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MR. MARTYN ROBERTS'S IRON BATTERY FOR BLASTING ROCKS BY GALVANISM.

Sir, It gives me great pleasure to find that my process of blasting by galvanism has been so successfully employed by your able correspondent "W. C. ;" and, on reference to the account of the operations at Dunbar Harbour, quoted in your 1000th Number, he will see that the simultaneous explosions on my plan were there most effective.

The iron blasting battery "W. C." wishes me to describe, I contrived in order that the cost of the apparatus should be reduced as much as possible, that its arrangement should be of the most simple kind, and that but little trouble should be needed in setting it at work or keeping it in order. Iron, as a material for the negative plate, is not only much cheaper than copper, but is also more effective. It is true that, under certain circumstances, (such as when loaded with rust,) it is less efficient; but when moderately clean, and excited by dilute sulphuric acid, I have found it far more powerful than copper as a negative plate in the galvanic series, (vide my experiments on this subject, as published in the Phil. Mag. for January, 1840;) and the cause of this superiority in iron I have pointed out in a subsequent Number of the same periodical, for June, 1841.

Before the iron plates are used, they should be cleaned of the dark blue oxide which has adhered to, or indeed been rolled into their surfaces by the process of manufacture they have undergone : this is best done by keeping them for half an hour in dilute sulphuric acid, or in a solution of sal ammoniac, and then giving them a dip in dilute sulphuric acid. There are no cells or partitions between the plates in this battery, and one great inconvenience is thus obviated. It is true that this arrangement prevents our obtaining the full intensity of the instrument, i. e., the power of carrying its electric force through a great length of wire; but, so arranged, we gain portability, simplicity of construction, and perfect security against derangement by any clumsiness of the workman using it. I could describe a battery of much greater power than this, but its complicated form would require an electrician to work it with constant success; and I think it better to sacrifice

a little power, in order to obtain the advantages I have before mentioned.

On reference to my pamphlet on the subject of blasting, it will be seen in what manner the power to overcome obstacles, or convey the electricity to a distance, and that to act upon bodies, can severally be obtained, without increasing the complexity of the apparatus. (See pp. 25 and 26.) The batteries I recommend for the use of workmen consist of twenty plates of iron, (copper may be substituted if preferred,) and twenty plates of zink, each 7 inches square. The thickness of the plates is immaterial: the iron need not exceed 15 or 20 ounces to the square foot. A wooden frame is made to receive these plates; the sides of the frame are bars, and the ends solid; these ends rise about two or three inches above the square of the top of the plates, for the purpose of supporting the apparatus for making contact. The bottom of the frame consists of two bars each, placed about a third of the width of the frame from the sides. These bottom bars not only support the metal plates, but also the strips of wood that maintain the plates separate from "ch other.

Fig. 1.

Fig. 1 shows the arrangement of the frame. The iron and zink plates are put into the frame alternately, that is, an iron plate is put close to one of the solid ends, then a zink plate next to the iron, then another iron plate, and so on, until the frame is filled, care being taken to finish the series by an iron plate. The plates are prevented from touching each other by strips of wood, ths of an inch square, and as long as the plates are

deep two of these strips are placed between each plate, and their lower ends rest upon the bottom bars. The plates should be jammed sufficiently tight together to prevent any motion in the strips of wood. The mode of connecting one plate with the other requires some little attention, as a mistake in this will greatly diminish the power of the battery. I have endeavoured so to contrive the connexion as to obtain the action of both surfaces of every plate, and yet to avoid any cross and counteracting currents of electricity. Let fig. 2 represent a section of 5 pairs: let the letters indicate the iron plates, and the numbers the zink plates.

Fig. 2.

2 3 4 5

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b c

d

e f Let a and b be joined together and stand free as a double terminal plate, or pole, having of course a wire proceeding from it as a conductor; then join 1 to c, 2 to d, 3 to e, 4 to f, and 5 in this series of 5 pair will be a zink plate unconnected with any iron plate, but having a wire soldered to it going off as a conductor in the usual way from the other terminal pole of the galvanic series. In the same manner is a series of 20 pair put together, and connected in the frame as in fig. 2, by means of thick wires or strips of metal carefully soldered to them. The several plates are separated each from its nearest neighbour, by the strips of wood already described. The plates being thus arranged, the wire soldered to the double iron plate (see fig. 3) is fastened to the fixed disk of the apparatus for making contact, described in the pamphlet, and the wire joined to the zink plate terminating the series (as 5 in

A

plate. It is needless for me here to describe the apparatus for making contact, as an account of it has already appeared in your pages.

The box for containing the exciting solution (1 part sul. acid to 16 of water) is generally made of 4th inch plank, the joints dovetailed, and set together with white lead; this will make it water-tight. The box should be about an inch longer and wider, and two inches deeper inside measure than the frame of plates; and I have found it convenient, that the box be fitted with two uprights, or standards, at the sides, with a sliding pin across from one to the other, for the purpose of supporting the frame of plates raised from the acid, and thus allowing the liquid adhering

to them to drip into the box; this cross pin is also useful in carrying the whole apparatus from place to place when the box is full of the exciting solution.

A, fig. 4, is the box for containing the acid.

B B, the frame plates supported by the cross pin going from standard to standard.

In the description I have heretofore given of the process of firing by galvanism, I have recommended that the fine steel wire of the cartridge be soldered to the horns of the cartridge communicating wires; but I now find it more convenient and equally efficient to bend the extreme points of the horns upon themselves as hooks; the fine steel wire is slipped across and under the two hooks, when a blow with a hammer on the hooks closes them, and fixes the fine wire securely, as thus. I need hardly mention the ne

Fig. 5.

cessity of having all the metallic surfaces perfectly clean. The use of the kind of conducting wire explained in sec. 72, greatly facilitates the operations of blasting.

If these operations are on a large scale, it is better to cover the conducting wire with twine than with cotton, as it is more durable, and ensures a better insulation of the wires from each other.

If "W. C." intends fitting permanent batteries in his works, I inay perhaps be able to point out to him some changes necessary for economy in such a mode of working the battery; and as it is possible I may shortly be in the neighbourhood of Liverpool, if "W. C." will send me his address within a few days, I will endeavour to call at his works, and be happy to give him all the information I can on this subject. I trust that all your readers that use my process will give a detailed account of their operations in your pages.

I am, Sir, yours, &c.

October 17, 1842.

MARTYN J. ROBERTS.

[Such of our readers as may be desirous of knowing more about the cause

of the superiority of iron over copper as a negative plate, may refer with advantage to the notices of Mr. Roberts's discovery, which appeared in the Nos. quoted by him of the Philosophical Magazine; as also to the Memoir on this discovery read by Professor Poggendorff before the Berlin Academy, and Mr. Roberts's answer to the Professor's Memoir which will be found in the same journal. ED. M. M.]

ON THE CONSTRUCTION AND USE OF COMMUTATION TABLES, FOR CALCULATING THE VALUES OF BENEFITS DEPENDING ON LIFE CONTINGENCIES.

Part I.-Introductory.

It is to a Mr. George Barrett, of whom nothing besides is publicly known, that we are indebted for the principle of the Commutation Tables, and for the method of computing, by means of them, the values of benefits depending on the contingencies of human life. The method was first introduced to public notice, after it had been refused a place in the Transactions of the Royal Society, by Mr. Baily, in an Appendix to the second edition of his Doctrine of Life Annuities, published in 1813. Mr. Griffith Davies, in a work on life contingencies, published in 1825, by certain additions to the Tables, and alterations in their structure, accord

ing to Professor De Morgan, "increased the utility, and extended the power of the method to an extent of which the inventor had not the least idea." Mr. Barrett's method was also briefly noticed in the Appendix to Mr. Babbage's Treatise on Life Assurance. The method, as improved by Mr. Davies, has since been treated, and a very large collection of Tables adapted to it, for both one and two lives, has been given, by Mr. Jones, in his work on Annuities, in the Library of Useful Knowledge. But by far the most valuable papers on the subject are two in the Companion to the Almanack, for 1840 and 1842, by Professor De Morgan, which contain the materials of many thousand formulæ, applicable to almost every case that can occur. There is also some notice of the method in the article REVERSIONS, in the Penny Cyclopædia, which article is likewise the production, we believe, of Professor De Morgan.

The above-named are understood to be the only works in which the new method is, in any sort, treated. They certainly are not numerous; but they are sufficiently so, and well enough known, to have induced a general adoption of this method, to the exclusion of that previously in use, but for two reasons. The first is, the want of Tables adapted to this method; and the second, the want of an elementary and systematic treatise on the subject. The first of these wants is now amply supplied by the valuable collection of Tables published by Mr. Jones, above referred to; but the second still exists. It is no disparagement to the able authors of the works above named, to say that this is the case. Generally speaking, it has not been their object to furnish a treatise of this kind; and they have accordingly taken for granted, on the part of their readers, the possession of a degree of acquaintance with the subject, which very many, to whom the power of using the Commutation Tables would be of the greatest service, certainly do not possess. Professor De Morgan, indeed, expressly says, that all that will be found of demonstration in his articles "is intended for those who are familiar with the subject." Now, although the formulæ, according to this method, are extremely simple, and easily intelligible to any one who is acquainted with the merest rudiments of algebra, and who will take the small degree of trouble necessary to enable him to comprehend the notation employed; yet it is a result of our own experience, which we have no doubt can be amply confirmed by the observations of others, that most people view with mistrust, and will not willingly have recourse to formulæ, the principles of which they do not understand. And while Professor De Morgan's papers, in particular, have, doubtless, well served the end which, from the remark quoted above, the distinguished author appears to have had principally in view, we do not see that this forms any good reason why others, to whom a knowledge of this method of computation would be of service, should be prevented from availing themselves of the vast fund of information, regarding this method, which these papers con

tain.

It is, therefore, as an humble contribution towards the supplying of the deficiency, which has been shown to exist,

that the present papers are intended; and if they shall serve to render more available than heretofore, to any of the numerous readers of the Mech. Mag., the valuable papers to which reference has so often been made, the writer will consider himself amply rewarded for his labour. While he thinks that the task of rendering more generally intelligible the principles on which the new method is grounded will not be a difficult one, he trusts that, should his success not be commensurate with his wishes, he may at least be found to have aided in clearing the way for some one better qualified to do justice to a subject, which is daily growing in interest and importance.

The peculiarities of the old and the new methods may be here briefly stated. In the old method, we are presented with a table of the values of annuities at all ages, which of themselves are rarely wanted, but from which, by operations more or less complex, the values of benefits of all other kinds may be computed. In the new method, on the other hand, we are presented with a table which, by mere inspection, tells us nothing; but from which, while the values of the ordinary benefits can be found by a simple division, those of benefits of the most complex description are found by operations consisting usually of nothing more than one or two subtractions and one division. In point of simplicity, moreover, in the deduction of the various formulæ, the methods admit of no comparison. For the establishment of what, according to the old method, required chapters, a few pages will suffice according to the new.

The opinion we have expressed as to the superiority of the new method, however, will probably be regarded as of little value; and that of Professor De Morgan, which is most unequivocally given, may perhaps be objected to, as the testimony of an interested witness, seeing he has bestowed such pains on the elucidation of this method. But Mr. Milne's testimony will certainly not be objected to on any such ground. He is the author of the best treatise that has appeared, or is now likely to appear, on the old method; and therefore his prejudices, if he has any, must be supposed to be all on the side of that method which he has done so much to illustrate. Speaking of Mr. Baily's work, he says, (En

* *

cyclop. Brit., seventh edition, article, ANNUITIES, Vol. 3, p. 200.) "In an Appendix to it ⚫ formulæ were given for calculating from tables of that kind [Commutation Tables] the values of temporary and deferred life-annuities and assurances, when the annuity, instead of remaining always the same, increases or decreases from year to year by equal differences, with considerably greater facility and expedition than the same things could have been done with by the tables and methods of calculation in previous use." And his testimony, be it observed, refers to the tables as devised by Mr. Barrett, and gives but a faint idea of their capabilities in their improved form.

We might now proceed to describe the Commutation Tables, referring for illustration to one which the Editor has kindly agreed to insert. But as it will be more convenient that the table should accompany the next paper, we prefer here disposing of some preliminary matters.

The construction of the Commutation Tables is effected by combining in a particular manner (which will be explained in the next paper,) the rates of mortality and interest; and, as in the tables adapted to the old method, any rates that are most approved of, as regards these elements, may be employed. But whatever may be the rates of interest and mortality made use of, the demonstrations and formula which will be hereafter given, being generalized by the employment of symbols, will be equally applicable to all tables of the same form.

The rate of interest according to which our table, (which has not been heretofore published,) is constructed, is 4 per cent.; and the rate of mortality is that given by Mr. Finlaison in his Twentieth Observation on the Mortality of the Government Annuitants (Parliamentary Paper, No. 122, 1829, page 58.) Tables of mortality in their usual form exhibit the numbers who, out of a number supposed to be alive at birth, or some other early age, attain each successive year of age, and consequently also the numbers who die in each year; and this form is the most convenient for the construction of Commutation Tables. But this is not the form in which Mr. Finlaison's data are arranged. What he gives are the probabilities, or rather the logarithms of the probabilities, that a life at each

age will survive a year. A preliminary step therefore was, by means of these probabilities, to construct a mortality table of the more usual form; and in doing so, as well as in the subsequent construction of our Commutation Table, Mr. Finlaison's data have been made use of to their full extent. It is thought proper to mention this, because there is an "abridged" mortality table of the usual form, deduced from Mr. Finlaison's data, published in the Report of the Select Committee on Friendly Societies, 1827, page 82; and some might be embarrassed by finding that the results of our Commutation Table do not exactly correspond with those which may be deduced from the abridged table referred to. This table states the survivors of 1,000 births to be, at the ages of and 7, for instance, 919, and 912, respectively; while the use we have made of the data enables us to say, that the survivors at these ages, out of 100,000,000 of births will be 91,912,811, and 91,239,410. As regards the correctness of our Commutation Table, it has been subjected to the severest tests in the way of verification, and we are confident that no error of any consequence will be found in it. Mr. Finlaison, in his Report, gives the values of annuities at all ages, at 4 per cent., as deduced from his data by the ordinary method, and carried to 7 places, which are two more than are usually given. The values derived from our table will be found to correspond with those to the last place. It has been thought proper to make these remarks as to the degree of confidence that may be reposed in our table, in case any one should feel disposed to apply it to practical purposes.

We shall now explain the notation, as regards the rates of interest and mortality, which we shall employ in our demon

strations.

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