fixed, and do not completely attain the object sought. Hence the aim of scientific men has been to invent an automaton, or self-acting instrument, for calculation, which alone can deserve the name of a calculating machine. The first attempt of this kind was made by Blaise Pascal, in 1640. His machine performed addition and subtraction mechanically; but it was so difficult to work, and the mechanism so imperfect, that it was soon discarded and forgotten. A similar destiny attended a machine for adding and subtracting, invented in England by Samuel Moreland, in 1673. His other mathematical instrument is nothing more than an adaptation of Napier's scale to circles for multiplication and division. The defects and insufficiency of these two inventions of Pascal and Moreland, gave rise to subsequent endeavors to improve them. Lepine in 1725, and Hillorin de Boistissandean in 1730, were not more successful than their predecessors; nor did Gerstein's invention, submitted to the Royal Society of London in 1735, afford any greater satisfaction.

In Italy, in 1709, Polenius tried his skill on a machine of this kind, but produced only a coarse unsightly abortion, incumbered with weights, that was far inferior to those which had preceded it. In all these cases the aim of the inventors was only to work addition and subtraction. Leibnitz sought to extend the operations of an arithmetical calculator to multiplication and division. The plan of his machine was submitted to the Royal Society of London in 1673, and met the approbation of the society. A similar honor attended it a short time. afterwards from the Academy of Sciences at Paris. But, despite the approbation of those celebrated learned bodies, the plan which looked so promising on paper proved impracticable in execution. Leibnitz labored hard during his whole life to bring his scheme to perfection, expended vast sums upon it, and yet effected nothing. Death carried him off, and his work remained unfinished and forgotten. In 1727, Leopold promised to publish to the world the plan of a machine that should perform addition, subtraction, and multiplication. He died, leaving behind him only a few fragments of his plan. After this it seems that no further attempts were made for a long period, until, in the year 1799, a minister of Wirtemberg named Hahn, came forward with a new machine, which, however, attracted no attention, as it was found to commit serious errors in arithmetic; its internal structure remains unknown, as does also that of a faulty instrument presented to the Academy of Sciences in Gottingen, by Muller, 1786.

The machine invented by Mr. Thomas Colmer in 1820, was a retrograde step in this branch of science.

In the year 1821, Mr. Babbage of London undertook to construct a machine for Government, which should by mechanical means form tables of progression for the use of surveyors. A portion of this machine, forming a progression up to five figures, was complete; £17,000 had been expended upon it already, and to perfect the entire work would have required twice as much more; consequently, in 1833, the project was abandoned, and it is not probable that the costly machine will be brought to a perfect state.

The fragment or member alluded to may be seen at the inventor's. Mr. Babbage is at present occupied with the plan of a machine which is to perform mechanically all the operations of algebra. Already he has 30 plans extant. Every friend of science must heartily wish that the inventor may be more successful with his new project than he was with the previous one. We come now to speak of the recent successful attempt before alluded to. For the last two years, Dr. Roth, of Paris, has been engaged in the construction of arithmetical machines, and the success that has attended his efforts hitherto proves he has accomplished his scheme for performing automatically all the operations of arithmetic, from simple addition, subtraction, multiplication, and division, to vulgar and decimal fractions, involution and evolution, arithmetical and geometrical progression, and the construction of logarithms, with teu plans of decimals. The machine in its present state works addition, subtraction, multiplication, and both kinds of progression, quite mechanically. In division alone the attention is required to avoid passing over the cipher. The arithmetical progression is of vast importance, as it operates from one farthing to millions of pounds sterling; and when we consider the variety and utility of the functions performed by a small instrument, not more than a foot wide, and its comparatively insignificant price, we cannot but congratulate the inventor on his decided success in the results hitherto obtained, and express our cordial wishes that he may meet with every encourage. ment to persevere in his highly interesting and important labors.

Mr. Wertheimber, the proprietor and patentee of this invention, has two descriptions of these machines: a larger one, which performs sums in addition, subtraction, multiplication, and division; and a smaller, which performs addition and subtraction only. These machines have been submitted to the inspection of several gentlemen eminent for their scientific attainments, all of whom, particularly Mr. Babbage, have expressed the most unqualified admiration at their unparalleled ingenuity of construction. Mr. Wertheimber had the honor of an introduction to the Royal presence, at Windsor Castle, when both her Majesty and Prince Albert were graciously pleased to express their approbation of the machines, and to order two of each sort to be supplied for their use. - London Paper.

BARON NAPIER'S invention, alluded to above, was curious and ingenious. He called the treatise in which he described it Rhabdologia, from the Greek gúdos, a rod, because he used several small rods, or slips of card or metal, for tools in his processes.

The apparatus was merely intended to perform those parts of multiplication and division which are usually strictly mechanical and dependent on the memory. For these purposes it abridges considerably the ordinary processes; but Napier's subsequent invention of logarithms entirely superseded it for general use. We are not sure, however, but a set of the rhabdoi might even now prove at times very con

venient.

The staves or rods are small slips, of any convenient size; the figures below are quite large enough. Each of these slips are arranged to show the nine first multiples of one of the nine digits. Care must be taken to separate the tens of the multiples from the units by a transverse line. Thus, in figure 1, below, the staff for 8 is represented. Its length, as will be seen, is divided into nine compartments, which, in their order, show the nine first multiples of 8, 8, 16, 24, &c.; the 1 and 6 which make up 16 being separated by the transverse line, and so of the figures denoting tens and units in the other multiples.

A number of these slips must be prepared, as we have said, for each digit; besides these, there will be needed one slip containing the digits themselves on its nine divisions. Figure 2 will serve to show what use is to be made of these different varieties.

We have supposed, in arranging it, that the number 1296 was to be the multiplicand in the proposed operation. For this purpose four of the slips of card, prepared for 1, for 2, for 9, and for 6, the digits. making up this multiplicand must be placed side by side, as in the figure. The card containing the digits in their order must be placed next them. This arrangement makes a multiplication table which is precisely prepared for the proposed process. The row of figures in the second line of

the table will give 2,592, the duplicate of 1,296, care being taken to add the tens on each slip to the units on the next to the left, with which they are connected in the transverse column. Thus there are given by the table

as will be readily perceived by a slight inspection of the figure. The third line will give the product of multiplication by three, and so of the others.

Suppose now that 3,456 is to be the multiplier in the operation to be performed. Instead of performing the multiplication by the separate digits of the multiplier, we have only to read off the products of such multiplication from the horizontal lines of the table, corresponding to them, and set them down as in the ordinary process, adjusting the tens on each card as we have directed above. Thus,

The application to division will be readily seen.

Suppose the pro

duct just obtained is to be divided by 1,296. The arrangement of the cards as above shows that the nine first multiples of that number are

1.

1,296

4,478,976 1,296

3,888 3,456

5,909

5,184

7,257

6,480

7,776

7,776

0

The division, like the multiplication, being performed as usual; but the mechanical process of multiplication in the calculations being performed by the arrangement of the cards.

The kind of calculations where the instrument would be most likely to be of use, are those where the same multiplier or divider is to be constantly employed, as in calculations for the reduction of amounts given in one system of weights and measures into those of another. The cards can then be arranged once for all, and the amounts of the different parts of the process immediately transferred for use.

To prevent the inconvenience arising from the use of so many different slips of card, or metal, a French artist has made a very neat

arrangement, which gives the apparatus in a very convenient form. He places several small cylinders in a convenient case, parallel with each other, each of which has, on its surface, in nine several columns, the multiples of the nine digits, in the same way that they are arrang d on the cards. These cylinders are each arranged to turn separately, so that they may be at once adapted for the operation, and remain fixed as they are wanted. The numbers of the several divisions are permanently fixed on the side of the case.

NEW INVENTION IN MACHINERY.

A LONDON journal gives the following description of a recent invention in Scotland. It is called an air engine, and is described as now working at the Dundee Foundry, a patent having been taken out for it. It is the joint invention of the Rev. Dr. Stirling, of Galston, and of his brother, Mr. Stirling, engineer, Dundee.

The principle of the invention consists in alternately heating and cooling two bodies of air confined in two separate vessels, which are so arranged, that by the strokes of two plungers, worked by the engine, the whole of the air contained in one of the vessels is sent to the lower end, immediately over the furnace, and is consequently made quite hot, while the whole of the air contained in the other vessel is at the same time transmitted to the upper end, which is cut off from any communication with the furnace, and is therefore comparatively cold.

The expansion caused by the heat renders the air in the one vessel alternately much more elastic than that in the other; and the two ends of the working cylinder, which is fitted with a piston similar to that of a steam engine, being respectively connected with the two air vessels, a preponderating pressure is produced, by turns, on each side of the piston, which is thereby pushed to the opposite end of the cylinder; and so, by the alternate action of the plungers in the two air vessels, it continues a reciprocating motion. and is applied to turn a crank in the same way that a steam engine does.

It has been satisfactorily shown that this engine may be worked with very great economy of fuel, as compared with a steam engine. The principal means of producing the saving is this: that of the heat which is communicated to the air from the furnaces, only a very small portion is entirely thrown away when it comes again to be cooled; for, by making the air, in its way from the hot to the cold end of the air-vessel, to pass through a chamber divided into a number of small apertures or passages, the great extent of surface with which it is thereby brought in contact, extracts from it in the first place, but only temporarily, the greater part of the heat; and afterwards restores it on the air on its passage back again from the cold to the hot end of the vessel. The