmetic

Copyrighted 1901 by the Author.

Mensuration

W. S. Carter

133.-The Circle and its Properties. A Circle is a plane surface bounded by a uniform curved line, every point on which line is equally distant from a common point within.

(Fig. 24 illustrates six circles.)

The Circumference of a circle is the curved line which bounds it.

(In Fig. 24 the curved line I m n o is the circumference of circle 3.)

The Center of a circle is a point within that is equally distant from every point in the circumference.

(In Fig. 24 the point b is the center of circle 1; the point s is the common center of the circles 3 and 4.)

An Arc of a circle is any part of the circumference.

A Radius of a circle is a straight line from the center to the circumference. (In Fig. 24 a b and p b are radii of the circle 1. The plural of radius is radii.)

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A Diameter of a circle is a straight line passing through the center and terminating at both ends in the circumference.

(In Fig. 24 the line er h is the diameter of the circle 2. A diameter divides both circumference and circle into two equal parts.)

A Chord of a circle is a straight line that terminates at both ends in the circumference but does not pass through the center.

(In Fig. 24 the line f g is a chord of the circle 2.)

NOTE.

The terms circumference, arc, radius, diameter and chord are also used to designate the length of such lines. The term circle is by custom applied to circumference, which is not accurate, as the circle is not the curved line, but the space enclosed by the curved line.

A Secant of a circle is a straight line which crosses the circle, intersecting the circumference at two points.

(In Fig. 24 the line c d is a secant of the circle 1. It will be noted that a chord terminates at both ends in the circumference, while both ends of a secant extend beyond the circumference.)

A Tangent of a circle is a straight line that touches a circle at one point only.

(In Fig. 24 the line ij is a tangent of the circle 1. It is customary to say that "the line ij is tangent to the circle 1.")

A Sector of a circle is a portion of a circle bounded by two radii and the subtended arc.

(In Fig. 24 that portion of the circle 1 which is enclosed by the two radii a b and p b and the arc a p is a sector of the circle 1. An arc that is enclosed of limited by two radii, or by a chord, diameter, etc., is said to be a subtended arc.) A Segment of a circle is a portion of a circle bounded by a chord and the subtended arc.

(In Fig. 24 that portion of the circle enclosed by the chord f g and the subtended arc is a segment of the circle 2.)

NOTE. A circle is said to be concentric to another circle when the two circles have the same center but different diameters, as in Fig. 24 the circle 3 is concentric to the circle 4. A circle is said to be eccentric to another circle when they have different centers, as in Fig. 24 the circle 5 is eccentric to the circle 6.

134.-Propositions Relating to Circles.

Prop. XXIII.-The circumference of a circle is equal to the diameter multiplied by 3.1416.

a

b

d

(There is no method by which the exact circumference of a circle may be determined, but approximately Prop. XXIII is correct. By inscribing a hexagon in a circle whose diameter is 2 inches, as in Fig. 25, we find that the perimeter of the hexagon is exactly 6 inches, that is, the perimeter of the hexagon is exactly three times the length of the diameter. In Fig. 25 the diameters a d, be and cfare each 2 inches, and the radii o a, o b, o c, o a, o e and of are each 1 inch. It is a fact that the six triangles formed in an inscribed hexagon are equilateral triangles, therefore, as ob equals 1 inch, and a b also equals 1 inch, a b+b c + c d +de+-ef+fa=6 inches. Now, if the circumference of the circle exactly coincided with the perimeter of the hexagon the circumference would also be 6 inches, but from the drawing it is evident that the

FIG. 25.

e

circumference is slightly more than 6 inches, that is, the circumference is slightly more than 3 times the diameter 2 inches. In Figs. 26 and 27 are polygons of 12 and 18 sides respectively, inscribed in circles. It will be noted that the greater the number of sides of the inscribed polygons the nearer the circumference of the circle coincides with the perimeter of the polygon. If we conceive an inscribed polygon of innumerable sides it is evident that the perimeter of the inscribed polygon will almost exactly coincide with the cir

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cumference of the circle. It has been determined that a polygon having 3,072 sides inscribed in a circle whose diameter is 2 inches has a perimeter of 6.28318420+ inches, that is, the length of perimeter is 3.141592 times the length of the diameter. This is considered to be sufficiently accurate for all practical purposes, in fact, only 4 decimal places are used, and it is said that "the circumference of a circle is equal to the diameter multiplied by 3.1416.") Prop. XXIV. The diameter of a circle is equal to the circumference divided by 3.1416.

(This proposition is the converse of Prop. XXIII.)

Prop. XXV. The area of a circle is equal to the square of the diameter multiplied by .7854.

(As in Prop. XXIII, this statement is only approximately correct, and has been determined by a similar course of reasoning, .7854 being one-fourth the circumference 3.1416.)

Prop. XXVI.-The area of a sector of a circle is in the same proportion to the area of the circle as the measurement of the subtended arc is to the measurement of the entire circumference.

(In Fig. 28 the area of the sector a o b is equal to 14 of the area of the circle because the arc a b measures 90°, and, therefore, is equal to 14 of the circumference. With the aid of a protractor (see Fig, 14, December, 1902) it may be determined that each subtended arc in Fig. 27, formed by inscribing a polygon with 18 sides, measures 20°. As every circumference measures 360° (see Art. 123, December, 1902) the area of each sector is equal to of the area of the entire circle, therefore, to find the area of the sector we first find the area of the circle and take such part as the arc is of the circumference.)

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