most simple and correct mode of describing the teeth (cutting he teeth I think a misnomer in these letters), and the adoption of such a system, whatever may be the number of teeth assigned to be the least wheel, would ensure perfect regularity and uniformity with all makers, and I see no reason why uniformity in gearing should not take the place of "rule of thumb."

For the information of W. Proudlock, let. 622, p. 113, and others, I may observe that if we assume fourteen as he number of teeth for the smallest wheel in each set, that is to say each pitch, the formula for the scribers will be P × 7

8-1416 =d, in which P is the pitch and d the diameter of
scriber for any given set; thus for 3in. pitch we say
3 x 7
3.1416

= 6.634in. for the diameter of the scriber, &c.

One mode of making and using the "scriber," together with the mode of delineating and striking out the teeth of internal wheels, worm and worm wheels. racks and pinions, will be found fully described in the work in question, as well as my reasons for adopting the number fourteen teeth as the least wheel of the set.

In order that your readers may judge of the proportions and form of curves for the flanks and faces of the teeth I herewith enclose you a lithograph re

A

THE ORGAN.

especially in small instruments, as far as my own
opinion is concerned, but that of course is a matter of
individual preference.

AN ADEPT.

Note. This is the plan respecting which so great a
diversity of opinion exists that, on the one hand, I
have heard it called "a pipe designed by a madman,
cut up by an idiot, and voiced by a fool," whilst on the
other side, an opinion has been freely expressed of its
surpassing excellence, and that it will supersede all THE TEETH OF WHEELS, ELLIPTICAL OR
other plans in time. I may observe that although
somewhat startling in appearance it is not difficult to
turn out of hand-at least I have not found it by any
means troublesome myself.

The mention of this variety brings us in the next place to the consideration of the class to which it belongs, viz., stopped pipes.

OTHERWISE.

[756] SIR,-At p. 397, Vol. XI., "J. K. P." has given a drawing of a pair of elliptical wheels in which the "flanks" of the teeth, namely that portion from the pitch line to the root, are made to converge in the centre of motion or axis of the wheel: the drawing is What is signified by the prefix "stopped" is the in- accompanied by a statement that such is the way sertion of a plug or "tompion," as it is technically elliptical wheels ought to be made, but never are. It termed, into the upper extremity of a pipe, as repre- would have been interesting to have heard what your sented in Fig. 82. This tompion should be formed as mechanical correspondents had to say on this subject, in the figure, the lower portion being covered with but they have been silent, and my engagements since leather carefully worked on over it, the fit being so the publication of the letter referred to have been accurately adjusted that it will slide up and down such as to prevent me paying that attention to the within the pipe, perfectly air-tight on all sides. The matter which I think it deserves. In order to profitting of this is all important, it must be neither duce equable motion in a pair of wheels it appears to too tight nor too free, and the depth of the por- me that the action of one tooth upon another ought to 1ion in contact with the inner surface of the pipe commence a little more than half the amount of the should never be less than that shown in the figure. pitch before arriving on the line of centres, or in other It is necessary to call attention to this, as a very words, the action of a pair of teeth should take place common practice is to make these tompions out of simultaneously with the leaving off of the preceding a piece of lin. board, with a handle similar to that of pair of teeth, and that the locus of such action should a bradawl glued into the middle for the sake of be in a line making an angle of about 75° with the cheapness, the practical result of which arrangement line of centres. This line corresponds with the line is, that in shifting up and down, for the purpose of EE in "W. T.'s" somewhat vague description of the altering the capacity in tuning, which will be treated teeth of wheels in let. 444, p. 36, of the present hereafter, it very frequently happens that the whole volume. Let such angle be what it may it must be affair is turned over diagonally, and as the diagonal admitted that the action of every tooth or pair of position occupies necessarily a greater space than the teeth should be the same throughout the entire cirperpendicular the immediate consequence is that the cumference in order to produce an equable motion of pipe is violently burst, to a greater or less extent, and the pair, but I do not find this to be the case with the the note is impaired in volume, or if the damage is ex- form of tooth recommended by "J. K. P.," who will tensive disappears altogether. This is one of the produce a much better form of working tooth by most fertile sourees of defective and unequal notes, rolling a generating circle of the required diameter and may occur even when the mischief is not dis-on the inside and outside of the pitch line, so as to cernible externally, but if the length of bearing surface produce an epicycloidal curve for the faces of the teeth is made as in the figure it is next to impossible to do and a hypocycloidal curve for the flanks; or, as I any damage in this way. have elsewhere recommended, draw each tooth

The musical effect of this arrangement is to halve the length of any pipe to which it is applied, but the resulting note is very inferior to that produced by an open pipe, as any practical reader, who has compared the effect of an 8ft. bourdon with a 16ft. open diapason, can readily confirm.

For this reason, of late years it has become gradually the practice to restrict the use of stopped pipes to situations where want of space or requisite diminution of expense necessitate their adoption. What the writer has therefore described in the earlier portion of these instructions is the system now generally followed, that is, to carry open wood pipes as far down as tenor C, making use of stopped pipes for the lowest notes only. The most usual form of construction for the mouth, cap, and block, of the system we are now considering is represented in Fig. 83, a section, and Fig. 84 a front view complete; the general arrangement is similar to that already described on page 410, No. 250, the peculiarities to which it is necessary to direct attention, being that the front of the pipe is only carried down as far as A in the figure, the lower portion, in which the mouth is formed, being constructed of oak or mahogany, and is joined to the front, either by an ordinary rabbet or a tongue-piece, as shown in Fig. 83. In addition to this the two strips, B B, also of mahogany, are glued and screwed on, as in the figures, the whole forming a very solid and perfect job, if properly constructed. These strips also fulfilling a purpose which will be described hereafter.

It is requisite to mention that the internal form of the cap is represented somewhat exaggerated in the section, as it is cnly possible to indicate, on a small scale, points which will be described in the concluding section "Voicing and Finishing."

Note.-I am well aware that a few years ago it would have been considered a species of "treason" to construct any organ without a "stopped diapason " throughout its compass, but what I have endeavoured to describe is now practically the best plan in use,

per

pendicular to a line drawn tangentially to the point of
contact of the two ellipses, which is practically the same
thing. If those readers of the ENGLISH MECHANIC
who are interested in the subject will take the trouble
to cut out a few teeth on cardboard on the principle
recommended by "J. K. P." I may venture to say they
will find no two pairs of teeth, during each half a
revolution of the wheels, the action of which is pre-
cisely the same; if, however, the teeth are drawn per-
pendicularly to a tangential line, the action will be
similar and analogous to the teeth of a pair of ordinary
wheels. If made to converge in the axis, as re-
commended by "J. K. P.," those teeth which are in
a line with the major axis of the ellipse will be per-
fect in their action, so far as perfection can be attained;
the action of all the following pairs will however be
dissimilar and imperfect, inasmuch as some pairs will
be found to drive with the point of one tooth against
the root of the one with which it is in gear.

Notwithstanding that the best form to be given to the
teeth of wheels has occupied the attention of mathe-
maticians for past ages, it is a remarkable fact, and
one that redounds little to our credit as a nation of
engineers, that scarcely two firms adopt the same mode
of describing teeth, the consequence is that wheels of
the same pitch by different makers will not work to
gether. With a view to removing such anomalous
practice I, in my "Second Course of Orthographic
Projection," p. 33, have laid down three simple rules
for the consideration of engineers, especially those
engaged in mill-work. The rules are as follows:-

1. That there shall be a generating circle for every
pitch, and that the pitch be stamped or otherwise
marked on each "scribe" or generating circle.
2. That the diameter of each generating circle be
equal to the radius of the least wheel of the set.
3. That the number of teeth assigned to the least
wheel be 14 for all sets of wheels for mill gearing.

Now the generating circle made of a piece of card-
board, as therein recommended, is unquestionably the

MOUNTING OBJECTS WITHOUT HEAT. [757] SIR,-The secret of mounting in Canada balsam lies in having the balsam fluid enough to just flow from the vessel in which it is contained at the usual temperature of the air. The best thing to keep it in for use is a half-ounce glass syringe, which can be got from any druggist for 6d. I would have written a long letter on "Canada Balsam and the Microscope," but I see you have announced an article on "Mounting" from an abler pen so will not occupy space needlessly.

To mount the diatoms, take up a drop or two of the fluid from the bottom of the bottle with a glass tube, and transfer to the slide, the latter being perfectly clean. As the drop evaporates prevent the diatoms from crowding by a dexterous shake or two of the slide. They may be mounted either " "dry" or in balsam, or both ways. Experient a docet WALTER WHITE.

heat.

[758] SIR,-If Mr. John James will dissolve his Canada balsam in chloroform to the consistency of gum he will then be able to mount his objects without After a long experience, I do not find the use of chloroform deleterious in any way. Mounting Prepared Diatomacea.-Select and clean your slides; then shake the bottle containing the diatoms, and place a small drop from the cork on each slide; then place a drop of pure water on each to disperse the diatoms; let them then evaporate before the tire slowly. After they are perfectly dry, mount them in the Canada balsam. Great care must be taken that no dust is allowed to settle on the slides; also that the slides are not too full of diatoms.

WAHSROF, JUN.

RAIN-WATER TAPS IN BEDROOMS, ETC. [759] SIR,-Why have we no force-pumps in our houses to raise soft-water from underground reservoirs? Air is 800 to 900 times lighter than water, but atmospheric pressure can support water 32ft. high, provided the pressure be removed from the water's surface. Burning a candle in a confectioner's cylinder turned upside down on a plate covered with water proves that one-sixth of the pressure of the confined air is removed, causing the water to rise to near one-sixth the height of the glass. In a like way pressure may, by means of a flame, be removed from any extent of fluid surmounted by confined air till the water, covered at the base, rises in the pipe, or vessel, or cistern to the height of 32ft., and by a tap to stop reflux may be retained there. The best way may be to connect the pipes, &c., with a large metal bulb, as a chimney with no outlet; and if rain-water be caught in a basement cistern, a pipeconnection will, by means of an enclosed lamp (to be inserted through an airtight-fitting door) quickly raise water to about one-seventh of the extent of the confined air, but not above 32ft. high, which may be distributed, if water supply adequate, by pipes to any distance at and below that level. I never knew this done, and yet I ask Why not? Like ventilation, it is perhaps among neglected desiderata.

With the pressure of our atmosphere, 45 miles high, its power is perhaps neglected in lifting by pressureremoval. Pressure of 15lb. on each square inch is not to be despised.] J. BARWICK.

HEATING GREENHOUSES WITH GAS.

[760] SIR,-Since last week I have thought of a very simple means of adjusting the regulator to any temperature by screwing a small tap in the top of the enclosed air-space. In making the regulator, screw the gas supply pipe nearly half-way down in its position, and then fill with mercury until the surface nearly touches the end of the gas-pipe, which will be seen by its beginning to turn the flame lower. This of course must be done with the air-tap in the other leg of the regulator open, which will allow the mercury to settle at the same level in each tube. When the greenhouse is at the lowest temperature required, close the air-tap, which confines the air in the space below it. Any alteration of temperature now in the greenhouse will cause this air to contract or expand and turn the gas on or off. If you wish to alter the regulator to any other temperature, all that is needed is to open the air-tap for a few seconds when the house happens to be at the temperature required and then close it. All the metal in the regulator must be iron, as mercury amalgamates with brass, and it should be carefully varnished inside and out to prevent rust. The air-tap may be brass, as the mercury never touches it. THOS. FLETCHER.

POST OFFICE CHARGES.

[761] SIR,-Perhaps the following "true tale" may throw a little light upon the mysteries of Post Office surcharges. I had this week, in a certain town, a book parcel charged 14d., because " closed from inspection." As this charge was not obviously just, I went to the nearest postmaster. "Why bless you, sir, they're making hundreds of pounds by it. They know people won't take much trouble about a penny. You can write to London if you like." Sir, I once did so foolish a thing. This, too, reminds me that six months since I lost a few parcels of stamps from letters. I complained, and was requested to see the officer who took charge of these things. Said officer said, "You deserve to lose them." Wherefore? "Because you were so foolish as to post letters with so many as five shillingsworth of stamps enclosed in a thick cover." Is there any connection between these phenomena ?

A CORRESPONDENT.

[A few days since, we received a packet which was over-charged. We wrote to the Postmaster-General pretty smartly about this, and the over-charge was returned. When the cat is away the mice will play Parliament is not sitting, and so some of the post officials indulge in a few vagaries.-ED.]

COTTON SPINNING.

SMALL MILLING MACHINE.

good service to him. As to the "crackers" of which of the bed of the lathe by means of the screw, which
he speaks, I don't know what they are by that name.
has the hand wheel on it, a distance of 8in. fore and
Query 5349, "A Cotton Spinner's Difficulty" may be aft. The top plate of this slide-rest has seven T-shaped
caused either by moisture getting into the machine, or grooves in it, which take hexagonal heads of the gin.
being in the cotton; or it may be the result of deficient bolts belonging to my planing machine, for the pur-
draught, caused by the pipes being "choked," the out-pose of bolting down the objects to be operated on.
let being too small; or the inlet for air into the The headstock is a single casting, carrying at top a
scutching room being insufficient, when certain doors barrel, each end of which is bored out to receive a
are shut; or it may be insufficient power of fan. As collar of Babbit's metal, and the pulley being outside,
he gives no details it is not easy to help him. About o is made as large as the lathe will admit, or nearly
what he says on the subject of the cotton spinning 10in. diameter. The nose of mandrel is Whitworth's
correspondence, I do not think it is the Editor's fault lin. thread of eight to an inch, and the chucks suit
that nothing has appeared of late, but our own, my new double-geared head, fitted to same lathe; the
because, when space was given to us, we did not use it mandrel is driven by a band from a speed pulley, with
wisely. However, for my own part, I shall always be five grooves, from about 6in. to 15in. diameter, keyed
glad to answer any question that I can upon the sub-
on to the crank shaft, and capable of being shifted
ject, if I have time, and can see in the question a way right or left a few inches, which I find advantageous,
of conveying some information to such as I know need as the mandrel head can be moved in like manner to
it most, but are not well able to ask for it; but I will suit different lengths of drills or cutter; and it is
give no more time for "chaff."
E. SLATER.
useful too sometimes to be able to do so for getting the
chucks on or off, after the work has been bolted on to
the slide-rest. I have made the treadle to pass beyond
the right side of standard, as I find it inconvenient to
be obliged, as a rule, to tread with the left foot. When
the bracket is wound up as high as it will go, the top
and when down is 19 in. below it. By this means and
of slide-rest is level with the centre of the mandrel,
the employment of a temporary hand-rest, such as
36in. fly-wheel. It is also a very useful arrangement
even the back of a chair, you can turn a pattern of a
for drilling, as you can ensure sets of holes being
or horizontally, the leading screws having graduated
bored any required distance asunder, either vertically
collars. Its principal object, however, is for milling
with circular cutters, for which it is most efficient.
For tap grooving, I put on the chuck figured in the
ENGLISH MECHANIC, October 22, 1869, with a suitable
poppit head. I have also a cutter-frame, which bolts
on the front of the headstock, carrying a horizontal
spindle at right angles to the mandrel, and driven by
a pair of skew worm pinions, which enables me to cut
a rack of any length, or by mounting my dividing
wheel with tangent screw on a chuck on the top of
slide-rest, I can cut the teeth of cast-iron wheels out of
the solid. I made this headstock with large pulley
expressly, but quite unnecessarily, for general use; in
fact, I have never used the largest groove yet, as I find
small cutters and quick action suit a foot-lathe best. I
should strongly advise any one who has two or more
lathes to adopt this plan with one of them, as it only
involves making a small wheel 15in. or 16in. diameter,
to be put on the right end of crank, and not even that,
if you have steam power; besides the vertical slide
may be bolted on to the end of the lathe, instead of
being in one with the standard, as mine is. My man-
drel is of homogeneous metal, a mild sort of steel, and
works well with attention to lubrication; otherwise I
find the Babbit's metal collars are apt to cut.

[762] SIR,-In reply to the query of "A Factory Hand," p. 110 (let. 605), the spindles of the selfacting mule are "driven and governed" by various means, but chiefly now by a quadrant wheel, with a radial worm attached to it, and a chain, one end of which is connected by a sliding boss to the worm, whilst the other is coiled round a barrel that travels to and fro with the carriage. The quadrant wheel has a reciprocating motion given to it corresponding to that of the carriage, but the latter travels backwards and forwards in a straight line, whilst the former moves to and fro upon its centre. The carriage in its upward movement recedes from the centre of the quadSMALL MILLING MACHINE. rant wheel the full length of the stretch, but from any point of its radius, a distance that varies as the dis- in the ENGLISH MECHANIC for a description of a ver[763] SIR,-There having been an inquiry made tance of the point from the centre, and this receding tical slide-rest for a lathe, ("Tometer," 4812), I sent motion of the carriage causes a certain length of chain to be pulled off the barrel, and the motion that a sketch of one I made some time ago, which you is thus given to the barrel is transmitted to the drum- drawing of the arrangement I have adopted to my published on September 23rd. I now hand you a shaft or cylinder by a ratchet-wheel and catch. If he lathe, except that I now exhibit it as a separate will examine the working mule, I think he may soon understand this very ingenious arrangement, and per- to B in this drawing represents the right hand half of machine. All that is on the right of the line from A ceive that any motion which the spindles may require for the winding of a properly shaped cap can be given my lathe as it stands, with the treadle altered to suit to them by adjusting the position of the chain's attach- the independent machine. The right hand standard ment to the radial worm, inasmuch as the length of chain that is pulled off the barrel by any stretch of the carriage, as I said before, depends upon the distance that this point is from the centre, as also does the varying velocity with which it is pulled off, and the consequent varying speed of the spindles. I would give him a sketch, but it would take up space, and he may learn more by watching and thinking. With respect to his other queries, as to which is best "for making level yarn,' or 2 thread rollers with dead weights, or 3 threads weighted by levers (2 threads, 4 threads, or 6, I presume), may remark that different localities prefer one arrangement or another, just as the "hands" of the various localities have got accustomed to it. I, myself, prefer the small 2 thread roller with its hook and dead weight. My reasons for this are, in the first place, with this roller the lap that often lifts up the roller when a thread breaks, can only spoil one thread, whilst the others can spoil 3 or 5. In the second place, the slivers are not so liable to run together with the lesser rollers. In the third, the irregularities of the leather covering are not so mischievous. Of course, the greater number of bearings require more oil, &c., but, I believe, the disadvantages of the small roller are more than counterbalanced by the gains from it. I have seen the several arrange

ments at work side by side, and the above are my conclusions. But "A Factory Hand" must not think

that these arrangements have a great deal to do with has a chamfer slide down its face, measuring 24in.
the making of "level yarn;" they have not. Let long, and on that slide works a bracket, which is
him carefully peruse former correspondence on "Cotton drawn up and down by a vertical screw, with a total
Spinning," in the MECHANIC, and I think he will see
the wherefore of this; perhaps an attentive study of
my letter of June 24th, Vol. XI., p. 880, would be of

range of 194in. On this bracket is a slide-rest, which
works at right angles to the main bed of lathe, with a
traverse of 10in., and which also works in the direction

The pulley is cast-iron, and carries the divisions that I am most in favour of for general working purposesviz., 800 outside; then 11, 13, 14, 17, 19, all in one row; 216, 140, 96, 84, space being left between the fourth and fifth rows for any other numbers that may take my fancy. Of course there is no need to have 14 when you have 140, but there was plenty of room for it in that row without any crowding, and the scheme is as much for manufacturing cutters as anything else, and they are more likely to have 14 teeth than larger multiples of 7.

186

ENGLISH MECHANIC AND WORLD OF SCIENCE.-No. 294.

These milling machines are preferred by the workmen when the head is on the left hand end of the machine, or as this drawing would appear, if viewed t. ansparently from the back; it is then necessary to nave the nose of the mandrel cut with a left-handed This was found to be the case in a milling machine that has a screw on both ends of the mandrel, one right-handed and the other left, and the workmen like the left-handed end best. J. K. P.

thread.

CURIOSITIES OF MATHEMATICS. [704] Sin,-Let the algebraical symbol z denote any arithmetical quantity, and let y denote { (x + † x) + f (x + 4x) }

[Nov. 11, 1870.

octagon, thence a polygon of 16 sides, thence of 32, and threes enough, but however late a 4 may be introsquare, and inscribe therein first a square, then an decimals can do so, for no repetition of 3833 will have twice as many identical right-angled triangles as it ing square-root is determined by writing 2, and not so on; and as every such polygon is composed of duced, it will be too much; or, just as a non-terminathas sides, he can deduce from each polygon the long by any amount of decimals. and short radii and circumference and area of that, with there been given a tedious job. Let him, by multiplytwice its sides, and thus, by a few square-root extrac-ing each of the same successive pairs of odd numbers, tions, get those of a polygon with more sides than any get the products 3, 15, 35, 63, 99, 143, 195, 255, 323, &c., "Gimel," however, has number he chooses to name, and thus as near the which are all the even squares, 4, 16, 36, &c., each circle as he chooses. Does he suppose this is more diminished by 1. than "any one " in a hundred generations of mankind fractions, all with the constant numerator 2, and let Make these the denominators of thought worth doing? mode the world knew till within these three centuries; that either from the square or the hexagon, was the only to 0; the others substractive from 1. Then he will find Well, this way, beginning the alternate ones beginning from the first be additive and "G. H." can, with our decimal arithmetic and rule of square root (both unknown to Archimedes) very easily go as far as that old Sicilian-namely, to the inscribed and circumscribed polygons of 96 sides each-that is but four doublings from a hexagon. As the circle is between these two polygons, both in area and circumference, he was enabled to prove in this way that the latter is between 3 and a 1,7th diameters, and 8 and 10-71ths. Thus, for a dia his upper limit, the ratio 7: 22, beside being much the meter of 497, it would be between 1,561 and 1,562. He limited to a range within a 1,560th of itself; but simpler, is now known to be about twice as near the trate as the lower; it has also a remarkable convenience that will be seen by turning to my mnemonic diagram, p. 70, where the two numbers 3 and 4

is also con

Then, not only is

constant, but

the mean

=

proportional between m and n = √m x n = unity whatever finite and determinate arithmetical value we may put on the symbol z.

No number of the subtractions above, nor of the quite meet each other; for the additive series mounts additions below, will bring the two sums to pass or towards, without ever reaching, the same goal toward which the subtractions reduce the square 1, without of the inscribed circle. ever reducing it quiet low enough, namely to the area

Now, sir, there can be no effect without a cause, and if you give your correspondent, Mr. J. Jones, the opportunity of tracing this effect to its cause, by inserting this communication in your next number, it may probably enable him to detect the fallacies that pervade his letter on the "Quadrature of the Circle," which appears express all that this does. If the two spaces so marked Snell's 55. Abraham Sharp carried them to 75; Machin, in the ENGLISH MECHANIC of Oct. 28.

JAMES SMITH.

were truly as 3 to 4, it is plain the circle and its enclosing square would be as 11 to 14 (either their areas or OUR CIRCLE-SQUARERS, “MOKE," ETC. perimeters), which is the same as saying the circumference and diameter are as 22 and 7. Also a sphere [765] SIR," St. Austell" (let. 253, p. 82) made a prism (see figures on p. 601), would be as 11 to 21. and its enclosing cube, or an ellipsoid and enclosing benevolent effort at raising this unfortunate class; but All these handy numbers are as near as the upper I fear that" to make themselves acquainted" with not limit of Archimedes, or within a 2,400th. only so common a fact as the existence of surd or incommensurable ratios,-and few of these geniuses ever trouble than this. But we are not to suppose no ancients took more reach even this elementary knowledge, but, as he that the Brahmins, in the remote times, when they From the Hindoo books it is found advises, with the principles of limits, fluxions, or the integral calculus, is a condescension to which the in--had taken much more. Yet, observe, they had their were men of science-who knows how many ages ago? spired will never be brought to stoop. Though it is matter of history that every age since Aristophanes "G. H.'s," their quadrators by feeling, too. One of them (and doubtless earlier, had there been a bard to sing by two other equal squares, and draw a diagonal across "felt" that if you flank the square enclosing a circle, them) has had its "Gimels," James Smiths, and all three, this would equal the circumference. Of course, "G. H.s"; and, as far as is known, however numerous they were, their values for were exactly as the length of this diagonal is 10 = 31622777 by Euclid's 47th proposition, calling the diameter 1, many, is it not marvellous that between 3 and 3 no erring about as much in excess as Mr. James Smith two should pitch on an identical fraction ?-their does in defect. Observe, however, this inspired quadgenerations follow like successive years' leaves; each rature, doubtless the oldest on record, showed con(observes their historian in the " English Cyclopedias," siderably more science than our Smiths in one respect. Quadrature") as ignorant-and contemptuously so-of It guessed truly that the ratio was incommensurable, the past as the future will be of them. The fact is, not, as they pretend, one to be stated in numbers. But as long and as surely as the conceit exists that a man's other Brahmins knew what investigation meant, and fellows have been a pack never worth his hearing or have left an uninspired value 200 times nearer than understanding, so surely must we have the false quad- either limit of Archimedes. rators, like the poor, always with us. and even his answerers mostly, who can tell how the 3-1416 of our engineers. Our "Moke," terms, 1250: 3927, which gives exactly the decimals This was, in its lowest earth was set in motion, and so much else that the giving Mr. Fenby's "multipliers" for rounding off The decimal form has here the great convenience of dividing by both 4 and 6, times nearer than that used even by Ptolemy, the area and solidity. This Hindoo value was several astronomer, with whom the science of antiquity on the matter closes.

Newtons, Laplaces, and Herschels have found utterly beyond them, are brothers to the quadrators, but a more modern, and socially far more noxious variety of the type, being as impotent for good, but not so for

evil. But "Moke" is of all animals about the un-
fittest emblem this writer could have taken. That use-

ful creatureis noted for patience, the very quality where-
of his would be namesake specially lacks the very idea!
I should like to hear of the real moke that ever as-
sumed superiority to all manner of scholars in their
several specialities at once-
Egyptian antiquities, Biblical exegetics, Arabic, &c.
astronomy, geology,
(see letter 551, p. 87). Did that ancient one of his
protended sisters, to whom he alludes as having spoken
Hebrew-did even she-who might have had some right
thereto, if any might, I think-display any such con-
lempt of human science in general?

Sir, I must protest on behalf of his generally dumb
and much-injured superiors against the disgracing of
their name by this usurper thereof in your pages.
What have the poor donkeys done to deserve this li-
belling? And no other correspondent has his pre-
sumption. Have you any letters signed "An Angel,"
or a (not mute) "Inglorious Milton," or, as a book
published during the last war, "A Superior Spirit"?
We have had enough of this writer's untrue and point-
less attempts to travesty a race above him. To return
to the upstart's real brethren, the quadrators: I think
"G. H." (366, p. 612) hardly seems of the real stuff
they are made of, and venture to hope he may not,
even under the influence of a "Gimel," become one;
though it is almost a fatal symptom when any one
"jeels convinced" that this or that is a "true geo-
metrical ratio." What a thing to feel!
a hope in the fact that his ignorance is not contemp.
But there is
tuous, he being even willing to learn (or at least ask)
"whether any one ever attempted to subject the excess
of the square over the circle to a similar process of
approximation?" Now, could not he, instead of asking
this, have just attempted it for one?
bably been through at least the first book of Euclid; or,
He has pro-
if not, he ought. Now Euclid never showed how to
square indeed any curved area, but he did any right-lined
area whatever, and, without going beyond Book I., any
that can be divided into right-angled triangles, two
sides of which are given. This, at least, "G. H." can
do, to any exactness whatever, by the arithmetical
rule of square root, if he believes therein (for to 999
people of 1,000, by the way, this, and even simpler
rules, long or even short division, are mere matters
of faith, they knowing they have been often worked
and never found to err, but far from being ready to
prove why they never can err). As "G. H.," then,
can by these elements bisect a circle inscribed in a

decimal till the fourteenth century after Ptolemy
Europeans had not that accuracy of the fourth
found them just at the point he had reached, comput-
ing tables of sines and tangents for the first time-about
when they began to print. Then soon came the "Gimels"
day. They gave pretendedly exact ratios that were
but, unlike ours, they were of some use in their
nearer than true science had yet gone;
in fact, the pushing it further to prove they were not
exact. There was really serviceable error, you see!
that required,
Cannot any of our blunderers find something in which
mokehood of such a kind as to compel the finding of
to blunder like that? We should all forgive inspired
new truth to coufute it! Something like the real
dignity of mokehood that! They would be as the moke
that carried the student's books in his pack.

centuries back, drove Metius, the Dutchman, to the
Well, in this way, the quadrators by feeling, of three
chance discovery of those wonderful numbers, 113:
355, that are 100 times nearer the ratio than a like
number of decimals, or than any two below 100 times
their magnitude. They also drove Vieta, the father of
Algebra, to extend the decimal value to 31415926535
as a lower limit, the last figure being below 7 as the
upper. They drove Adrian Romanus to go five decimals
further. Lastly, they drove Ludolph van Koelen to the
that has been, or now ever will be attempted; he found
most laborious working of this Archimedean method
most improbable that for any purpose, even in the
the decimals to 36 places, or 35 after the integer. It is
niceties of astronomy, one-half of these "Ludolphine"
figures will ever be found worth employing.

Many other ways then were found of working the problem with no square-root extraction at all; and as they were simplified, so were the decimals extended beyond at the beginning of last century, to 100; De Lagny to the last 4 of his figures have been found wrong. A note 128; and Vega, the great logarithmist, to 140, but was found in a MS. at Oxford stating them to 154 advance, and detection of these errors, was not till figures, now known to be all right but two. The next 1846, when Dase computed 200 figures; and the next year Clausen, a Russian, 250. Now Dr. Rutherford, of and his former pupil, Mr. Shanks, resolved to wop Woolwich, had published a value whereof the last 56 figures were found wrong. To wipe off the stain, he between master and pupil, which only stopped in 1853, creation. Accordingly a regular competition ensued when the former had gone to 440 figures, in which Mr. Shanks agrees with him, but has himself pubAstronomer Royal has remarked on these, that wherelished 60s, including the 3 integer! The Scottish present can explain. as we might expect 60 or 61 of each digit, there are 3 threes to every 2 sevens; a mystery that nobody at

up the exact labour it will involve to get his result by Now in case either of our friends would fancy to a decidedly shorter check Mr. Shauks in his last 168 figures, I will reckon averages 301 figures, as they taper regularly from 608 way. Each line necessarily have then 255 divisions by the divisor 289; thirty less down to nothing. Of such average length you will divisor 25; one by every odd number from 8 to 603; by the divisor 103; a hundred and twelve by the easy of Os only, and one from a line of 608 figures. To obtain eleven score pairs of lines to add separately; and two sums of 150 lines each; 255 subtractions from lines more or fewer, the labour will be exactly as the square whole finding in this way of Ludolph's 36 figures would of their number; and I have ascertained that the likes, I will send him, so ruled and prepared that he side of a foolscap sheet, which, if " Gimel " or " G. H." go into two columns of the ENGLISH MECHANIC; or one cannot in reason miss his way through it.

first, that proved by Gregory and Newton, that if any These very abridged methods depend on two facts; arc's radius be called 1, and its tangent t, then that

arc itself measures

tll + &c. [ad. infinitum.

Thus the two

always incommensurable tangents, and commensurable
tangents belong to incommensurable arcs, yet, what-
The other is, that though commensurable arcs have
ever arcs have their tangents commensurable, so too
differ by that whose tangent is a seventh of radius; and
arcs whose tangents are the half and the third of radius,
have the sum or difference of such arcs.
they together make an
evidently
quire thousands of terms to fix even the first few
octant, whose tangent is
decimals of the octant's length by the above series,
= the radius or 1. Now though it would re-
which then becomes 1

no work to compute and add together the two above cause all the powers of 1 are 1, yet it is comparatively decreasing, and the alternate ones (which alone are powers of 1 are replaced by those of, which go on ares that make an octant, since in one of them the wanted) fourfold at every step; and in the other they compose the former arc by adding together the latter, ninefold at every step. But again, it is still quicker to are replaced by alternate powers of a third, which sink alternate powers of this fraction sink by 49 at a step and that whose tangent is a seventh, because the instead of by only 4. Thus we have only to compute the second arc, double it, and add the third to make an octant.

the greatest discoverer of the time, invented how to
Then came the first improvements of method. Snell,
tractions, that, with less labour than Ludolph's, he not
work this problem with so many fewer square root ex-
only verified those figures, but carried them on to 55.
All this was before the grand century of modern dis-
covery-the seventeenth-had opened with Galileo, the
pendulum, barometer, air-pump, telescope, and loga-
rithms, to lead to integration, the crown of Newton necessary to anticipate a little the progress of mathe-
and Leibnitz.
To treat these matters intelligibly, it is almost
Brounker, and Gregory were the first to give a deter- and coin at least one word not yet in use, out of several
minate value of .
In that age our countrymen, Wallis, matical nomenclature (the slowest of any, I believe),
number, there would be nothing to tell you, supposing radius is 1 and tangent n, the attingent of n, or “at. n"
they stopped, say at a million, what the 1,000,001st (I would similarly call that whose sine is, the adsine
In the 36 decimals, or 55, or any that are sorely wanted.
should be. Now the fraction that "St. Austell "
Let us call the arc, whose
on p. 83, does this. It determines the complete value, just and sin. -1 r, to which, apart from their length in
gives of x, or ad. z. They are now written, if at all, tan. -1 μ‚
as completely expresses one-third, though no finite printing, there are very grave objections). As the

attingent of 1 is an eighth of a circumference, or a fourth of a to radius 1, we can then express or compate the value of either of these ways:—

There are cases where, as in the mensuration of

each will be an endless incommensurable decimal,
their combination as directed shall give the 440 figures
of Shanks and Rutherford, or as many as he likes to
compute of them; and in every case the same.
E. L. G.

A CHEAP AND EFFICIENT LOW-WATER DE

TECTOR.-A correspondent of the Scientific American
says "Drill a fin. hole at the low-watermark, either
in the head of the boiler, in the crowning sheet of the
fire-box, or the upper part of the flues. Tap out the
hole to a full thread with a common taper tap. Make a
plug of common tinman's solder, the shape and size of
the tap used; screw in the plug (it will cut its own
thread); cut it off smooth with the outside surface of
the boiler. If well put in it will never blow out under
any pressure of steam; and so long as it is covered
with water the plug will not melt. If the water falls
below the plug, so that the iron gets to a dangerous
heat, the solder plug will melt out."

figures composed of ares of different circles, it would be EXTRACTS FROM CORRESPONDENCE.
found to involve less ciphering to recur to these first
principles than to approximate their measures in
degrees and use the "mnemonic multipliers," or
aliquot parts of . A case in point is the first query of
Country Gabie" (5280, p. 120). That sewer oval,
Fig. 1, is by far the best for its purpose I ever saw
figured or executed. It seems formed, as very many
things in practical building and carpentry used to be
in more practical times, by an application of what was
called "Plato's triangle," namely that whose sides are
as 3, 4, and 5. The oval's width and height are evi-
dently meant to be as 3 to 4; and dividing it into
squares, 8 in the height, the head is described with a
radius 3; the foot with radius 1; and the sides from
B and C with radii of 6. Thus CAD or BAD is Plato's
triangle; whose acute angles, observe, always measure
twice the attingent of, and twice the attingent of .
Hence all the arcs are formed of these two attingents;
and their tangents, as placed round Fig. 12, are all as
simply related as the radii, both to those radii and
each other. Now to get the areas of the sectors (which
observe, are all incommensurable with degrees or the
circle), put a for the attingent of to radius 1, and b for

that of to the same radius. Then the 8 arcs composing one half of the oval, descending from the top, are 3b, 3b, 3a, 3a, ba, 6a, b, b. Each successive pair being of equal radius as well as length, we may collect and multiply each of the four by its radius thus: 18b + 18a + 72m + 26. This exceeds the whole oval's area, then, by the triangle BCD, by which the sectors BCE and CBF overlap, which is = 12. Collecting again then, we have for the whole area,

Oval 90 at. + 20 at. - 12.

But we have seen that much computation is saved by dividing the at. so as to convert the above sum dato this:

Thus the oval area barely exceeds the square of its breadth BC. The above divided by 36 gives 1.0045, or exceeds it by only a 220th.

Whenever Plato's triangle is applied, similar convenient and simple relations will be found to prevail among the straight lines and arcs. But to return to our squarers. The most unmathematical might obtain that kind of experimental conviction that the mathematicians are right, which a clown or savage gets, through eclipses, that modern astronomy is not baseless. Suppose only two dissimilar pairs of fractions given them, whose attingents they compute and add, and find the sums agree to 20, to 40, to 60 decimals, or to as many as they like to try. If the principles on which they were chosen are false, the results must diverge at some attainable figure. But we can give them innumerable such combinations, mostly untried. That above proposed as the most expeditious, namely == 32 at. 8 at. 239 + 16 at. 10 has not been worked to a single figure. But if an experimenter wants to be quite sure that fresh ground is broken, he can easily be so. Let him choose any fraction he will, as one of the combination; and I will name others, as few as may be, under the condition than none shall be less readily calculated than his own; and whereas the attingent computed from

-(8 at.

1

515)

515

BISMUTH (let. 719).-"A Student" says:-"I believe Un Irlandais' will find that little is required for assaying the ore of bismuth but heat. If the ore be broken into small fragments and put into an iron crucible covered, then the fire be raised very gently, so that the ore becomes rather red, he will soon find the bismuth at the bottom of the crucible. The ore should be stirred a that the heat be very gentle; a violent fire would dissi pate a great portion of it. If he thinks it worth his labour he may mix the remaining earthy matter with a little black flux and borax, when he will no doubt obtain a little more of the metal from it."

little from time to time. Great care should be taken

DISCONNECTING PADDLE WHEELS.-An anonymous correspondent says:-On the river Mersey many tugs are thus provided, and the fact may often be verified by any one gifted with what Professor Roscoe calls the "faculty of attention," in observing a tug bringing up in a tideway, when one wheel is rapidly worked, whilst the other is quiescent. I think I may safely say that all the side wheel steamers on the Ohio are fitted with disconnected engines, and are thus easily enabled to bring up head to stream at the various calling points on that rapid river.

IMPROVING GAS.-"Cam" says: "I have made the tin box, as per Jack of all Trades's' letter, and find it does not answer so far as improving the brilliancy goes; the result is a thick, heavy, smoky flame."

EVOLUTION OF LIGHT.-Under the above heading in your present number of the MECHANIC (page 168) you say " A simple discovery of the evolution of light has been lately made by Andrew Pritchard, the author of a History of Infusoria.' He found that on tearing a piece of new calico in the dark a line of light was observable along the torn edges," &c. Will you kindly allow me to state that this discovery was made by my self some years ago? My first experiment was made with I tore it quickly in two in the dark, and was delighted a piece of white calico about twice as big as my hand. to see the rupture attended with a slight flash of light, like that produced by rubbing what lads call "fire stones" together. Since then the experiment has been pretty frequent with me, and always with like result.WILLIAM COTTERELL, F.R.A.S.

REPLIES TO QUERIES.

In their answers, Correspondents are respectfully requested to mention in each instance the title and number of the query asked.

[4492.]-RAISING WATER.-I owe my most sincere
thanks to "Psi," for the very considerable trouble he has
taken to answer my query. I do believe his ingenious
arrangement would answer the purpose fully, and I
should have little hesitation if the well were mine in

adopting it. Could " Psi" give me a very rough idea of
the probable cost of such apparatus without fixing? Of
course the chain would form a very serious item; my
friend intended to use the old one.-A. C. G.

Its power

G is a square

[4613.]-TREE STUBBER (Unnoticed Query).-From
the Scientific American I take the following account of
an improved stump extractor patented through the
Scientific American Patent Agency on May 3, 1870, by
G. L. Howland and Wm. M. Howland, of Topsham, Me.,
U.S.:-"The engraving represents a new and improved
stump extractor, which may also be applied to load them
on trucks in place of the ordinary derrick.
may be made to reach to any extent within the limits
of strength of the materials of which it is constructed.
The frame is composed of two legs A, and the leg B
hooked together at the top by the long crotched and
bent hook C, and the swivel D. E is a metal frame sus-
pended on the hook C by pivot bolts.
hoisting bar, arranged to slide up and down through
suitable holes in the top and bottom of the frame E.
Gripe pawls H, with square holes, through which the
bar G passes, are suspended by rods I from the short
arms of the levers K pivoted on the axis L, and con-
nected at their long ends to the vibrating hand lever
M by the rods N, one on each side of its axis, so
that when one moves one way the other moves the
other way. The gripe pawls H are also connected
by small rods O to the spring levers F, also pivoted
on the axis L and connected to the bar Q on the
leg B, the bar Q being arranged to slide up and down on
leg B. When this bar Q is shoved up, the spring levers
press the pawls down and cause them to grip the bar as
soon as the levers K begin to draw them up, thereby
causing the bar to be raised by the alternate up and
down movement of the pawls, and when the bar Q is
shoved down the springs have a lifting action on the
the end of the lupward movement of the levers; so that
pawls which prevent their gripping the bar, until near
the further upward movement will lift the bar out of the
grip of the pawls below, which being thereby freed will

rise on the ba. while it is lowered by the other, until near the end its upward movement, when, as before, this one will grip and force the bar from the other at the

K

N

The

lower position, and so on, letting the bar down. The
to raise or lower the bar as may be required.
springs thus shift the pawls readily to cause them
swinging frame gives the bar freedom to work ob-
liquely to either side of the vertical position, and in case
it requires to vibrate perpendicularly thereto the hook
and leg K will vibrate in that direction. By shifting the
lever rods I, into holes nearer the central pivot of the
hand-lever, M, the speed is reduced and the lifting
power is increased, and vice versa. The tripod form of
the machine also adapts it for use on rough and uneven
land.-SERGIUS.

[4756.]-MAGIC LANTERNS (Unnoticed Query).See Nos. 148, 149, 150, and procure Cox's Catalogue of Magic Lanterns, at 26, Ludgate-hill.-AB INITIO.

[4762.]-DISPLACEMENT OF SHIPS (Unnoticed

Query). I am sorry that I have not had an opportunity to answer the question put to me by "G. B. D." before, and though I have not the time to comply with his request in giving a sketch I hope the following will fully explain what he wishes to know. Now a model is supposed to be exactly like the proposed ship in shape, and every part in that model bears the same proportion to the corresponding parts of the ship in question; therefore the rule for computing displacement of ships which I gave in a back number requires that the model should be made of (at least) two pieces, one to represent the part that is to be below water, and the other the part above. This is done in the following way: after determining what proportion the extreme length, depth, and width wood, one the extreme breadth, depth and length of the are to bear to each other of the ship, get two pieces of part that is to be below water, and the other in like manner for the part to be above, and after you have screwed them together and carved them until (the now solid block) assumes the desired shape, you may unalready mentioned in the back number above menscrew them and compute the displacement by the rule tioned.-W. FELTON.

[4788.]-CONVEYANCE OF

WATER (Unnoticed Query).-An overshot wheel is always the best way of utilizing a fall of a few feet, such as twelve, and ought to utilize three-fourths of the entire power. Where the fall is much greater, the turbine is more economic; where much less, an undershot wheel.-E. L. G.

As

[4825.]-ELLIPTICAL CUTTING FRAME.-I had than "Wahsrof," as we seem to please to differ in opinion, not intended to write again on this subject any more still, as he will misquote my letter I will for this once set him right again. In my letter on p. 45, I said I had never made one of the first mentioned (elliptical), but had in part at least one of the "latter" (rose cutting). Now as to my "well educated" reason; I do not see any frame than there is in calling the chuck an oval more harm in calling the frame an oval cutting chuck, which is what I have always heard it called, though "Wahsrof" says there is no such chuck. the inventor called his frame "elliptical" I agree that I ought to call it so too, but the frame cannot be said to be elliptical, any more than the gardens of the Botanishould be called so; and 1 fancy if we wanted to be cal Society are themselves botanical, but botanic, and pedantic, it would be more "well educated" to call it an ellipse cutting frame, or an elliptic cutting-frame. Lastly, as to the general use of the term oval; as an adjective I find in the "Imperial Dictionary" which is a good one, that oval as a substantive, "is a popular term for any "Curvilinear, with both ends of the same breadth," and curved figure approaching to that shape, "viz., an ellipse.

J. K. P.

[4841.]-SPONGES (Unnoticed Query).-The best method of treating sponges is by washing them well every week in salt and water. I have adopted it for some years, having been instructed by a sponge merchant.-R. 8. B.

[4867.]-AUSTRALIAN NUGGET (Unnoticed Query) -The querist might melt his gold by a jet of oxygen blown through a spirit lamp, and, I suppose, cast it in a clay mould. The oxygen may be stored to sufficient

quantity for this in a bladder, with stoprock and jet. A hote: flame is got from mixed oxyger and hydrogen, through a safety jet, which costs pernaps 5s. more; but he must be careful to keep the mixed gases from risk of catching fire elsewhere than through the jet, or their explosion will be serious.-E. L. G.

[4871.]-TRANSPARENT SIZE (Unnoticed Query).Try gelatine. If soaked in cold water for three hours it very readily dissolves; is perfectly transparent and colourless; and weight for weight is from two to three times as strong as glue of commerce.-T. S. U. [4872.)-PRESERVING MUSHROOMS (Unnoticed Query). I believe mushrooms may be dried in a hot-air chamber to the consistency of leather, and in that state will keep in a dry place. They of course require soaking in cold water for some hours for use.-T. Š. U. [4894.]-HEATED CHAMBER (Unnoticed Query).--You will see what you want at any calico printer's.-T. S. U. [4959.]-DYEING WOOLLEN.-"J. B. N." will have to dissolve in boiling water a little bichromate of potass and a little red argol, then boil the cloth in it for an hour, take them out and let them hang for about half a day, rinse them well in cold water. Now dissolve a lump of cutch, enough to make a dark liquor, boil the cloth in it for about half an hour, afterwards rinse well in cold water and dry, and he will have a fast brown. I have done thousands of yards with success.-BINDA.

[4959.]-DYEING WOOLLEN.-Try the aniline brown: full particulars on each bottle. All the aniline dyes are peculiarly suitable for using on animal fibres, and they are readily and easily applied.-M. C. D.

[4982.]-HEAVY FLUID.-Those heavier than water and not mixing therewith in all proportions, are nearly all either violently active chemicals, or very volatile, and fetid or dangerous in the vaporous state. I copy for Mr. Hindle the following names of the few tamest or most manageable, chiefly from a paper of Dr. Gladstone in Phil. Trans. 1868:

Mercury.

Mercuric Methyl..

Sp. Gr.

Boiling Pt.
Cent. 850
93
above 61°
158°

18.6

3.06

*Bromoform

2.63

Mercuric Ethyl

2:44

Iodide of Propyl

1.71

Iodide of Amyl...

1:49

*Sulphide of Carbon *Oil of Wintergreen Chinoline

1-27

1-14

1.08

Parsley Oil.

1.07

These marked are just soluble enough in water to give it a flavour; the others, I believe, insoluble. The more volatile, especially sulphide of carbon, will dissolve iodine, sulphur and phosphorus (together or separately), in quantities enough to become somewhat den

ser.

To the second question, no metal but arsenic, and possibly thallium, is known to be more volatile than mercury: and it is not likely any two could be vaporized together.-E. L. G.

[4995.]-DYEING GOLD COLOUR.-" T. S. L," should try Manchester Yellow, which is made from naphthalin. It will produce on silk, wool, and leather brilliant shades of gold. The proportions of course depend on what kind of shade he requires.-M. C. D.

[5004.)-RAISING WATER BY FLANNEL.-Thanks to "R. F. B. R." The only questions I can suggest on which further information about the hair-rope machine seems desirable, are the power he found necessary to raise the six gallons a minute, and the speed of rope when doing so. Six gallons disposed in a tubular layer half an inch thick with a bore of three quarters, will only extend 45ft. and I suppose his rope was driven much faster than 45ft. per minute. The theoretic question, why does water thus adhere to either hair-rope or felt,-is it an electrical effect, or what ?-is also interesting, and touched on in no work I have seen. Could "Sigma" say anything upon it ?-E. L. G.

1ft. long riveted in. Mind not get barrels too hot in cast- for moving the body backwards and forwards, a disc of
ing lead in them.-GUN.

ferring on page 164 to answer to this query on pp. 116-117
[5082.]-NORTH POLAR STAR.-" E. L. G. " in re-
says he never has " made out " Jack on the middle horse
in this country. Never heard of him till the Oct. 21
number came out; but on, I think, that very evening, I
saw the" Great Bear" and made out the small star in an
instant. I fetched a small telescope and was surprised
to see so very little difference in the apparent magnitude
of Jack and his horse. I have seen the star every
evening since when the "Bear" has been visible.
Mr. Slater told me, five or six years since, that I had a
sensitive eye, but I feared that an illness, seventeen
months ago, had seriously damaged my vision. I have
better hopes again. Not to make a mistake, I see the
star about in the position of half-past 10, as measured on
centre of clock face, at about 9 p.m., i.e., 45° up to the
a clock dial, compared with the middle horse as the
left.-J. K. P.

monly called sulphuric acid, boils at 325° C., emitting a
[5107.]-HYDROSULPHATE.-Hydric sulphate, com-
vapour, a litre of which weighs 245 criths. To exist as
SO2 HO2 = 2 vols., a litre ought to weigh 49 criths;
dissociation, therefore, takes place at its boiling point,
and decomposition into water, oxygen and sulphurous
anhydride at a red heat. The second part of question
43: I should say No. 1, as they both are nearly equal in
illuminants, No. 1 being the best, as it only contains
half the diluents as No. 2, nearly twice the hydrogen and
a fifth more carbonic oxide.-GEORGE E. DAVIS.
I have softened the tone of a harmonium without injury
[5151.]-SOFTENING TONE OF HARMONIUM.-
to the instrument by removing one spring entirely from
the reservoir, and shifting the other to the centre. The
result was satisfactory to-A COUNTRY ORGAN.

"dry Voltaic pile." Volta's arrangement was a "pile [5236.]-VOLTAIC PILE.-I have never heard of a consisting of a series of zinc and silver discs, with moistened cloth interposed between each." The cloth was soaked in water, slightly acidulated, and to prevent the pile from falling the discs were supported by pillars and a weight on the top of each set, to keep them pressed together. A set generally consisted of 50 of each sort.-R. G.

your requirement, and save you a lot of trouble with [5254.1-PARCHMENT SIZE.-Reply 4871 will suit antiseptics.-T. S. U.

matic, and having only a short range (about 9in.). Brown[5259.]-TELESCOPE FOR SPECTROSCOPE.-All ing, of the Minories, would supply one fit for the purthat is required is, that the telescope is perfectly achropose.-GEORGE E. DAVIS.

[5267.]-BALLS.-In reply to "J. K. P.," allow me to remind him that in Fig. 1, the plug would be large enough to make a fusee hole, capable of allowing the extraction of the iron support in a finished cast. In the mould, Fig. 3, there is a mistake. The inner circle now represents the outside of ball, and touching the diameter as the pattern, Fig. 1) round the circle which should be omitted, and another circle drawn (same edge of the flange on the support. But there is no limit to the shape of the support, so long as it will hold the

core.-FRED ROE.

[5295.]-THE MICROSCOPE (Drawing from).-I have small power, and should never dream of resorting, howcopied optically both from microscope and telescope of more refined than a fragment of thick plate-plass, fixed ever rich, to the optician's camera lucida, or anything before the eye-hole at any inclination between 30 and 45° to the axis of the instrument, so that your line of glass must be rather thick because, unless you limit the sight may be turned between 60° and 90° downward. The upper reflecting surface to a width barely exceeding the thickness, you will have a reflection from the lower surface, interfering with the one you are copying. The only difficulty is as to the mode and materials of drawing, which will be found easiest with a white crayon on a good surface, and if the pencil is grey, it should be black surface. The "flexible slates" now sold are a coated with white, to make it more visible to you. In copying distant objects without a telescope, there should be either a concave lens between them and the reflector, or a convex one between the reflector and drawing. Nothing between the reflector and eye can be of any use. E. L. G.

be either too wet or too dry,or the mould too hard rammed, culty may arise from various causes; the facing sand may [5300.]-IRON CASTINGS.-"Young Moulder's" diffthe first two, this must be left to his own judgment, as or the metal too slow poured into the mould. To prevent if too wet it will cause the iron to bubble and invariably some qualities of sand can be wrought wetter than others; out of the face of the mould, particularly around fore the metal, and in some cases will wash large pieces scab, if too dry the blackening and sand will run bethe gate. scab, Hard ramming will cause the mould to the casting; if heavy, must be rammed hard to the ramming depending on the weight of prevent it from swelling, consequently the mould must pouring gate firm, and clean pour your metal quick and be well vented and pricked in the face. Make up your the above it will assist you in making the castings solid. hot; never mind though skin is rough. By attending to

what assistance I can. Let him first cut his vencer a (5160.]-VENEERING.-I will give "Troublesome " little larger, as it slips a little while laying; it is first roughened on both sides with the toothing plane, or a rough rasp; this removes all grease and saw-marks; the surface to be veneered is treated in a similar way. This roughening causes the glue to adhere. They are then well warmed at the fire; this is very essential, as the warmer it is the better and the easier it is to lay on. He must now clear the bench of all encumbrances; save glue-pot, hot water, sponge, and veneering hammer; and likewise get some assistance. Now wet both sides of the veneer and apply plenty of glue; lay the veneer down on its bed, the assistant holds one end firm; now take down on the head with the left; begin at the middle and the veneering hammer in the right hand, press hard work zig-zag ways towards the end and sides, pressing out, as he goes, all superfluous glue; turn the work round, begin at the middle again, and work off at the other end, going over it several times until it has stuck; keep it damp all the time with the sponge; a slight tap with the back of the hammer will tell if it is firm by the sound; lay a weight on it and set it to dry near the fire. Veneering, like all other work, requires practice.-R. Fox. "Troublesome" will find it troublesome at first. [5181.]-HOW TO MAKE A MICROSCOPE.-To a culty, and any one who can braze on solder with the person expert in the use of tools, this presents no diffiespecially if he has the use of a lathe. There are no blowpipe will be able to make one without assistance, the ENGLISH MECHANIC, and eagerly swallow any infordoubt a great many amateurs or "cobblers "who read mation which may be given for the making of philosophical instruments. I confess I am one of these "Jacks of all trades," and being intent on possessing a better instrument than I could afford to buy, I began to make one of paper, paste, and perseverance; but on trying to work with it, the paper tube was so clumsy that I disstill far from perfection. But when I asked myself the carded it and took to tin, which answered better, but was plain question" Why not make a proper brass instru--J. T. H. ment," I saw no reason why not, and made one. Pre[5010.]-SMOKY STOVE.-J. Bull must try and dis- microscope knows the principles on which it is consuming that the amateur who intends making a cover if the stove is in fault or whether it is the old story structed, I need not touch on that part of the subject. of a smoky chimney. You should have mentioned what The glasses may be procured at any optician's, much the sizes of flue and chimney are, if the chimney is built against a house, and of what thickness of brick- teurs generally. Procure a price list of Cox, Ludgatemore easily and better than they can be made by amawork; but one might ask twenty questions and then not hil, or other respectable maker, and select quantity and be able to give "advice" in the matter. Try and get a quality according to purse. To make the instrument, look at "A Treatise on Chimneys," by Eckstein; you may get a hint from it as to where the fault lies.-A. Č. G. procure a brass tube, the proper length and diameter (cost about 6d.) for the body. The eyepiece may be [5038.]-PODURE.-"A. S. C.'s" description corre- easily made of a small toy one-draw telescope (1s.). sponds with that of the genus Macrostoma. The dif. Take out the glasses, which are no use for a microscope, ferent species are common; are found in such places as mentioned; are amongst the largest of the Poduride the eye and field glasses in opposite ends, you and cut each tube to about 1in. in length, fixing (full grown specimens attaining a length of in., in- will then have an erecting eyepiece with variable cluding the antennæ) and the scales resemble those of power. This should the Lepismide. They are not Podurm, as this genus is of the large tube. The object-glasses may be prothe upper end furnished with hairs, but has no scales. If the antennæ cured fitted into cells to screw together. This saves a equal the length of the body, are four-jointed, and the great deal of trouble to the amateur, and is in fact neceseyes six on each side, they belong to the genus Macro-sary to the proper centering of the lenses. He will be stoma. As yet, the knowledge of these interesting crea- likely to spoil his work if he attempts to make the cells tures is by no means perfect. Lubbock in "Transactions of Linnean Society;" also the body, get an inch of brass pipe, smaller in diameter Vide papers by Sir J. himself, unless very expert at the lathe. To fix them to fourth number of Monthly Microscopical Journal.than the cells, and file a few threads of a screw on one FELLOW OF ROYAL MICROSCOPICAL SOCIETY. end to screw the cells to. Get another inch of tubing larger of the two to the end of the body tube by a hollow a little larger, for this to slide into, and fasten the cells from the tube each time of using. The two bits cone. By this arrangement you avoid unscrewing the of tube may be procured at any barber's or tobacconist's, being sold as connections for the mouthpieces of pipes. You have now the optical part of the microscope complete. Next get a bar of brass or other material 9in. or 10in. in length. To one end fasten a piece of tubing for the body to slide in. About the middle fix the stage, which may be of brass or tinplate and blackened; and a couple of inches below this, place the reflector, cutting a hole in the stage to admit light to the object. To find the exact position for this aperture, slide down the body till it touches the stage, then mark a circle round the end of the tube. The stand may be made of a piece of raahogany for a foot and a brass pillar stage are fixed to the top of this by a joint, so as to be able about 8in. high. Fasten the bar to which the body and is the most simple plan of making a microscope that I to place the instrument at any angle required. The above can suggest. The form of the instrument is so well known as to need no further description, and an ingenious famateur will find no difficulty in making one from these directions, with such improvements as his fancy may suggest. If he can adapt a rackwork motion

[5039.]-BORING GUN BARRELS.-The way to bore gun barrels by hand is this:-Make a steel rod with a square bit about 8in. long on one end nearly the size of the barrel, the whole rod 1ft. longer than barrel; harden bit end and temper to a purple; see that it is very true and perfectly cylindrical, then pack up on one side with strips of brown paper, and one thin strip of deal rounded on one side. When it fits barrel tight take a cut right through, and pack again until the barrel is a perfect cylinder inside. This may be known by casting a small ingot of lead in. long in the muzzle and forcing through with a rod. Having done this, cast a lead about 8in. long on another iron rod (in the barrel) and smooth with coarsish emery and oil. Now if a muzzle loader, open at breech a little, about 6in. down, and muzzle about 3in.; if a breech-loader about 9in. from breech only; shoot the gun; if it does not shoot strong enough breech more, if not spread enough, ease a shade at open at muzzle, but be very careful about this. use a machine to produce the cylinder, but any gun can Gun-makers be altered by the lead and emery. A good shooting gun should place with 24 drachms powder, and 1 shot (No. 6) at 40 yards on a 3ft., iron plate, 180 shot placed regular all over, and through one side of a canister, and split the other. For the ends of boring rods a cross piece

slide into

he wants to know the pressure upon the bottle from
Mr. Rhodes's question appears paradoxical; but whether
[5302.]-PNEUMATIC QUESTION.-The first part of
the external air, the air being completely exhausted
inch. And the why is, that the atmosphere presses upon
from the bottle, or if it is the pressure of the air itself in
everything on the surface of the earth to that extent,
a sealed bottle, in both cases it is 15lb. to the square
and the separation of the internal from the external air,
by sealing the bottle, does not cut off the pressure which
existed in the bottle previous to sealing.
try an analogous experiment by plunging a bottle into
water, and, when filled, press your thumb on the neck
You may
able to perceive that the condition of the water in the
to prevent egress and ingress of water, when you will be
bottle and the bottle itself exist under exactly the same
from the bottle, the bottle has to bear the whole of the
circumstances as before. But if you exhaust the air
in the bottle is subjected to atmospheric pressure, and
pressure. And the reason a bottle filled with water is
being denser than air presses outwards; therefore the
not crushed by atmospheric pressure is that the water
the external air as he supposes.-J. BUTCHER.
bottle has to resist the pressure of the water, and not

into account the weight of the water inside), the pres
[5302.]-PNEUMATIC QUESTION.-When you cork
a bottle, whether it contains air or water (not taking
sure of the fluid enclosed against the sides of the bottle
when it was corked (so long as the temperature remains
will be the same as that of the atmosphere at the time
the same), and the internal pressure will be counter-
atmosphere outside the bottle. Now place the bottle
balanced by a like pressure, due to the weight of the
completely exhaust the air, you would get the original
beneath the receiver of an air-pump, and if you could
pressure inside the bottle unsupported by any outside
it. This might amount to 15lb, on the square inch.
pressure will be the above minus the pressure of the
course, as a complete vacuum is unattainable, the trus
air remaining in the receiver. This will answer both
branches of the query.-O. F.

milion; as it stiffens, put the wax on a wire frame with
[5303.]-WAX BASKETS.-Whilst melted mix Ib. of
wax with about 2d. worth of carmine and 1d. worth ver-
& soft brush.-B. G.

have is what is termed in the trade a "pair of turns;
they are used with a drill-bow.
[5308.]-WATCHMAKERS' LATHE.-The tool you
work, or putit on an arbor pointed at both ends; put on
to it a screw ferule, and put it between the centres of your
Centre or point your
turns; give the drill-bow a turn round the ferule; ad-