of territorial aggrandizement. The extension of her boundaries in Asia, though apparently aggressive and possessing military significance, has thus far been confined to ethical and political lines, and would remain so even if Bokhara and Kashgar were included. Russia's political power is fully established in Central Asia, and there is no danger of her losing her present territorial possessions; and being fully aware of this she has inaugurated a policy having in view the industrial progress of the country.

MEETING 384.

Statistical Tabulation by Machinery.

BY MR. CHARLES F. PIDGIN.

The 384th meeting of the SOCIETY OF ARTS was held at the Institute, on Thursday, February 14th, at 8 P. M., Prof. Davis R. Dewey in the Chair.

After the reading of the records of the previous meeting, the chairman introduced Mr. Charles F. Pidgin, of Boston, who read a paper on "Statistical Tabulation by Machinery.”

Mr. PIDGIN's opening remarks related to the origin of statistics. The science, as regards census-taking, is of great antiquity, for there are several allusions made in the Bible to the numbering of the people, and the book of "Numbers" is the census-volume of the Bible.

The manner of counting first used was undoubtedly to stand the people in rows or assemble them in groups, and then actually count or number the individuals. Natural steps forward would be made after the introduction of letters and figures, and signs, symbols, or marks of various kinds would be used to record the enumeration and the necessary aggregations in order to arrive at totals.

Despite the antiquity of statistics the science made no material progress until 1790, when the United States, the youngest of nations, inaugurated the federal census, of which the eleventh will be taken in 1890.

The leading statistical associations in the world, at the present day, are the American Statistical Association; the Convention of Chiefs and Commissioners of Bureaus of Statistics of Labor; the Royal Statistical Society of London; and the International Statistical Institute, composed of the leading statisticians of the world.

In this country, since 1873, the growth of statistics has been marvelous. Instead of one State bureau, there are now twenty-one, and the National Department of Labor is finely equipped as regards material, money, and progressive officers. The people demand thorough and honest investigations, and honest and accurate presentations of results. The colleges have recognized the coming demand for statisticians, and in a tentative way are turning the attention of young men to the science as a possible vocation. Scientific men necessarily base their economic articles on statistics, and political speeches bristle with figures drawn from the statistician's laboratory. A needed advance is the addition of statistical editors to the staffs of our leading newspapers. As society becomes more complex the nature of the statistics needed for public information and use becomes "finer," that is, more in detail; and it is this great increase in the labor necessary to collect, prepare, and print statistical tables that turned the attention of inventors to the matter of providing labor-saving devices for quick computations and tabulations.

The speaker said the practical part of statistical work consisted of five branches: first, the preparation of the blanks or schedules ; second, the writing of suitable instructions to guide the party filling the blank, agents, or census enumerators, in their work; third, the examination of the schedules to note omissions and to correct errors; fourth, the tabulation of the returns; and, fifth, the presentation of the results in print, accompanied by necessary explanations and analyses.

The speaker then said that he should take up only the fourth division of the practical science, tabulation, and would explain the uses of the printed and mechanical devices which he had invented and put in practical use in the Massachusetts Bureau of Statistics of Labor.

The two principal operations in tabulating are counting or tallying one at a time, and addition, or the aggregations of large numbers. Besides these two mathematical processes many averages and percentages have to be figured for use principally in analyses of statistical tables.

Counting or tallying was originally done by the use of peas, beans, shells, which were dropped into some recepticle, and then counted to arrive at results. The next move would be to make dots or checks to represent persons or things, and then count these dots or checks. We are all familiar with the four perpendicular and one cross line to indicate five. In 1875 I prepared and copyrighted a "Self-Counting Tally Sheet." Upon these sheets the dots were already printed, and the tabulator, by encircling the dots and adding certain checks, could tabulate 9000 points on a sheet six by nine inches; and, what was of particular importance, could carry out the results at once, the sheets being so arranged as to "self-count" the check marks. The self-counting tally sheet was used to prepare the population and social statistics of the State Census of 1875. Seaton's tallying machine, used in the United States Census of 1880, was ingeniously arranged to receive the check marks in prepared columns, but it was not self-counting, and the aggregations were necessarily laborious and tedious. A tallying machine used in the Royal Bureau of Statistics at Rome has figures on the peripheries of wheels, and when these upturned figures are inked with a printer's roller, impressions may be taken on paper for use as bulletins. In 1882 I used, for the first time, a mechanical device for tallying or counting. This was named the "Pascal" counting machine. It registers from 1 to 999, and beyond that, by an ingenious device, its capacity may be indefinitely extended. The single machine is intended to count one at a time only. By combination of a number of machines the series may be used for addition or multiplication.

The Pascal machine is the foundation of the "Automatic Door Counting Machine," by means of which the population and social statistics of the Massachusetts State Census of 1885 were prepared. By this machine a great gain is made over previous methods, both in speed and accuracy. With the old form of tabulation sheet but three points of statistical information were secured at a time, while the machine referred to has a capacity of 144 points at one handling of

the schedules. It is, in reality, a wooden tabulation sheet, with 144 columns, requiring no ruling, and always ready for use. It acts automatically, and the clerk has only to copy the results from the dial plates when the manual labor of classification is completed. The machine can be adapted to every kind of tabulation or statistical aggregation. It can be used as an adding machine, and can be utilized for the highest form of statistical work, including the most complicated tables. Its efficiency is from five to twenty times that of the old methods of tabulation.

For addition both printed and mechanical devices are used. The printed one is called "Self-Counting Form, for Adding Values, Quantities, and Numbers." This form, based upon the decimal disintegration of numbers, was used in aggregating the Industrial Statistics of the Massachusetts Census of 1875. It supplies a means of adding, paradoxical as it may seem, without the use of figures. To add "50,000," "100,000," or even "1,000,000," requires but one check on the sheet. The electrical adding machine is based upon this invention.

In 1882 mechanical adding machines were introduced into the Bureau. The first one used was the Pascal counter, used in a series, as previously explained. To secure the total required a peculiar result slip and some little time to add the respective columns of results. To overcome this delay a new machine, called "The Billionaire," was invented, which gave a continuous total easily read by a glance at the dial-plate. In this machine the "carrying" device was controlled by the eye, its action not being automatic. The next invention was the "Cylinder Adding Machine," in which the ear, or sound, was relied upon to govern the carrying device, and it was a material advance upon the Billionaire. The succeeding improvement was the "Button" machine, in which "touch" took the place of eye or ear, and was found to be more efficacious than its predecessors.

There is an intermediary process between counting one at a time and the addition of large numbers. This is the addition of small numbers, running from 2 to 50, or even 100. To do this kind of work expeditiously the "Rotary Counting Machine" was invent d. By its use such small numbers can be added automatically, no attention being required by the carrying device. The capacity is 25,000, and it is small enough to be carried in the pocket.

The speaker next referred to his "Electrical Adding Machine." This machine is based upon the decimal disintegration of numbers,

the same principle as was made use of in constructing the "SelfCounting Form for Adding Values, Quantities, and Numbers." The capacity of the machine likely to be most used is 999,999,999, but the capacity may be easily extended indefinitely. Machines can be easily constructed on this plan to add yards, feet, and inches; pounds, shillings, pence, and farthings; fractions, in fact any collocation of units, the machine doing the necessary reductions automatically, and showing a consecutive total on a dial plate.

Electricity has been adopted as the motor, because it is the only power that will operate the automatic carrying device, thus saving the eye, ear, or finger the necessity of "carrying." It reduces addition to simple notation, or the writing of numbers the same as they would be written on a sheet of paper. When the writing" on the machine is done, the numbers are added, and the total is visible upon the dial plate of the machine. Any digit may be put upon the machine with one motion, that is, a "9" can be added as easily as a "1." The advantages of the machine are numerous. It avoids brain wear. Ten hours' work with the machine is less fatiguing than three hours with pencil and paper. It places the ordinary clerk on a level with the expert accountant, and yet aids the expert by lightening his labors. Its comparative efficiency depends naturally upon the operator. Other things being equal, its efficiency is from two to six times that of the old method of computation. Besides, the weary brain is prone to error, but there is no reason why the electrical adding machine should do any the less accurate work at six o'clock in the afternoon than at nine o'clock in the morning. A cog-wheel. adding machine may be broken, and the machine keep on working, but naturally giving erroneous results. On the other hand, as soon as anything interferes with the accurate working of the electrical adding machine-the machine stops! This machine, by a simple process, may be used for multiplication, but it is not intended to do subtraction or division.

With a view of inventing a machine, or rather a system, which would give the same opportunities for addition as the Automatic Door Counting Machine does for tallying, I devised the "Chip System." The chips are contained in a case, and are taken from it the same as