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other parts of the process are to be con power being thereby nearly doubled. ducted at the station. The engine itself When the stock of liquid material is is proposed to be constructed in the man consumed, it is to be replenished at the ner represented in the accompanying en station; and the carbonate of ammonia is gravings.

to be withdrawn from the condenser, Fig. 1 is a sectional elevation ; CCC E E E, by the removal of one of the are a series of wrought iron tubes charged hemispherical ends which are shown in with liquid carbonic acid. The screws the drawing are very firmly connected together by Another mode of employing the con. screws and tic-bolts, and are subse denser, which Mr. Baggs points out, is quently rendered perfectly sound in all by effecting a solution of the salt which the joints by soft solder. B is a screw it contains, and allowing the liquid to valve for permitting and regulating the flow out. escape of the carbonic acid. K is the in In fig. 3, is shown a contrivance for duction pipe, which establishes a com preventing the escape of any ammoniacal munication between the tubular reservoir gas into the atmosphere. L is the piston CCC, and the cylinder D. Before the rod; P P the stuffing-box; M M is gas, however, is allowed to enter the an air tight, flexible tube, capable of excylinder, it is made to play round a li tension or contraction, and fixed at one mited portion of the circumference of the end to the stuffing-box P, and at the condenser E E E. F F are the eduction other end to the head of the piston rod pipes leading from the cylinder D to the L. If any gas escape between the piston condenser. (The valve gearing is not rod and the stuffing-box, it will immeshown in the engraving, as it is the same diately flow down the tube N into a as that usually employed.)

quantity of muriatic acid contained in the Fig. 2 is a plan of the engine. A A vessel 0, where it will be absorbed. A is a tubular receptacle for liquid am muriate of ammonia will be thus formed monia, similar in its general arrange which may be removed at intervals from ment to that used for carbonic acid. the vessel O. G is the valve, and H the induction A still better method of promoting the pipe for the ammonia. This latter is escape of both the gases would probably arranged in the same way as the in- be, to form a similar elastic covering duction pipe for carbonic acid, and the round both piston rods, and establish a ammoniacal gas is made to circulate free communication between them both to round another portion of the circumfer the condenser. ence of the condenser E E E.

Some mechanical difficulties may very To throw the engine into action, after likely arise in the course of working out it is charged with the two liquids, it will Mr. Baggs's ideas, but none which the be only necessary to open the valves B perfect workmanship, for which our enand C; the carbonic acid and ammonia gine factories are so justly celebrated, will immediately flash from the reservoirs does not justify us in expecting will be in the form of gas through the induction

The invention we consider pipes K and H; flowing into their re sound in principle, and hope soon to see spective cylinders, and thence escaping it applied on such a scale of practical through the pipes F F into the condenser magnitude, as will effectually determine E, where they will enter into combina the question of its practical utility. tion.

The condensation of the gases in E, will be attended by the evolution of a

DOCTOR PAYERNE's METHOD OF PUGI. great quantity of caloric, and, in order FYING THE ATMOSPHERE OF A DIY to reduce the amount of this in the condenser, as well as to increase the elas. Sir,–Of all the wonders of the present licity of the gases before they enter the age, there is, perhaps, not one that has working cylinders, the induction pipes attracted more universal attention than are made to embrace the condenser, the fact, proved by Dr. Payerne, that a

By the transfer of caloric (thus effected) man may exist several hours below water from the interior to the exterior of the without having any communication whatcondenser, the pressure within will be lessened, and that without increased, the

ever with the external atmosphere, and it not being altogether known how the



ceiver of an air pump, a machine capable of resisting great atmospheric pressure, and of great powers, is absolutely necessary; but where the pressure on the inside and the outside is the same, no such strength or power can be required-even a common pair of bellows would, I should think, answer every purpose required.

Dr. Payerne's method of purifying the atmosphere of a diving bell is a very ingenious and a highly philosophical application of chemical science, and oue that will afford the means of definitely ascertaining the cffect of respiration on the atmosphere ; any attempt therefore, on his part, to throw the veil of mystery over that which he has donc, can bave no other cffect than to detract from the praise he is so justly entitled to.

F. C. London Mechanics' Institution,

November 8, 1812.


doctor purifies the air, which, like other men, he must vitiate by, respiration, I beg the favour of your giving publicity in your journal to the following remarks, lest, from the desire that now so universally exists of applying to practical purposes whatever discoveries are made in science, any one should think of repeating Dr. Payerne's experiments with such means only as he Arpears to avail himself of.

It is well known that Dr. Payerne takes with him into the diving bell an air pump, and a vessel containing cream of line and potash, and that he has therefore all the requisites for abstracting from the air the carbonic acid gas generated by respiration; but that body being formed by the combination of the oxygen of the air with the carbon of the blood, the question arises, how does he replace the oxygen consumed ? It is evident, that if it be not restored to the air, the functions of the lungs cannot be properly performed, and death must soon ensue.

Chemical science does not show how the oxygen could be extracted from the carbonic acid gas generated and absorbed by the lime, nor does it appear how it could be obtained from the water in sufficient quantity for use, even supposing the apparatus used for decomposing walor to be at hand, and that the hydrogen could be got rid of, and it therefore seems to me, that it must be taken into the bell in a compressed form in some part of the doctor's apparatus.

Supposing this to be the case, the expense of the application of Dr. Payerne's discovery to the common diving bell, compared with that of the air pump, may readily be ascertained by those who are familiar with the use of that instrument.

An adult consumes about 125 cubic feet of air per day, equal to 25 or 26 cubic feet of oxygen, or rather more than 1 cubic foot per hour, and this quantity cannot be made and compressed into a vessel at a less expense than 1s. per cubic foot. To the expense of the gas is to be added that of the apparatus, such as the air pump, vessels to contain the gas, &c.; but it appears to me, that if, instead of the air pump that is used in the bell for forcing the air through the lime, a silk bag moving in a frame were adopted, a far more efficient machine would be ob. tained at a considerably less expense. To exhaust a vessel of its air, such as the re

Sir,-You expressed an opinion, a short time back, that no perfect alloys of any of the metals have as yet been performed by the electrotype process. Now, I have deposited on copper an alloy of lead and iron, two of the most difficult metals to make an alloy of; and, as it may be interesting to some of


readers, I will describe the very simple process of doing so.

In a nitric solution of lead I put a solution of sulphate of iron (copperas ;) the solution was cold, and not very strong ; -when the solution was too strong, the sulphate of lead did not precipitate, but became a black liquid, which did not

The liquor remaining, after the sulphate of lead has been precipitated in white powder, is the solution containing sufficient iron and lead to electrotype wiih. The alloy was much harder than lead—would not melt at a strong heat, considerably above the temperature that lead melts at-aud was magnetic, yet could be cut with a knife. The most singular part of the circumstance is, that


• Our correspondent is evidently not aware that Dr. Payerne has taken out a patent for his invention (in the name of Mr. Vigers,) the time for lodging the specification of which has not yet elapsed. Dr. Payerne, therefore, is doing no more than prudently availing himself of the time allowed by law for specifying his invention.- Ev. M. M.


the two most unmanageable metals, lo fully to the extent of 11 per cent? But make alloys of, can by electricity become your correspondent contends, that if such the most manageable.

be a fact it is incumbent on Mr. Parkes I am, Sir, &c.,

M. to prove (as the increased power, he says,

could come from no other quarter),

that there must be less friction in MR. LUCY'S SUBSTITUTE FOR THE FLY

the new apparatus than there was with

the old fly-wheel. I do not consider Sir,-I am obliged to your corre this a very logical conclusion, for it spondent “7," for referring me to amounts to this, that unless he proves the work where Mr. Lucy's improve an impossibility, his facts must go for ments on the steam-engine is fully de- nothing. Mr. Parkes, according to his scribed. It has no fly-wheel whatever, notion, must connect his facts with your it appears, but in place of it there is a correspondent's conclusions, while at the cogged-wheel made fast on the crank same time he will not connect his matheshaft, the diameter about twice the length matical conclusions with the facts which of the throw of the crank; and this wheel

he admits are undeniable. He expresses takes a smaller wheel, made fast to the himself also in a strange way, with respect axle of a second crank, which latter is to the statement made by Mr. Scott one half the dimensions of the former, so Russell; as for instance, that he is sur. that two revolutions of the large wheel prised he should have stated such and will make the small wheel give four. buch facts, doubts whether he knew the Farther, there is a connecting rod and bearings of them, that it is to be regretted beam to the second crank, and a cylinder that he did so, &c. Why, did your corand piston rod at the other extremity of respondent expect that Mr. Russell would the same, which cylinder has a bottom have acted so disingenuously and improbut no top, and is the pneumatic appara perly, as to be deterred from stating facts tus for equalizing the motions, for which even had they gone counter, as they have, purpose the arrangement is admirably in this instance, to his own published contrived. A little consideration will

opinions ? show, that the pressure of the atmosphere One example of the mode in which acting on the piston of the second cylin your correspondent draws erroneous conder, will make the main crank pass the clusions from facts worth nothing is centre by a simpler arrangement than particularly deserving of notice. No would be required with a double engine ; doubt a hundred apples purchased at the and I am surprised that your correspon market will not, with any newly discodent should have expressed himself in vered basket deliver 111 apples at the manner he has done, relative to this home; but he concludes from this that improvement, which appears to me to be another hundred apples sent home in one of greater consequence than any another description of basket, could not which has been made in the crank engine deliver less than the hundred. With for many years. Your correspondent holes in the basket, for instance, there admits that Mr. Parkes's authority, as far might be several lost, and but 80 delias the stating of facts is concerned, is un vered. The analogy is anything but questionable ; the same also with respect complete; mathematicians are not bound to Mr. Scott Russel). Now the latter to connect mathematical facts with gentleman admits that the increased work practical ones; but practical facts, accordof each pair of stones was in the propor ing to his views, must be proved not to tion of 56 to 52, and Mr. Parkes states vary from mathematical ones; while at that an additional pair had been put up the same time it is admitted, that all the in the mill. And these, be it observed, elements connected with the practical are not inferences but naked facts; and fact are not embraced in the other case. your correspondent himself admits that In conclusion, I should be glad to know the friction with the new coptrivance your correspondent “ M's." opinion on must be, as no doubt it is, considerably Mr. Lucy's improvements; I mean whegreater than the friction with the fly ther he would think there is any loss by wheel. Why then, let me ask, can he such an arrangement of crank movedoubt the inference drawn by Mr. Parkes ments. from these data, that the power of the

I am, Sir, engine is considerably increased, and




THE VALUES OF BENEFITS DEPENDING ON LIFE CONTINGENCIES. [We find it will be more convenient, instead of the notation proposed in our first paper, (p. 428,) to represent the indications of the table of mortality, to make use of the following, which will therefore be adhered to in the remainder of these papers. We shall employ l, with the age attached, not as a suffix, but enclosed in parentheses, to denote the number who attain each age. Thus, the numbers represented by the table to attain the ages 0, 1, 2, 3, ...... x years, will be respectively denoted by 1(0), 4(1), 7(2), 4(3), ...(1). And hence, the number who die in their 1st year will be denoted by ?(0) 1(1)




1(2) 1(3) xth

1(3--1) 1(x) (1+1)th

1(3) — 1(*+1) and so on.] Part II.-Description and Properties of the Tables. We propose in the present paper to the corresponding numbers are denoted describe the Commutation Tables, ex by D («), N (w), &c. plain their construction, and show the al The columns are constructed as folgebraical properties that belong to them lows: Take any age, 20, for example. in virtue of that construction. We refer The number in column D, opposite age for illustration to the Table contained in 20, is equal to the product of the numthe two following pages.

ber represented by the mortality table to The Table consists, it will be seen, of attain the age 20, into the present value two side columns containing the ages, and of one pound due at the end of 20 years. five inner columns, headed D, N, S, M, So that the algebraical expression will and R, respectively. There is another be, D (20) = 1 (20) v20. column headed C, which is essential to And generally, the number corresthe theory of the tables, and the proper ponding to any age in column D, is equal place for which, if inserted, would be be to the number who complete that year of tween columns S and M. But as this their age, multiplied by the present value column is not required in practice, it is of one pound due at the end of as many never exhibited. The letters D, N, S, &c., years as are equal to the age. Hence, are chosen quite arbitrarily, and have no the general expression for the value of reference to the signification of the co the numbers in column D will be, lumns at the head of which they are D (x) = {(x) v*,* x denoting any age. placed.

Hence also, if the age be 0, we have, The number in any column, opposite D (0) = 1 (0) 09 = 1(0), since vo = 1. to any age, is denoted by the letter at the That is, the first number in column D head of the column, with the age attach is equal to the radix of the Mortality ed, enclosed in parentheses. Thus, the Table. number corresponding to age 20 in co Column N is formed from column D, lumn D, for example, is denoted by by inserting opposite each age in N the D (20), in column N, by N (20), and so sum of the numbers opposite all the of the other columns. If the age be x, higher ages in D. For example,

N (20) = D (21) + D (22) + D (23) + &c. to the end.

N (21) = D (22) + D (23) + D (24) + &c.
So that the expression for the general term of this column is

N (2) = D (x + 1) + D (x + 2) + D (x+3) + &c.
X, as before, denoting any age.

higher ages. The expression for the geIt follows from this that the last N in neral term is, therefore, the Table is 0.· For, since N (x) = S(r)=N(X) + N(x + 1) + N(x + 2) + &c. D (x + 1) +...., if x be the highest age, Dle+ l) and all the following terms va

By an expression for the general term of a

series, is meant, an expression in which a variable nish, since there are no survivors at the quantity is introduced, and which, by giving any ages denoted by x+1, &c. Also, the particular value to the variable, gives the term of

the series corresponding to that value. Thus, in first Nin the Table is equal to the sum the above general expression, D(n)= 1(x) , ot, of the D's except the first; or N (0). which denotes the age, is the variable; and if we D(1) + D (2) + D (3) + .

give to it a particular value, we have immediately

the term of the series corresponding to that value. Column S is formed by inserting in it, For instance, if x=20, the expression becomes, opposite each age, the sum of the num

D (20) = 1(20) 720;

and this is the value in column D corresponding to bers in N, opposite that age and all the

age 20.

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