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Working this out by the tables we find P' to be 941b. Let it now be required to find the pressure P necessary to keep the wedge in its place when driven. In this case we have the frictions μ Q, Q aiding P, so that we must have P = 2R sin. (i φ).

From this last equation we see that as long as i is greater than, P has some positive value, and that consequently if P be removed the wedge will start from its position, since it requires the force P to keep it in its place.

If i be less than 6, or the angle of the wedge be less than 2P has some negative value, or a force acting in a direction opposite to that which forced the wedge into its position is necessary to extract it; the value of this force is given in the value for P' above, consequently if P' be removed the wedge will not start.

Now as a wedge to be useful should not start when the pressure is removed, it should be so constructed that its angle When of cleavage is less than twice the angle of friction. this is the case it will remain fixed in any position into which it is driven. It is this property which distinguishes the wedge and renders its ase so universal in the mechanical

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Or, in words, ten times the force required to produce the
pressure Q is expended in overcoming friction. We thus sec
that although the efficacy of the wedge is due to friction, still,
in this, as in every other case, friction diminishes the effects
of forces applied to machines.
We shall now pass to the dynamical theory of the action of
the wedge, and suppose that the blow is caused by a given
weight P falling through a given number of feet h. This
weight at the instant of striking the back of the wedge has
accumulated in it an amount of work or energy represented
by Ph, or, if be the velocity in feet per second of P at the
instant of striking the wedge, the number of units of work
stored up in it is represented by the well known formula P x
v2
v2
Now this energy is expended in over-
coming the tendency of the resisting surfaces to collapse, in
overcoming the friction, in compressing both the weight
itself and the wedge, and in giving motion to each.

since h 2g

2g

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Now,

sin. (+)

Since U2Q x D E, and U is a definite amount of use-
ful work, when DE is very small Q will be very great. This
accounts for the enormous resistances which the wedge can
overcome when driven by blows.
In the equation

Work employed = Ph,

it is clear that we can increase the work done by increasing
or by increasing ht, that is, by increasing the weight of the
hammer, or by increasing its velocity, but it is found in prac-
tice that a better result is obtained by increasing the velocity
than by increasing the weight. This has been accounted for by
supposing that a rapid blow causes a tremor of the sub-
stances, and momentarily destroys the friction.
I shall now conclude this article with the following
example:-

Ex. Express as a decimal 5

4

10

Here write down the whole number and numerator as a whole number, thus 5 and 4, counting the number of noughts in he denominator, one, then mark off che figure from the right as a decimal, thus, 54.

15

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Example 12.-The ends of an iron girder, 30 tons weight,
resting on two granite piers, are simultaneously raised by
means of wrought iron wedges, in the form of a right-angled alter their value, thus 1 remains equivalent to
These wedges are driven
triangle whose height is lin.
home by 25 blows each of a hammer weighing 14
and which is moving at the rate of 40ft. per second at the
instant of striking the wedge. Find how much work is ex-
pended on prejudicial resistances, including friction, &c.
The number of units of work developed by one hammer in
the 25 blows is equal to
40 x 40
2 x 32

written 100000, but if we add noughts to the left the value
is altered, thus 1 = but 01 =

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Now if there were no prejudicial resistances, this amount of work should have raised a weight of 12 times this number of foot pounds, or 105000 to the height of lin. (which is the height the girder is raised), but from the question each wedge only raises 15 tons or 336001b. to the height of one inch, therefore the work lost by friction, &c., is 105000 33600 = 71400lb. raised lin. or 5950 foot pounds, or about of the total work expended.

§ 33. 1

(To be continued.)

MATHEMATICS.
BY C. H. W. BIGGS.
CHAPTER III.

DECIMALS.

(Continued from page 58.)
Units.

In the number 1111 to the left of the vertical line above we observe that as the value of the tens, place tis ten times that of the units, and that of the hundreds ten times that of tens, and so on, conversely the value of the units' place is one-tenth that of the tens', one-hundredth that of the hundreds', and so on. Now, if we write digits to the right of the units' place, and agree that the law just noticed shall hold for the value represented by them, it is plain that the first to the right of the units will be one onetenth of the unit, the second will be one one-hundredth, and so on-i e., a series of ones written after the units' place will represent the fractions one

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I would have every one write what he knows, and as much as he knows, but no more; and that not in this only, but in all other subjects: For such a person may have some particular knowledge and experience of the nature of such a person or such a fountain, that, as to other things, knows no more than what everybody does, and yet to keep a clutter with this little pittance of his, will undertake to write the whole body of physicks: a vice from whence great inconveniences derive their original. Montaigne's Essays.

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The object of the invention is to dispense with a large portion of the ordinary clock-work gearing, with its attendant expense, and, in fact to eliminate from the clock all the wheels which come before that This gearing in a which actually drives the hands. clock of the ordinary construction, but actuated according to this invention, will consist of three wheels -namely, first, one which goes round once an hour; second, the escapement wheel; and, third, a wheel connecting the other two. The wheels and driving gear are arranged in the manner shown in the accompauying drawing, in which Fig. 1 represents an eleva31 tion of a turret clock constructed according to the improvements, and provided with striking gear; Fig. 100000 2 is a side view of the same. It will be seen that to the axles of the central wheel a (on the axle of which thus 751, the hour hand is mounted) is applied a water wheel, which is driven by a flow of water from a suitable reservoir above. This water wheel may be of any convenient construction, but the form most suitable for this purpose, and which is shown in the drawings, consists of four or more pipes, bb, radiating from a centre b, and furnished with small buckets 2 b2, at their extremities. These pipes are each provided with a tap or cock, on the spindle of which is mounted a tappet wheel cc, so arranged that as the arms of the wheel revolve in the direction of the arrows 1 1, one of the arms of the tappet wheel c is brought against a pin d, so placed that it will turn on the taps c at a certain point as the wheel goes round in the direction of the arrows 1, 1. Water will then pass down the pipe e from the reservoir above to the centre b1, and from thence up the armb into the bucket 62. The flow of the water down the pipe e into the bucket is stopped as soon as the bucket in question is full by the tappet wheel c of the tap coming against another pin d, which will turn off the tap and stop the water from flowing into the bucket. By this arrangement the splashing of an ordinary water wheel is avoided, and a very regular pressure is obtained. The hour wheel a gears into a pinion on the axle of the wheel ƒ. The wheel gears into a pinion on the axle of the escapement wheel h. A pinion on the axle gears into and drives the wheel i, on the face of which are pins 2 2, which as the wheel i rotates lift up the tail of a lever j, the other end of which is connected by a wire to one end of a lever k, which is connected at its opposite end by a wire to a lever / below, having its fulcrum at 3. As the tail of the lever is raised it will draw the catch t into the position shown by dots, and will (by releasing the pin 4 on the lever u) allow the other pin 5 to drop on the back of the catch t. Now when the pin 2 on the wheel passes the tail of the lever j the latter will fall back into the position shown, and the pin 5 being released from the catch t will allow the lever u to drop down until stopped by a pin 6 at the end of the double lever ve, ou which it will rest in the position shown by dots and by means of the wire u this lever u will turn on the tap s, and allow

2.

51

251

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251 100

51

or 2.
100

In Fig. 14, let the dotted lines A'B'C' represent the posi
tion of the wedge A B C after it has received a blow.
as the resisting surfaces are supposed to move in a horizontalone followed by two noughts, because there are two places of
direction only, if D be the point of application of the mutual decimals in the given number.
normal pressure before the blow, D' must be the correspond-
ing point after, therefore the normal resistance, which we
shall call Q, has been overcome through the space D E in its
direction, therefore the work expended on Q is equal to Qx
DE. Also, in consequence of the blow, the point D on the
wedge has been moved to H (vertically under D), therefore the
space passed over by the rubbing surface in the direction in
which friction acts is equal to EH, but E H = DE cot. i,
since HD = 4, therefore the work expanded on friction is
equal to μ Q× D E cot. i, and neglecting the mutual com-
pression of the weight and wedge, &c., we must have

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Ex. Express 0010101 as a vulgar fraction.
Here write 10101 as a whole number.
Underline 10000000

Then write one followed by seven noughts, as above.
Ex. Express 353-03 as a vulgar fraction.

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water to pass down the pipe s into the arms o and, strike 720 times, under this plan only sufficient power | 8000m. long and 7000m. wide. The above spot tra buckets of of a second water wheel for actuating the striking part of the mechanism.

In applying this invention to the striking movement, the advantages are very great, first, because the weight here employed is greater than that required to actuate the clock itself; and, secondly, because in this case two trains of wheels are eliminated. The inventor applies the power of a water wheel to the cammed wheel n, which consists of three cams, as shown by dots in Fig. 1. These cams, as they are rotated by the action of the tubular arms o and buckets ol, act on the tail of the lever p, which by the intervention of the wire pl lifts the hammer of the bell in the turret above. As the water wheel o will only revolve at a steady pace, the regulating fans usually employed in the striking gear of ordinary turret clocks may be dispensed with. The only wheel required in this arrangement, with the exception of the cam wheel n for lifting the hammer through the lever p and wire pl is a ratchet wheel q to drive the locking plate r. The ratchet wheel 7 has three teeth, and is mounted on the same shaft as the cam wheel n, and therefore at every third of a revolution moves the locking plate r one tooth. It will be evident that so long as the arms o of the large water wheel continue to move round they will carry round with them the cam wheel n, and will consequently act on the hammer lever p, as already explained, and also on the ratchet wheel q, which will drive the locking plate r one tooth for every stroke of the hammer on the bell. The striking will therefore continue until one of the twelve pius 7 7, on the face of the locking plate r comes against the tail v of the lever v, on which the lever u rests. The pin 7 as it moves forward will push back the tail l of the lever, and thus cause the pin 6 to raise the lever u into the position shown in the drawing, an thus allow the counterbalance lever s2 on the cock s to turn off the water from the arm o and buckets ol, and Thereby stop the cams and ratchet q until one of the pins 2 of the wheel i comes round again at the end of the hour and turns on the water again in the pipe s'. When there is any difficulty about introducing a water wheel large enough to act in the manner above described, or where complicated movements such as chimes are required, the main advantages of this system can be obtained by making the weight and drum of any ordinary clock of power sufficient to strike twelve o'clock with its chimes, if any, and then arranging a small water wheel to wind up the striking movement after every time that it has acted. Thus, for instance, in a non-chining clock, where it is necessary at present to store up power sufficient to

is required to strike twelve, thus diminishing the strength and solidity requisite in constructing the clock.

THE SUPPOSED PLANET VULCAN. SIR,-To the list of observers which appeared in the ENGLISH MECHANIC of the 1st inst, should be added the names of the Rev. Fred. Howlett, F.R.A.S., and Messrs. Thomas Petty and W. R. Bland.

The weather has, fortunately, up to the present time, been exceedingly favourable for solar observations. There have been, and are now, several magnificent groups of spots visible on the sun. Four of these spots have been distinctly visible to the naked eye. At 6h, on March 31, I saw with great distinctness the two groups and large isolated spot near the W. limb, and am pretty certain that another cluster situated on the

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E. edge of the disc was also visible. On March 28, at sunrise. Mr. H. Ormisher, of Manchester, discovered three of the groups without telescopic aid, and Mr. E. B. Knobel, of Burton-on-Trent, writes that on March 25, 26, 27, 28, and 30, he distinctly saw one or more of the spots with the naked eye. It may be appropriate here to give some measures of the size of the largest spot visible. Mr. T. W. Backhouse, of Sunderland, writes that on the 24th March it was 46,000 miles long, and the principal nucleus 19,000. On the 27th it was 45,000 miles long and 36,000 miles wide. It then contained two umbræ, each 8500m. long. On the 1st April it was 48,000m. long (in a direction nearly parallel with the limb, and 31,000m. wide. Its northern umbra was

versed the sun's northern hemisphere, and was visible from March 23 to April 4 inclusive. Several other large spots have been visible. On March 24 Mr. Backhouse measure the largest spot of a cluster in the S. E. quadrant, and found it was 36,000m. long.

Observers have noticed several rapid changes in the form of some of the spots. Mr. E. B. Knobel remarked a phenomenon of this nature on March 26. He says: "I began to observe the sun at about 10.40 a.m., and gave my attention almost entirely to examining the large spot then visible in the sun's northern hemisphere. I made a sketch of it, which I completed by a few minutes after 11 a.m. At 11.10 a.m. the sun was obscured by clouds, which cleared off at 11.15 G.M.T. I immediately directed my attention to this spot, and was astonished to observe a change had taken place in the bridge across the large umbra. A bright patch seemed to have broken out in the middle of the unbra, which then appeared as in Fig. 2. The moment I had the spot in the field of the telescope it caught my attention, and I felt confident at the time it had not presented that aspect when it had clouded over five minutes before. I should say the bridge was much brighter than the penumbra. I hope other observers have noticed the same phenomenon." The following are the sketches of the spot referred to:Several other observers have observed somewhat similar phenomena.

No planetary body, or any strange appearance whatever, has been visible on the disc of the sun, or it would have been detected immediately.

I find, on observing the sun this morning with my 4in. metallic reflector, that an immense group of spots have just appeared on the E.N. E. edge of the disc. The photosphere in the region of this group is greatly disturbed, and there are numerous faculæ visible. From the present appearance of this cluster, I imagine it will be of greater dimensions than any other group recently visible. If the weather continues favourable, I will forward you sketches of the appearance of this group, and will duly send you particulars of further

observations.

WILLIAM F. DENNING, Hon. Sec., Observing Astronomical Society Ashley-road, Bristol, April 5.

SHAND'S IMPROVEMENTS IN STEAM PUMPING AND FIRE ENGINES. SIR,-The following description of Shand's recent improvements in steam pumping and fire engines may not prove uninteresting:

Mr. Shand claims that they enable him to obtain by

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simple and direct means an uniform action in his pump and perfect equilibrium of all the parts in motion, that is to say, he obtained a continuous flow through suction inlets and delivery outlets, very desirable when used as a steam fire engine, and in effect resembling a rotary action. Greater thoroughfares through the valves are also obtained than can be by the usual means in equal areas of barrel and bucket. The steam pumping engine is composed of three steam cylinders arranged in line with each other, and the pistons or each attached through its rod directly to a ram and bucket, each of which works in one of three pump barrels, also in line opposite the cylinders. In the attachments of the piston rods to their respective rams a slot is formed, or what is generally known as a slotted crosshead, into which work the journals of a three-throw or equilateral crank, the shaft of which having three eccentrics fitted thereto, each actuating a slide valve to admit and discharge the steam working the pistons, all the working parts are thus made to balance each other. For compactness the three-throw crank may be worked by means of slotted cross heads, but ordinary connecting rods may be used for this purpose. Each pump barrel is connected at bottom to one suction chamber, and at top to one pump head, by which the supply and the delivery is made common to all three pumps, producing the uniformity before named, rendering the action soft, unaccompanied by the violent thud and vibration produced by the ordinary reciprocating pump when speedily driven. The steam and exhaust pipes of the cylinders are also connected each into one, thus constituting but one engine and pump, with continuous instead of the jerking and intermittent action usual in the ordinary pumps. The suction and delivery valves are usually composed of a number of vulcanised india-rubber discs fixed over as many gratings, the outline of each grating being circular, these being formed in a flat plate (also a disc) and forming the foot valve or bucket, and of suitable diameter to the barrels. The size of the rubber disc is by this arrangement limited, as being circles within the boundary of a larger circle the valves can be made no larger than to touch each other.

The seats are of a pyramidal form, the inclined faces of which allow of larger circular gratings than can be obtained in the flat valve seat of disc form before described. By these means the thoroughfares through the gratings are increased and an increased flow of water through the suction and delivery valves is obtained.

Fig. 1 is a front elevation, in which are shown the slotted cross head and the connecting rod arrangements. Fig. 2 is an end elevation with the frame broken away to show the arrangement of cross head; and Fig. 3 is an end elevation, partly in section, showing the arrangement of connecting iod and the pyramidal valve seats.

A are the steam cylinders, the pistons of which are connected directly to the rams B by the two piston rods C in the connecting rod arrangement, and by the single piston rod D and the foot piece E in the slotted cross head arrangement. The connecting rods For the slotted cross heads G transmit motion to the threethrow or equilateral cranks II, producing a rotary

motion of the crank shaft I, on which are fixed the three eccentrics J for working the steam slide vales. Attached to the ram B is the bucket K, in which the gratings of the pyramidal valve seats are shown, also the india-rubber valves in section with their guards L is one of the foot valves, shown in section, also of the pyramidal form and fitted to the bottom of each pump barrel; M the inlet to suction chamber N from which each pump is supplied; O the pump barrels; P the pump head receiving the delivery of each pump; Q the discharge outlets, of which there may be one or several, as required. FIREMAN.

THE TELESCOPE, &c. SIR,-A 4in. object glass which will show the 6th Star in the trapezium of 01 Orionis needs no encomium of mine to make the owner most legitimately proud of it. I can only tell Mr. Alston (p. 40), that had he paid Dallmeyer (whom I take to be our first living object glass maker), 60 guineas for a 4in. objective, it could not have possibly done more than his Wray." I scarcely know a more severe test in the whole Heavens than the 6th Star in the trapezium of Orion fer an instrument of the size he refers to.

I can give "G" (2273), p. 45. little or no information as to what has become of Kitchener's instruments; which are scattered all over the country. It may, however, assist him in tracing the "Beauclerc telescope, if I tell him that it was advertised for sale for £130, by the Rev. A. F. Padley, of Lincoln, in the Times for February 9th, 1861; who bought it, or whether it was ever disposed of at all, I cannot say. Mr. J. H. Ward (2275), same page, will find glass of a very dark neutral tint, or of that hue known to Opticians, as "London Smoke," the most pleasant to use as an eye-cap in viewing the Sun. He must be careful, though, either to employ the "Hodgson" reflector (ENGLISH MECHANIC, Vol. IX, p. 180), or to constrict the aperture of his telescope to 2in., or less. Otherwise he will find his dark glass crack at once. "W. H. P." (2287) can do nothing with his telescope. Lenses are not like trained soldiers, they won't stand fire.

"Astronomer" (2315), p. 46, is delightfully vague. In the absence of any details as to aperture, &c., I can

only conceive that his little telescope is a very good one, and his bigger instrument an exceedingly bad

one.

"H. A. C. "(2847), also on p. 46, is apparently speakiug of a reflecting telescope, albeit he says nothing directly to indicate that such is the case. He further omits to state whether it has a vertical motion upon trunnions, or in fact (save by an ambiguous reference to its being "raised or lowered by means of two nuts") whether it has any vertical motion at all. Assuming, however, pro hac vice, that he can move it in a truly vertical direction, he must stretch a perpendicular spider line across the centre of the field of his eye-piece; and then obtaining his exact local time, calculate in the way exemplified on p. 2, the precise time of transit of any star near the horizon. He must then bisect this star by his wire, just before its culmination, and, moving the whole instrument bodily after it, stop at the calculated instant of its appulse to the Meridian. His telescope will be then as nearly due North and South as ever he is likely to get it, and he may now lower it and see what terrestrial object forms a meridian mark.

To set the instrument east and west, he may describe a circle on the ground, having the longest leg of his triangle as a centre, and the distance between it and either of the others for a radius. If now he will notice where this shorter leg touches the circle when the instrument is in the Meridian, and will nove-t round the exact quarter of the circle from such position, he will have obviously shifted the telescope, either into an easterly or westerly position, according to the direction in which he has travelled round the circle.

As for his device for looking at the sun, it is nothing in the world but the "Hodgson" reflector referred to above. It is the best and safest way there is of examining solar detail.

His third query, albeit very indirectly a telescopic one, I may as well answer here by saying that N. P. D. may be converted into declination as follows. When it does not exceed 90°, subtract it from 90°, and the remainder will be North Declination; when it does exceed 90°, subtract 90° from it, the remainder will be South Declination.

For example the N. P. D. of a star is 47° 10', what is its declination? 90° 47° 10' 42° 50′ Dec. North. Or. what is the Declination of a star whose N. P. D. is 105° 12'2 105° 14'-90° 15° 12' Dec South.

An unexpected fine night has enabled me to redeem my promise to look at Ursa Majoris with Alcor and their neighbours. In preceding column is a sketch of the field of view of a 4in. telescope with a power of 74, when directed to Mizar. I must, however, expressly caution "Jupiter," or any one else, not to accept the apparent magnitudes of the small stars indicated as correct. I do not think that your engraver could possibly cut some of them without making the punctures so minute as to fill with ink in the process of printing. My querist must therefore regard my diagram merely as an eye map of the position of the points of light which were visible when I made it.

With regard to the letter of "a Ursa Minoris " (p. 59), I am just in this difficulty, that my 10th Vol. of the ENGLISH MECHANIC is now in the binder's hands

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So that I have no means of referring to the reply to him to which he adverts. On this account his reference to "24 Lyncis" is a puzzle to me; 4 and 14 Lyncis are both pretty test objects, each about 1" apart, but 24 and 31 are unknown to me as doubles. What "the first Star on F.R.A.S.'s' list" was, I have not the most distant conception either, in the absence of such list from the cause specified. Your correspondent ought certainly to divide the closer pair Equulei with the Optical means he possesses; its components are now just over 1" from each other. The Star" about 15" (really 11") to the right and below' it is the third component of the triple asterism.

The list of objects resolved by a Ursa Minoris," is creditable to his instrument, albeit it contains some of various values as tests.

Apropos of the 6th Star in the trapezium of Orionis, I am disposed, as I have before stated in your columns, to put a 4in. achromatic as the smallest instrument with which, under the most favourable circumstances, this exceedingly difficult object can be glimpsed. If however Mr. Cooke's 3in. did show it, such telescope must have been unique as a production of its manufacturer. I should perhaps add, in fairness that suspicion exists of this Star's variability. Uranus were invisible in anything less than a 2ft. I never intended to indicate that the Satellites of mirror. Some one whose letter bore internal evidence that he was in possession of a 3in object glass, or something of that sort, asked what magnifying power was necessary to observe these moons? I jestingly inquired in return if he had a 21t. mirror, that he put the question? I am quite familiar with all that Arago has written on the subject, and know the story of Lamont and the 11in. Merz refractor, probably very nearly as well as a Urse" himself. I will try and be more serious for the future.

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I have assumed that my querist's longitude is 8m. 78. in Mean Time west of Greenwich. If it be 8m. 78. sidereal time, he must convert this into mean time, which he will find to be Sm. 578., and add that.

I can only reply to Mr. W. F. Swallow (2361), p. 68, that I have nothing to explain, modify or retract with reference to what I wrote with regard to the gnomon (loc. cit.), in your last volume. Mr. Swallow asserts that the length of the shadow of a gnomon at the time of the equinox is not an arithmetical mean between the two lengths of the same shadow at the Solstices; and I say that it is. Utrum horum mavis accipe.

A FELLOW OF THE ROYAL ASTRONOMICAL SOCIETY. contrast was only obtained by sacrificing truth to

iden.

PERSONAL.

SIR, I lower my sword to Mr. Proctor. I see the force of his objection with reference to my determination not to argue under any circumstances whatever and can quite conceive that too rigid an adherence to such determination may often render me liable to misconstruction. Pro hac vice then, I candidly admit that my spectroscopic illustration was a most unfortunate one, and my use of the words "a priori," blush," certainly calculated to convey the impression where I should have said, and only meant, "at the first that I was enunciating, what I believed to be, a scientific truth. There is less excuse for me, because I was familar with the form in which the Astronomer Royal had stated his difficulty, and the immediate and convincing reply that was given to him; but I wanted an illustration and, it seems, could only furnish one in this slipsbod form. I should be very sorry that it should go forth to the world that I believed that the dispersion of the two dissimilar spectra, might have theoretically been expected to go on, pari passu, although on reading may own words over (litera scripta manet), they certainly appear to convey that There is a gentleman signing himself "Veritas," who has honoured me with a considerable amount of attention for some weeks past. It may perhaps save him the expenditure of a great deal of paper and ink if I refer him again to the article "Venus on the Sun's Face," which has formed the text from which he has Ying it once more, he will find that I absolutely rebeen preaching. If he will honour me by rendpudiate rigid accuracy in my figures, my sole object having been to render apprehensible, in the most popular form that I could devise, the principle on which the measurements described, are made. To have gone into all the details and refinements of calculation would have been to have expanded what into a thin octavo volume. Once for all, then, I used filled some 6 or 7 columns of the ENGLISH MECHANIC, round numbers everywhere, and it is of no use "Veritas "founding any theory upon them. THANKS-Permit me to thank Messrs." Saul so promptly answering my question as to engraving Rymea and G. E. Crick, p. 44, for their kindness in trouble he has taken to reply to me on p. 66. on slate. I have further to thank Mr. Leicester for the is beyond the reach of a mere amateur. rather fear, though, that the process which he describes A FELLOW OF THE ROYAL ASTRONOMICAL SOCIETY.

Mr. Baguley, p. 63, asks me for some tests for a 3in. refractor. He may try y Leonis, 49 Leonis, Urse Majoris, v Leonis, 127 P.XIII Virginis or & Bootis, for separating power. All these are easy objects. He will find more difficult ones in 156 P. XIII Ursæ Majoris, 70 P.XIV Libræ, 2 Scorpii, or X Ophiuchi. For a trial of his light-grasping power he can look at 13 P.VIII Caneri, 67 P.VIII Cancri, 15 Hydra, Urse Majoris, Hydra or Ursa Majoris. The comes to Crateris will be just beyond his capability. He may also attempt the resolution of that gorgeous mass of stars 13 M Herculis. 1 shall be happy to learn what success he has had in the resolution of these few objects; and shall be glad to supply him with a supplementary list, should he be successful with the one I now give him.

I suspect that" Neptune" (2436), p. 70, is merely laughing at me. He has, according to his own showing, got hold of a flint disc of abnormally high dispersive power, but what its exact index is of course I must be ignorant. He tells me the focal length of the crown, and that of the whole combination, and he professes to have such stupendous faith in my mathematical juggling as to suppose that I can from this compute the curves he requires "in a few lines." I do not know whether Neptune" has ever calculated the curves for an object glass himself; but I can assure him that I have, ab initio, and I made a vow when I had finished, that I would never voluntarily wade through such a dreary waste of figures again. To get out accurately, the four surfaces of an achromatic combination of the size of your correspondent's, would involve, imprimis, the most accurate knowledge of the refractive and dispersive indices of the materials to be employed; and then a mass of elaborate calcula tion which I really have neither the time nor the inclination to face. It is not like a terrestrial telescope, or other small instrument, in which Sir John Herschel's simple formula can be employed: it is a serious undertaking, as " Neptune" may satisfy himself by reference to any standard book on optics. A FELLOW OF THE ROYAL ASTRONOMICAL SOCIETY.

TIME.

SIR,-" Not a F.R.A.S." (2425), p. 70 is slightly confusing two different things. All he has to do is to calculate his own local mean time accurately, and then by adding 8m. 78. to it he will obtain the Greenwich mean time at that instant. The addition of 1-838. is to the apparent Right Ascension of the Suu at his local mean noon, beruse the Earth turns from West to East, and in the interval between the Greenwich Meridian coming under the Sun, and the arrival of that of your correspondent there, the Sun himself will have travelled a little way in the Ecliptic, and have increased his Right Ascension by the 1:338.

An example scarcely seems necessary, but for perspicuity I give one, worked out at length. What will be the Greenwich Mean Time at 6h. 14m. 50-39s. Local Sideral time in Longitude 8m. 78. W., on the 15 April? Turning first to p. 63 of the "Nautical Almanac," we

find

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1

THE SUN'S DISTANCE FROM THE EARTH. LIII, page 1, of the Phil. Trans. for the year 1762, with SIP,-The following information I copy from Vol. comment, for the notice of your correspondent, "S. B.," in your number for April 1st, 1870, p. 38:"Of the Sun's Distance from the Earth, deduced from Mr. Short's Observations relating to the Horizontal Parallax of the Sun. By Peter Daval, Esq., V. P. of R.S. To James Barrow, V.P. of R.S.

quently simply shows the belts as dark dense bands across the planet's disc. Mr. Purkiss dissents from the opinion that no pigments or materials with which we are acquainted can be made to accurately represent the differences which really exist, but such is really the case, and, as an instance of this kind of difficulty as applied to the delineation of terrestrial objects, we may mention that an artist who introduced a lily into one of his pictures was compelled to represent it in different depths of grey, but still preserved the relative purity of the flower in question, although it would obviously be untruthful to call a lily grey, and the requisite force of effect, by unduly darkening the rest of the picture. Mr. Purkiss thinks I am in error in stating that Mr. Browning's drawing is over-coloured, and adds his own opinion that the error lays in the other direction, for, according to his humble opiniou, the colour was even contradiction to Mr Browning's own words, quoted in more vivid than shown in the drawing. This is in direct Mr. Denning's letter, where he distinctly says:-" The coloured print taken from my drawing is decidedly over-coloured, the yellow and red are too bright, and the ashy blue, or grey, far too dark. And Mr. Purcould be desired." Surely such evident contradictions kiss, in thanking Mr. Denning for h's reply, says: "It is concise and appropriate, and everything which in the writings of a gentleman of his eminence in optics and astronomy deserve explanation. On another point I need some little enlightenment. Where can we see paintings which not only equal, but surpass Nature herself?-in which there is preserved throughout such a glowing luminosity as to far exceed the brightest tints of the landscape? I do not profess to be a judge of paintings, but I have spent many a happy hour in contemplating scenes of beauty portrayed on canvas with marvellous fidelity, but could not venture to assert that the gorgeous sunset of the artist equalled, much less exceeded, the real beauty with which the great orb of day gilds the of clouds. western heavens as he slowly sinks to rest on a bed

Mr. Purkiss complains that few skilful draughtsmen practice astronomy, and so difficulties are made of things which ought to be comparatively easy. Now if celestial drawing is so easy, why not favour us with some delineations of objects observed with mirrors of his own manufacture, since he states their definition to be excellent, and I have no reason to doubt for one moment their superior quality. would, however, be an additional satisfaction to read the testimony of some other observers who are working with his specula. CHARLES GROVER.

It

COVERING THE KEYS OF PIANOFORTES, ORGANS, AND HARMONIUMS. SIR,-" Progress," No. 2342, inquires if his worn enamel. Many patents for covering the keys of muharmonium keys can be faced-i.e., re-covered with sical instruments with glass and enamel, have been taken out, but those materials have never come into general use, and almost every one prefers ivory for the purpose.

Re-covering keys with natural ivory is a daily practice and any keymaker will do it for "Progress," and a suitable consideration. Perhaps "Progress" would progress fastest if he sent his keys to Messrs. undertake to cover them with enamel. Brooks, supposing he would be satisfied with natural ivory. I don't think he will find any one who will

Artificial ivory has been made of tolerable quality by the French, but by far the best specimens i have seen were the productions of Mr. H. J. Brown, who although best known as a public writer and poet, was by hereditary descent a comb maker. He made excellent combs of his artificial ivory, the composition of which he kept secret, but I think a chemist might give a shrewd guess at its component parts. Henry Brown was the man the late W. J. Fox alluded to in his article in the Westminster Review on "The Poets of the People." After mentionEbenezer Elliot, he wrote of Henry Brown:There is a man who makes combs in Whitechaple," and compared him to Crabbe, giving deserved praise to his really beautiful peem "Sunday," which, with his "Mechanic's Saturday Night," and his "Saint Monday," graphically portrayed the working man of that period. Of course ye working man" is now quite a different being, he having been educated into a civilised, refined, intellectual, and moral Christian, who is quite innocent of "Old Tom," and unacquainted, practically, with the meaning of the words "pot of beer."

According to Mr. Short, the mean horizontal parallax of the sun is 8" 65. Now, this parallax is the angle which the semi-diameter of the earth subtends, as seen from the sun. Therefore, as 8-65 is to 360° (the whole periphery of a circle), so is the semi-diameter of the earth to the periphery of the earth rounding the sun. But as 8" 65 is very nearly the 149826th part of 360, as may be easily proved by division, according to the latest observations, the mean semi-diameter of the earth is 3958 English miles, which being multiplied by 149,826, produces 593,011,308 miles for the circumference of the orbit of the earth. The distance of the earth from the sun is the semi-diameter of this orbit; and the periphery of the circle is to its semidiameter very nearly as 6,283,185 to 1. Therefore, if we divide 593,011,308 by 6,383, 185, the quotient, which is very nearly 94,380,685, will give the mean distance of the earth from the sun in English miles.

As the orbit of the earth is an elli pse, not a circle, the distance of the earth from the sun will be greater in its aphelion, and less in its perihelion, than here assigned.

The result obtained will depend, of course, upon the true value of the mean horizontal parallax. R. H.

rected.

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THE HARMONIOUS BLACKSMITH.

COMFORT FOR TRAVELLERS BY RAILROAD
AND STEAMER IN AMERICA.
SIR,-English railway directors are not greatly cele-
brated for the care they exhibit for the comfort of
passengers; perhaps if they exhibited more care for
their passengers' comfort than they do it would
hardly be appreciated by the majority of travellers,
especially if it were accompanied by an increase in the
fares, for however Britous may wish to be well-
served for nothing, they, as a rule, prefer being served
badly without payment, to being well served and pay-
ing a fair price for it, and this rule holds good not
only in the matter of railway travelling, but also in
the administration of justice (I should have written
law. They are not invariably identical, or our great
unpaid, which is only another name for our greatly
inefficient, would not be so popular with that nume-
rous class who fancy that a thing which costs nothing
must necessarily be cheap, which is usually the re-
verse of true.)

THE COLOURS OF JUPITER. SIR,-I beg to reply to Mr. Purkiss's letter in your last issue; at the same time I may be permitted toiaform him that I have not the slightest wish to enter into a long discussion on the points in question. If I have erred in making it a question of colour instead of relative brightness, I am quite willing to stand corI cannot agree with Mr. Purkiss that large apertures and high powers do not enable us to discriminate delicate gradations of light and shade as well as of colour. The fact that this is the case is abundantly proved by the detail shown in a correct drawing of the planet with a large aperture of either object glass or speculum, and by the utter absence of such detail in drawings made with small telescopes. On some English railways first-class passengers can The simple explanation of the fact that the belts obtain the luxury of foot warmers in winter, but as actually appear darker in a small than in a large tele- our climate-the experience of the last six months scope is that in a large instrument we get sufficient notwithstanding-is not quite so extreme as those of power to perceive the belts diversified with many Sweden and North America, of course it don't matter irregularities of light and shade, and hence they do if the mass of travellers who, as they go second and not appear to be such a dense dark mass as when third class, do travel with cold toes, for the feelings viewed in an instrument in which there is not suffi- of such "common people cient power to reveal these details, and which conse-ance, notwithstanding that their fares are, perhaps, in can't be of much import

most instances, the only ones which yield a profit; for it is the opinion of some experienced traffic managers that first-class passengers are often carried at a loss, On American railways the practice of heating the cars in winter is universal, so not only can the passengers warm their noses (and their toeses, as the Frenchman designated his pedal extremities), but if I am rightly informed the cars are now also cooled in summer, it is stated, by allowing solid carbonic acid to evaporate, and considering that a temperature of 90° in the shade is not uncommon in the Southern States, this must be a great luxury for travellers, nor will it in future be confined to those who travel on land, for it is stated in the Food Journal that it is to be extended to those who go down to the sea in (steam) ships.

"HOMINY."

suitable for carriages, &c., but certainly is by no meaus admissible as a driving wheel.

As a singular coincidence I also notice, illustrated whilst at Cardiff in 1861, but one which does not on page 61 of the same number, a device of mine, answer in practice, by reason of the impossibility of both on the ancles and on the wheels through the keeping one's balance, and also on account of the strain weight failing on one side, instead of directly over the Neither do I believe these single wheel skates have ever been used as shown in your illustration. EDMUND M. T. TYDEMAN, 9, Mighell-street, Brighton.

wheel.

AMATEUR FARMING, &c.
SIR,-Now there is such an improvement in our
MECHANIC, I think it would not be a bad idea to place

SIR-During a long sojourn in the United States,
largely, of hominy, a very wholesome and strengthen
And while dwelling in the South, I partook daily, and
ing food, well known to Southern residents. I bad
never tasted this food before, and discarding rice alto-
gether, which is also largely eaten, took to hominy
almost entirely; and since my return to England
have done my best to produce a similar article
for my own use, but have not yet obtained the
exact thing; and I now venture to ask our American
friends to be kind enough to inform me how the article
is prepared. I may mention that the instructions given
in the numerous recipe books for the making of it are
not reliable, and I should therefore prefer to have the
information from a States man, one who has had prac
tical experience in preparing it. The mill which I use
grinds the grain into five qualities of flour, and in the
making of hominy I take the coarsest, including the a column (as a trial) to questions and answers respect-
and the next two qualities to that, and mixing the breeding, keeping, and rearing of horses,
for two, or three, or four days in winter, but for one day
A sufficient quantity is then soaked in water cattle, pigs, agricultural implements, &c., as I am sure
only in summer, or it might become sour. Boiling it in a
a good many of our readers have hobbies of that kind,
as well as lathes, organs, &c; but before I say any
certain quantity of water for 15 or 20 minutes, stirring more, I should like to hear other opinions on it, as I
it all the time, it is then allowed to thicken gradually am sure it would take well in the country, and even in
on the hob, as near to the fire as possible, and it there the towns.
R. W. P.
remains, sometimes for hours, until it thickens and
most of the water has been thrown off by steam.
[Perhaps our correspondent would be good enough
to set the ball rolling. We will place some space at
must be frequently stirred, for it soon burns.
cold it becomes somewhat hard, like pudding, and is
his disposal.-ED. E.M.]
most nutritious. since it contains the very qualities
spoken of by Liebig, and which are cast away by
unwise people as dross. I could give much informa-
tion as to the best way of using it, but it requires beef,
pork, or ham fat, and is excellent with rabbit or fowl
fricasseed. It can be eaten in various ways, and in
making it palatable people must study their own appe-
tites. Its effects on the stomach and bowels are
admirable, and most people like it better if a few
bread-crumbs be mixed with it.

them.

A steamer trading between New York and Galveston is fitted with apparatus 'for condensing carbonic acid, and in a recent experiment, its cabin, 66ft. long; 33ft. wide, and 13ft. high, had its temperature reduced from 15 F. to 26 below zero in eight minutes. It is not stated if any living beings remained in the cabin dur-bran, ing this experiment, but I fear if they did the effect would have been to induce coma, for it is obvious they would have been compelled to inhale an atmosphere containing an abnormal proportion of carbonic acid, and this, however conducive to sleep and anesthesia, is hardly conducive to longevity. That carboric acid in the gaseous state might be employed economically in the treatment of paupers and criminals may be quite true, as I stated in my former communication on the "relief" of the poor and the ratepayers, but it is quite unsuitable for those who can "pay their way," and may be expected to pay their way in their fares more than once, for it would render them quite incapable of paying twice, which is just the thing traffic managers desire, and term development of pas

senger traffic.

We have imported several American inventions to our advantage, and I think the present is pre-eminently the time to import this refreshing, or rather refrigerating, one, for it might be applied most advantageously at the present time to further the progress of national education by cooling that religious fervour which, strange to say, exhibits itself in a Christian land by preventing little children from being taught the three It's, political economy, and their duties to their neighbours. Of course if we continue to bring them up in ignorance we continue to manufacture thieves and paupers, whether we intend it or not can hardly expect to gather grapes from thistles, for in morals as in horticulture, verily as ye sow so shall ye reap. THE HARMONIOUS BLACKSMITH.

TO MILLERS.

branch of business.

We

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SIR,-As there have been several discussions about China grass lately in your paper, I think that the following extract from a notification by the GovernorGeneral of India in Council will be interesting to MINNEHAHA. many of your readers :

"The Government of India, after communication with various agricultural and horticultural societies in India, and with persons interested in the subject, has arrived at the conclusion that the only real obstacle to the development of an extensive trade in the fibre of Theea or China grass is the want of suitable machinery the fibre from the bark, the cost of effecting such sepafor separating the fibre and bark from the etem, and ration by manual labour being great. The demand for the fibre is now large, and no doubt might be extended with reduced prices, and there is a practicably unlimited extent of country in India where the plant could be grown. The requirements of the case appear to be some machinery or process capable of producing, with the aid of animal, water, or steam power, a ton of than £50 per ton in the English market, at a total cost, fibre of a quality which shall average in value not less all processes of manufacture and allowance for wear and tear included, of not more than £15 per ton.

QUANTITATIVE ANALYSIS, &c.

SIR, Mr. Somerville and others, who have addressed queries to me, may think perhaps I have forgotten them; such, however, is got the case. I have been exceedingly busy, and now having a little spare time, I send the answers to their queries.

Estimation of Ferrocyanogen in Tea.-A good general sample of the tea should be taken, and of course, examined qualitatively. If Prussian blue be present, take one ounce or so of the tea, add warm water in a flask, and shake well for a few minutes, strain off the leaves, and let the rest settle, pour off a great deal of the water, add a solution of caustic potash, and then acidify with hydrochloric acid. Make a solution of potassium permanganate by dissolving 3-162 grains in 1000 grains of water; this is to be added to the above aciditied solution until a faint pink coloration is produced. Now, the amount of Prussian blue cannot be determined from the amount of solution used, as the organic matter present consumes a certain quantity. A second determination must be made of the amount of ferricyanogen which exists in the solution; this may be effected by adding fodide of potassium, allowing the liquid to stand for some time, and then neutralising the solution with sodium carbonate. The amount of iodine which is liberated is then determined by dissolving 12-4 grains of sodium hyposulphite in 1000 grains of water; each 10 grain division of the burette will equal 0422 grains of ferrocyanide of potassium, from which the amount of ferrocyanosolution must be used as an indicator. The determigen or Prussian blue can easily be calculated. Starch nation of the ferrocyanogen should never be made by burning the tea, and estimating the amount of iron found in the ash. Sulphate of iron is often used for blackening speut leaves; in such a case, the iron which naturally would occur as sulphate, would erroneously be set down as existing in Prussian blue. The sulphate may be detected by its reaction with barium chloride.

SIR,-It gives me great pleasure to find that so many of our dusty tribe are becoming readers of the ENGLISH MECHANIC, and that a few of them are also correspondents. I should rejoice greatly to see the latter multiplied. It would be the means in an indirect way of promoting its circulation among the former, a class of men to which a scientific paper had no charms if it did not treat upon their particular In No. 262, A. Stoneman has published his "notion" to the world respecting millstone balancing, a notion to me quite new, and I believe he will find the universal experience of all practical millers, as well as the laws of centrifugal action or force, to the reverse of his notion, notwithstanding his own to the contrary. He says that a standing and running balance are the As he has expressed his willingness to learn, a few hints from one twelvemonths his senior, may be of some service to prove the impracticability of this assumption. It is certainly new to me that millers said processes are to be understood to include all the details which will lead to a good general result.

same."

have been looking to the face of the stones to find out the cause of the dragging. Most millers know perfectly well that the cause is not in the face, but in the unequal distribution of burr and plaster. The specific gravity of each being as 1 to 2, some burrs are a third heavier, consequently, when the stone bas obtained its proper velocity, the centrifugal action or force of these two species, causes the apparent waving or, as it is termed, "being out of balance." It will exhibit this symptom when at perfect standing balance, and I call such to be when a pound weight will turn the centres. It is also quite new to me to find that the level of the bedstone has anything to do with balancing the runner, providing the neck is in good order. We do not shut our eyes to the fact that the bedstone must be perfectly level, but this has nothing to do with balancing, which is done most effectually by a belt running over pulleys attached to the spindles by bolts, the same being in two halves. As a further illustration of what I have stated above, to save space, I refer him to a diagram (intentionally somewhat exaggerated) by Mr. Smith, on page 588, No. 257, Vol. X. A careful study thereof will, I think, throw his motion" quite out of balance.

Now a word about wire flour-dressing machines. Mr: Sharpe has sent us a description of onethe once had, which dressed the modest quantity of six sacks (20st. each) per hour. A machine of the same dimensious as his, with revolving cylinder and external brushes, 6in. fall, covered with five sheets of flour wire. the internal brushes running 520 revolutions, will dress 20 sacks per hour-average produce, 75 per cent. I don't know how many machines there are in Ireland, but I know one in England that does what I have stated above, and the quality of its work will compare favourably with some of that of the silk machine, which I presume he would recommend Mr. Scott to put down in his mill; I would also advise him to do so in preference to the wire. Its work is finer, and takes better in the market. THOS, EVANS.

SIR,-Your correspondent, "A Stoneman," quoting from my letter, asks me to explain how "stones working well out of standing balance only proves that they are in running balance." I did not mean to convey that because they are out of standing balance, that therefore they must be in running balance. But "Salisbury Miller" asked how it is that stones work well although being out of standing balance. I concluded that if they worked well, they must be in running balance; but I very much doubt that they would be found out of standing balance if properly J. SHARPE.

tested.

The

operations performed after the cutting and transport
of the plant to the place of manufacture, to the com-
pletion of the manufacture of fibre of the quality above
described. The machinery must be simple, strong,
durable, and cheap, and should be suited for erection
at or near the plantations, as the refuse is very useful
the invention or adaptation of such machinery or
as manure for continued cultivation. To stimulate
process, the Government of India hereby offers a prize
of £5000 for the machine and process that best fulfils
all the requirements named above. Rewards of mode-
rate amount will be given for really meritorious
inventions, even though failing to meet entirely all
the conditions named."

THE "PHANTOM" WHEEL,
SIR,-In the last impression of "our MECHANIC
I observe an advertisement by "The 'Phantom
Veloce and Carriage Wheel Co., Limited (Reynolds
and May's Patent)," wherein is set forth as a new
invention a wheel of a precisely similar kind to the
one I published in your journal four years ago, and
which you will find on page 335, No. 68 of Vol. III.,
illustrated under the heading "The Spider Wheel.'
It was constructed for me by my brother-of Bedford-
in 1864, who also afterwards made a velocipede upon
the same principle, the first, I believe, that was ever
constructed with pattens fixed directly on the cranks.
The form of wheel under discussion-i.e., on the sus-
pensory principle, was finally abandoned by us on
account of several defects that appear to be insepara-
ble from it.
1st. It was found to have a tendency to flatten at
the spokes after a short time using.
"taut,"

in

2nd. The wires being necessarily drawn up
the slightest blow was certain to break them-ample
evidence of which was afforded by a countryman,
examining the machine, putting his foot through seve-
ral of the spokes.

Estimation of Organic. Nitrogen, Carbon, &c., in water. I shall not give all the minutiae, but only those

Take two pints (32 oz.) of the water, add to it in a glass flask half an ounce of a solution of sulphurous acid, boil for five minutes, and transfer to an evaporating basin, evaporate steadily, and finish off in a drying oven to prevent loss by spirting. Mix the dry residue with oxide of copper and chromate of lead, and transfer it to a warm combustion tube, fill up with warm oxide of copper, and end by placing some clean copper filings in the anterior portion of the tube. This part of the tube is now connected with a Sprengel pump and the air drawn out; the end of the pump is then placed under the end of a graduated tube (this may either be graduated into cb. inches or cb. centimetres, the latter is much to be preferred), 50c. centimetres graduated into 250 parts. Heat is then applied to the copper, and gradually carried back until all the tube is at a full red heat; when no more gas is given off, work the pump again to abstract any gas which may remain in the tubes, and let the receiver cool is observed, and the temperature and pressure also down to the temperature of the laboratory. Its volume noted. The height of the column of mercury having been taken in millimetres (or inches) above the level in the trough, the amount must be subtracted from the height of the barometer; this will give the pressure to 0° C. and 700mm. to which the gas is subjected, which must be calculated A moistened ball of potash (or a concentrated solution), must then be introduced into the gas to absorb the carbon dioxide, the amount of absorption being read off as this latter gas, making the necessary correction for the tension of the bubble or two of oxygen is then added to detect the aqueous vapour with which the gas is saturated. A is added to absorb the excess. presence of nitric oxide, and pyrogallic acid solution The pressure and temperature being noted, the volume of carbon dioxide is weight can easily be obtained. known, from which the amount of organic carbon by

The amount of ammonia present in the water must now be estimated by comparison with a standard solution coloured by Nessler's re-agent.

3rd. The passing of the wires, or hooks, through the
felloes or rim of the wheel was found greatly to weaken
it, and to lead to the first-named defect, however care-02 C and 760mm., and the weight found. The weight
fully made; and

4th. What altogether condemned it for use as a crank wheel or moving power was that lacking the rigidity of the ordinary wheel, there was a springiness in moving it by the cranks when loaded that caused a considerable loss of power in driving it. Otherwise it is very elegant in appearance, and a wheel that will bear an immense weight, and I should say-barring the 2nd defect mentioned above-would be found very

The amount of gas left in the tube is calculated to of nitrogen in the ammonia is subtracted from the weight of the gas, and set down as organic nitrogen. The amounts of carbon and of nitrogen, if multiplied by five, give the organic carbon and organic nitrogen per gallon. This is Frankland's process, but as practised by him the receiving apparatus is much more exact, though, as here stated, the process will give good results. The cut on next page shows the apparatus in full work.

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