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law of thermal expansions is sensibly the fully by hand, until the water bottle is same for all of them; of this, Hubbard's close to the surface, when it is let go, experiments afford satisfactory proof. In and the line allowed to run out without the table which gives the results of all a check. During its passage downwards his experiments, he takes the volume of the water courses freely through it, water at 60° Fahr, as his unit. In order being considerably assisted by the conito avoid much useless calculation, I have cal end pieces k, K. When the requisite been in the habit of reducing my results depth has been reached, the line is to the same temperature (15.56° C.), while, for a like reason, I have retained the specific gravity of distilled water at 4° C. as the unit. The choice of a common temperature, to which the results should be reduced, and of a unit of specific gravities, is a purely conventional matter; and in choosing the above-mentioned ones, in the first instance, I was moved solely by a desire to save calculation. For every water, however, there is one temperature to which it would be natural to reduce its specific gravity, namely, the temperature which the water had when in its place in the ocean; and in this sense all my results during the cruise have been reduced. Hubbard's table of the change of volume of a mass of sea water, with change of temperature, enables us very easily to reduce any observed specific gravity from the temperature of observation to any other temperature, say 15.56° C.
Collection of Sumples of Water.The water from the bottom was usually collected in the so-called “slip" water bottle, which has been described by Professor Jacobsen. Water from intermediate depths is obtained in an instru- checked again at the same mark, and ment represented in section in Fig. 6. It finally hauled in altogether by the donis made entirely of brass, which, how- key engine. When the line is hauled in ever, might advantageously be nickel. at first
the flap p falls down into a horiplated. It consists of a cylinder a, ter- zontal position, when it is caught by the minated at both ends by similar stop movable piece of brass F, which moves cocks B B, which are connected by the around an axis f, and is supported on rod c. This rod carries, near its upper the side opposite to E by the rodo, extremity, a piece of stout sheet brass D, which rests on the spiral spring h. The 10 centimeters long by 15 broad, soldered water rushing past D, when thus in a to the casting E, which is movable about horizontal position, exercises a sufficient the axis e. The function of this part of pressure upon the rod to close the stop the apparatus will be more easily ex- cocks B, B. When the speed with which plained by describing the manipulations the bottle is hauled through the water is necessary when collecting water. increased, the pressure on d becomes so
When intermediate water is to be ob- great, that it overcomes the tension of tained, the water bottle is firmly attached the spring h, and E passes the catch v, to the sounding line, which carries at its when the rest of the journey upwards is end usually a lead of 56 lbs. or 1 cwt.; the performed with the flap, D, hanging stop cocks are then opened, giving them, down, and therefore offering the least with the rod c, the position represented in possible resistance to the water, The the figure. The line is then lowered care-l object of at first hauling in only a couple
of fathoms or so, and letting the line go prussiate of potash was sunk in the lake, again, is to insure the cocks being closed. until the surface of the water was on a For, supposing after the first hauling in level with the upper stop cock when the they were not quite closed, by letting the stop cocks were opened, and the lime let instrument descend through the water go. On being brought up again the the flap D gets itself again, and, on heav- contents were treated with the solution ing in, it shuts down the stop cocks, of perchloride of iron. It was found which were before but partially closed; that, when the bottle had been sunk to or, if they were closed before, it only a depth of a fathom and a half, the water shuts them the tighter. When the water had been entirely changed, the iron bottle has been brought it is only neces- solution being wholly without action on sary to substitute for the lowermost it. We may be certain then that the brass funnel a small nozzle, when the water which we obtain by this means is water may be tapped into any vessel an average of the last two fathoms destined to receive it. This done, the bot- through which the bottle has passed. tle may be at once lowered to any other The weight used as a sinker should be required depth, much time being spared chosen so as to impart sufficient velocity by not having to detach it each time. At not to lose time unnecessarily over the the upper end of the bottle a small operation, and, at the same time, not to spring safety valve, I, is introduced, in give an excessive velocity at the depth order that the considerably denser water where the water is to be collected, befrom below may be able to make room cause the rate of change of water defor itself as the surface is approached. pends on the friction of the water inside In order that the instrument may prop- the bottle, and so on the velocity of erly do its work, it is evident that, first, descent. In practice, for depths over the stop cocks should be so stiff that the 100 fathoms, a weight of 112 lbs. was weight attached to their levers be not used, and for depths from 25 up to 100 sufficient to close them; and, secondly, fathoms, a weight of 56 lbs. was used. the spring should be so strong as to For less depths the weight of the bottle ensure the shutting of the cocks before itself was sufficient. The velocity of it itself gives way. These conditions are descent at the depth where the water is secured by the following means of ad- to be collected should not exceed 12 feet justment. The stop cocks can be made per second. The mean velocity for the stiff in the usual way, by lightening the interval between 75 and 100 fathoms screws which screw the “keys ” in the from the surface was, with 66 lbs., nine bands; the tension of the spring u can feet, and with 112 lbs. eleven and a half be increased or diminished by means of feet per second. & screw at the lower end of the tube con When once let go, it is essential that taining it; and the mobility of the stop the line should run out to the required cock can be regulated by means of the depth without a check; it is then, howscrews m, m. Although from this descrip- ever, immaterial, as far as the water tion the operations of adjustment may bottle is concerned, what interruptions appear complicated, it is, in fact, practi- occur in heaving in. The fulfillment of cally very simple. After the first time the condition of running out without a of use it is rare that any further adjust- check never presented any difficulty on ment is required than a turn of the board the “Challenger," depending as it screws M, M.
The diameter of the aper- does on the care of those who take the tures at either end is necessarily smaller line. When, however, by accident a than that of the cylinder ; it is, there- check does occur, the line is stopped, and fore, impossible for the water in it to the water bottle brought up again, reset, be entirely changed while descending and sent down again. In order to utilize through a distance equal to its own any such accidents, it is usual to take length. It became a question, therefore, the water from the greatest depth first; for experiment to decide what actually then, if a check does occur, it may occur was the rate of change of water. To this at one of the desired intermediate end a few experiments were made in a depths, and so no time would be lost. In fresh water lake. The bottle being designing the water bottle, it had been filled with water containing some yellow my intention to use it not only for collect
ing water, but also as a flask, so that the waters, but there is no reason why it atmospheric gases could be boiled out of should not be used for bottom water; it without transvasing the water. In indeed, where the sounding lead does not practice, however, I have not been able weigh over 1 cwt., it is frequently used to get air-tight stop cocks, besides for this purpose. In the case of deep which, it would make an inconveniently soundings however, where a weight of large apparatus in a very small labora- three, and sometimes four hundred tory. I have spoken of this water bottle weight is used, the “slip” water bottle as being only used for intermediate is always preferred.
MOMENT OF INERTIA OF PLANE FIGURES OF ANY FORM.
The moments of inertia of figures of Then: simple geometrical form are most readily
a, found by integration. Those of irregu
; or, x,=h lar figures, such as a rail section, can be Y,
(a). determined by graphic methods alone.
a,' The following simple general method Y, h
; or, k, =h
y. is believed to be entirely new.
and so on. Suppose that the moment of inertia of the trapezium abcd about any axis XX is trapezium about XX is 8(,'y,')=hE(x,'y,)
Now the moment of inertia (I) of the required. Draw any ordinates 2; 2,, ... but (a,y)=Y.E(<,') of the trapezium and produce them as shown. Draw any line ra perpendicular of gravity of the figure rsq from XX.
Where Y is the distance of the center to XX. Let y, y, ... be the respective Hence calling A the area of the figure rsq perpendicular distances of 2, 3, ... from XX, and let h be the perpendicular
I=h.Y.A. height of the trapezium. From r set off To determine I, therefore, it is necesr3 equal to any ordinate a,; join 3q cut. sary to know the area of rsq, and also ting 2, produced in 3'. Repeat the pro- the position of its center of gravity. cess for all the other ordinates x,, x,, So far the construction is of course an, ... (obtaining the points 1', 2', 4'...) perfectly well known. finally make rs=ab.
Now, make rt=h and draw tv perpen. Let x,',a,', ... be the ordinates of 1', dicular to XX, and cutting the produced
measured from ra; i.e., æ,'=1,1'; ordinates in 1", 2"...; join any of these æ,' =2, 2', etc.
points; e.g., 2"' to 9 and draw 2'0 par
allel to 2"q. Call the distance 2,0, x," But (=the area of the figure and set off 2,'' horizontally from 2", thus tpv=A' and 3(x,y,°)=I. Hence obtaining the point 2,". Repeat the con
I=A'.h. struction in the case of a,', æ
Since h is known it is merely necesobtaining the ordinates
sary to obtain the area of the figure tpv. the points 1,", 3,", ...; finally draw sn This can be done by cutting it up into parallel to tq and make tp=rn.
approximate trapeziums, or very conThen:
viently by a planimeter. 2,"
The curve sg, which need not, of i, or, x, h
course, be drawn, is evidently a parabola.
The method is perfectly general and Similary x," Pand so on, but from (a) can be applied with equal facility to h
figures of all forms with any positions of ; , etc.
the axis XX, and its great simplicity will h h
be appreciated by any one who tries it. 1
The construction requires very little Hence ma
more time than the ordinary one, and
when completed, it remains merely to 1 x,y
find the area of a figure instead of an ha
area and a center of gravity.
THE GASKILL COMPOUND PUMPING ENGINE.
BY JOHN W. HILL, M. E. The Gaskill pumping engine is a new quarters on the fly wheel shaft mounted design of compound engine for city in bearings on the gallows frame overhead. water supply, built by the Holly Manu The contract between the City of facturing Company, of Lockport, N. Y., Evansville and the Holly Manufacturing the first specimen of which was fur- Company provides for “two sets of nished the City of Evansville, Indiana.
duplex pumping engines, each of four By the courtesy of the trustees I am millions (4,000,000) gallons capacity each permitted to publish the following pre- twenty-four (24) hours at a piston speed liminary report upon the performance of of one hundred and eight (108) feet per the engines:
minute." COMMITTEE ON WATER WORKS:
With engines pumping direct into the
distributing mains, it is impossible to GENTLEMEN—Acting under your in- measure the water delivered through the structions, in behalf of the City of force pipe by any of the usual methods, Evansville, I have made test trials of the and as the supply is drawn from the engines recently erected in your pump- river (Ohio) through long lines of sucing house by the Holly Manufacturing tion pipe connected to the suction of the Company, of Lockport, N. Y., for your pumps, and subject to wide differences city water supply, and have to report to of head, it becomes practically impossiyou thereon as follows:
ble to measure the water on the suction The engines, two in number, are of side of the pumps. I have therefore the compound condensing type, with adopted the only convenient method for cylinders set parallel, and centers separ- determining the capacity of the engines, ated eight feet. The high pressure cyl- that of calculating the discharge and inder has a diameter of twenty-four (24) deducting therefrom a minimum slip. inches, and the low pressure cylinder a The data for this purpose were taken diameter of forty-one (41) inches. Each by myself in the presence of your piston has a stroke approximately thirty- superintendent (Roberts) and a represix (36) inches. The pistons of each sentative of the Holly Manufacturing engine are connected to cranks set at Company, and are as follows:
Engine No. 1:
2(18' X.7854)-(3.422' x.7854) X 35.967 H.P. cylinder pump piston, diam., 17.98 ins.
3.376 L.P. 18.00
=77.811 3.422 HP.
stroke,“ 35.965 gallons, calculated capacity of the pump L.P.
35.985“ worked by the piston of the L. P. cylin
der, per revolution, and aggregate calcuFrom which I estimate the capacity of lated capacity of both pumps, per revoengine No. 1 as
lution, 2(17.98* X.7854)-(3.376' X.7854) X 35.965
155.693 gallons. 231
mean stroke in feet of both
pumps is gallons, calculated capacity of the pump worked by the piston of H. P. cylinder
=2.9995 per revolution, and
2 x 12 2(18* X.7854)-(3.422 X.7854) X 35.985 corresponding to
108 x 60 x 24
2.9995 gallons, calculated capacity of the pump worked by the piston of the L. P. cylin- revolutions per day of twenty-four hours der, per revolution, and aggregate calcu- at "contract” piston speed of one hunlated capacity of both pumps, per revo- dred and eight (108) feet per minute, lution,
and capacity with an estimated slip of 155.503 gallons.
four (4) per cent. of calculated disThe mean stroke in feet of both charge, pumps is
155.693 x 25932.6 x.96=3,874,628 gallons. 35.965 +35.985 =2.9978
The contract provides that the duty 2 x 12
shall be eighty millions (80,000,000) foot corresponding to
pounds, per one hundred (100) pounds 108 X 60 X 24
of coal burned under the boilers, with =25938.01
an evaporation from the temperature of 2.9978
feed of nine pounds of steam per pound revolutions per day of twenty-four hours of coal; and that the duty shall be estiat "contract” piston speed of one hun- mated from the calculated discharge of dred and eight (108) feet per minute, pumps per revolution, the revolutions of and capacity with an estimated slip of engine during the trial, and the total four (4) per cent. of calculated discharge, head pumped against as the numerator 155,503<25938.01x.96=3,872,101 gallons of a fraction; the denominator of which
shall be the net water delivered as steam Engine No. 2:
I to the engine divided by nine hundred H.P. cylinder pump piston, diam., 17.99 ins. ' (900). “The weight of water pumped
to be taken at 8.34 pounds per gallon." L.P.
“Each engine to be operated continuH.P.
stroke“ 36.023 lously for twenty-four (24) hours for duty L.P.
35.967 “ trial.” From which I estimate the capacity of
The duty trial of engine No. 1 com
menced at 11.15 a. M., January 27th, and engine No. 2 as
terminated at 11.15 A. M., January 28th. 2(17.99* X.7854)-(3.376' X.7854) X 36.023
The counter reading at beginning
1392 =77.882 And, at end of trial, was....... 27762 gallons, calculated capacity of the pump Difference-revolutions...... 26370 worked by the piston of the H. P. cylinder, per revolution, and
The head pumped against in feet, was: