that of the joint in the upper valve or piston.

Fig. 3. Shows the relative position of the piston and valve during the upward or effective stroke.

Fig. 4. The same in the downward,

or return stroke.

ANCIENT COMBINATION LOCK.

Sir,-Perhaps the following description of a well-known lock of combinations may interest some of the readers of the Mechanics' Magazine. It has been translated by a friend from the old German work from which I have already furnished you with some extracts. The work itself bears date 1636, and in the account of this lock you will observe that reference is made to a still older work. Few who possess the lock are, perhaps, aware of its antiquity.

I am, Sir, with respect,

Yours, &c.,

U.S. HEINEken.

Sidmouth, November 27, 1841.

Of a Lock without a Key. Gustavus Selenus, in his Cryptographia, p. 489, explains, from Cardanus Johannes Butens and Johannes Jacobus Weckerus, how to make a lock which may be opened and shut without a key ; and as such locks are common, both in our own and foreign countries, I will endeavour to explain in this place how they ought to be prepared, but at the same time refer the readers to the above-mentioned authors. The form of the lock is this, (see figure, a fac-simile of the ori

53

may be rightly understood, we will, as we have said, give instructions how to make a table. And, first, we will suppose that there is only one ring; afterwards, two; and then, three; and lastly, four. But we will show it, not by transposition of the letters which are graven upon the lock, but by means of numbers. They shall have, then, the numbers 1, 2, 3, 4, 5, 6. If there were only one ring, a table of six numbers would be enough; if the lock has two moveable rings, there would be thirty-six changes, as is seen from the annexed table; with three rings, the table would be made from the second table, by setting them after one another in rows, six times, and then before the first rows to place 1, before the second, 2; before the third, 3; before the fourth, 4; before the fifth, 5; and, lastly, before the sixth, 6. Thus, there are 216 rows. Lastly, suppose the lock to have four rings: the table would be made from the third, by placing it six times, as by — (?) the others; and before the first rank, every time, put 1; before the second, 2; before the third, 3; and so on with the fourth, fifth, and sixth. Then such a table will comprise 1296 changes. So, when the lock has five moveable rings, the table must be made from the preceding rings, and will produce 7,776 changes; for 6 multiplied into 6 will produce 36, and 6 times 36 = 216; again, 6 times 216 1,296; and, lastly, 6 times The sixth table would 1,296 = 7,776. have 46,656 changes. I will here subjoin a table with three rings, (as the table with four rings may be easily made from it,) in order that this proposition may not become too long. (See Table I.)

=

As we have said above, that we have used the numbers instead of the letters graven on the lock, it follows how the preceding numbers may be expressed by letters. Let us suppose that in the fourth table the first ring has six letters, O F CSDA, the second ring OTOAE M, the third TDLN VA, the fourth RETAST; and, preserving these four arrangements, let such letters be represented by one of the numbers 1 2 3 4 5 6, in any order that you please, in the manner in which the following table is made. (See Table II.) Thus, if one reads the rows one after the other, from top to bottom, you have the six words, OVTR, FTDE, COLT, SANA, Now, in the DEUS, AMA T.

fourth table, these words will be represented by the numbers 1 3 6 4, 34 1 1, 2525, 6243, 5156, 4632. One can also, by another arrangement of letters, find other words upon the ring, as FTAT, STLE, DTVT, AULA, to which will answer the numbers 34 32, 6421, 5455, 4323. Now, he who wishes to open the lock, and does not know the name on it, must try every arrangement, one after the other, from the table, and at every arrangement draw the upper part of the lock towards the righthand, until it comes out, and the opening of the lock must certainly follow.

Q. E. D. [From Schweuter's Delicia PhysicoMathematica, 1636.]

PRACTICE AND PRACTICIANS, v. MATHEMATICS AND MATHEMATICIANS. -MR. CHEVERTON ON S. Y.'S REJOINDER.

Sir, I would gladly haye been saved the necessity of making any remarks upon the last communication of your correspondent S. Y.; but it is impossible for me to be silent under the imputation of having myself written the censure which I lately quoted from the pages of your Magazine, as having been inflicted upon him, many years since, "by one who appears to have known him well."* I am not aware that my notions of what is fair dealing are too refined; but if I had really been the author of that censure, my writing respecting it in the manner I recently adopted would, in my estimation, have been nothing less than a deliberate falsehood. I must, however, do S. Y. the justice to admit, that he may not have viewed the imputation in this offensive light; for those blunted perceptions of what is just and right, which have enabled him without compunction to put forth gross and deliberate, because written, misrepresentations of another's opinions, may naturally enough incapacitate him from distinguishing clearly the respective boundaries of truth and mendacity.

I have no apology to offer S. Y. for the personality of my remarks: a writer who descends to the gross misrepresenta tions of which he has been guilty compromises his character, and therefore to

The censure in question appeared in your third volume, at page 438, and the communication which contained it was signed, "James Yule, 631. Red Lion-street, Clerkenwell." For nyself, I know nothing of your correspondent S. Y., beyond what has appeared in the pages of your Magazine.

value of the mathematics, as displayed in its proper sphere; or even to the occasional and partial utility of its more mixed investigations, if used with proper reserve, and with strict subserviency to physical science;" and yet, in the face of such a declaration as this, your correspondent says, that I "do my best to persuade him and others that the mathematics is a noxious science "-and S. Y. is an honourable man! Sir, I shall not have written in vain, if an earnest denunciation of wilful misrepresentations should excite in the breasts of your readers such strong feelings, as to the moral obliquity which the practice involves, as shall secure for it on all occasions an indignant and deterring reprehension.

I conclude with one word to the general reader. It may by some be thought superfluous to descant on the abuses of a subject: so it would, if they were generally recognised as such; but the misfortune is, that they are perpetuated precisely because, the mask not being taken off, they pass current as the proper use of things.

I am, Sir, yours, &c.,

66

BENJAMIN CHEVERTON. P.S.-As the opportunity offers, I may as well avail myself of it to correct a very amusing misconception (nothing worse) which S. Y. entertains of the class of men to which I refer by the designation of "Practicians." He actually appropriates it to himself and the operative mechanics, and very modestly declines the praise which I have bestowed on "practical men,' practical talents," "practical processes, and "practical methods of investigation." Nay, he says that his is the less educated class ;" and he cannot think of admitting, what he imagines I have been doing my best to persuade them, that his, "the less educated class, is the superior of the two"-the two being the working men and the mathematicians! I should have as soon thought of calling the manufacturing chemists, who furnish our laboratories with potassium and sodium, philosophers, on the strength of the discovery of those metals by Sir Humphry Davy having justly entitled him to that appellation, as of bestowing on our worthy and industrious artisans the honour and praise which belong to a Brindley, a Smeaton, a Watt, a

Rennie, and a Telford. These were "practical men," but they were men whose shoe-latchets few of our mathematicians were worthy to unloose—men, whose fame will descend to all times, and in respect of whom, or at least of one of them, whose fortune was no bar, Arago has said, that it is a reproach to the na tion he was not raised to the peerage. Of the same class, though possibly of a lower grade, are the men whose practical talents have originated, and brought successfully into action, the various enterprises which characterise our times. Take, for instance, the projectors of steam navigation; and, for a late example, the parties whose practical acumen and professional skill have contributed, in any department, to the success of the Great Western steam-ship. It is to directing minds like these that the terms "practical talents," and "practical men," are applied, by every one who understands what he is talking about; but your acute correspondent, S. Y., it appears, has been dreaming all along that they refer-in the case of the Great Western, for example, to the shipwrights, the "engineers," and the stokers employed-to the last class of men especially, for they are more "eminently practical," that is to say, harder working, than any of the others.-B. C.

LEWIS'S PARALLEL MOTION FOR PUMP

WORK.

[Registered pursuant to Act of Parliament.] The annexed engraving exhibits a lifting force-pump recently designed by Messrs. Lewis and Co., of Stangate-street, in which they have introduced a novel substitute for the slings and guides heretofore employed for preserving the parallelism of the piston- rod. The novelty of this arrangement consists in the employment of a movable fulcrum, which describes the arc of a circle, while the piston-rod, and the end of the lever or handle to which it is attached, moves up and down in a straight line.

In the illustrative engraving, a is the working barrel of a lifting force-pump; b, the piston-rod, attached directly to the lever or handle c d, at c, and furnished with an anti-friction roller, which works in a slot formed in the upper limb of the pump-frame or standard. e is the ful