constructed a difference engine for the University of Pennsylvania said to be less expensive than Babbage's and less complicated than Scheutz's. In 1883 the application of electricity to tabulation was made by Mr. Herman Hollerith, of New York, and in the same year, by the author of this book, to addition. Thus, at the present time, the principal tabulating, adding, and arithmetical machines in use in the world are the inventions of Americans, two being residents of Boston. It should not be supposed that the machines previously referred to are all that have been invented to secure rapid computation. The following list, compiled from Knight's Mechanical Dictionary, gives an idea of the fecundity of inventors in this line. As indicated in many cases by their names these calculating or registering machines are used for a great variety of purposes, but few, however, being of practical value in statistical work. By this we mean proved value. An inventor may claim that his machine is better than any other one made, but its practical use may disclose unforeseen drawbacks in some points which neutralize acknowledged gains in other directions. We have not the space in which to describe the various machines, but shall simply state their applicability to various kinds of statistical work. It is not intended to advertise any particular machine, but to mention all known to the author and enable statisticians to make their own selections for special work. In machine tabulation or aggregation the "scheme" adopted in itself fixes the style of machine to be used. The "factory system " when applied to tabulation means sub-division of labor as it does in other industries, and each part of the labor, each sub-division, requires its own mechanical device. The calculating machine that will do everything is on a par with the patent medicine that cures all human ills. Each particular tabulation requires its peculiar "result slips " upon which to record the results of the machine work, and as much invention is required in some of them as the construction a new calculating machine would call for. In some instances, the manner in which cer tain results obtained by machine tabulation are entered upon the special result slips supplies the statistician with ten times the material for use that the original counting furnished. Thus it is that the brain that invents the "scheme" for machine tabulation and records its results upon novel result slips does more than any machine can accomplish-in fact, the machine is useless without it. The clerk who runs the machine may need to do but a small amount of brain labor, but this diminution should not be credited to the machine nor its inventor, but instead to the one who invents the 66 scheme" to use the machine, and whose brain labor dominates every movement of his mechanical servant. These plain words are written so that parties who start to use mechanical devices in statistical work may not be disappointed if the machines do not run themselves. The present application of printed or mechanical devices for rapid computation to statistical work are as follows: I. Counting or tallying one at a time: (a) The Self-counting Tabulation Sheet. (d) The Rotary Counting Machine. (e) Seaton's Tallying Machine. (f) The Electrical Tabulating Machine. (g) The Electrical Adding Machine. (h) The Chip System. (i) The Automatic Door Counting Machine. (j) Italian Tabulating Machine. (k) Benton's Counting Devices. II. Counting or tallying small numbers from 1 to 100. (a) The Self-counting Tabulation Sheet. (b) The Rotary Counting Machine. (c) The Electrical Adding Machine. (d) The Chip System. (e) Column Adding Machines. (Various makes.) III. Counting or tallying from 1 to 144 points at one handling of the schedules. (a) The Automatic Door Counting Machine. IV. Counting or tallying more than 144 points at one handling of the schedules. (a) The Chip System. (b) The Printing Tabulator. V. Adding one series of numbers, showing consecutive totals from I to 1,000,000,000. (a) The Valuation, Quantity, and Number Self-counting Sheet. (b) The Billionnaire Adding Machine. (c) The Electrical Adding Machine. (d) The Cylinder Adding Machine. VI. Adding from 1 to 144 series of numbers, each aggregating any amount. (a) The Chip System. VII. Processes used in preparing schedules for tabulation. (a) The Slip System. (b) The Chip System. (c) The Slip-Chip System. VIII. Other devices for quick computation. (a) Thatcher's Percentage Machine. (b) Percentage Charts. (c) Addition Percentage Tables. (d) The Arithmometer. (e) Electrical Multiplying Machine. (f) Bookkeeper's Trial Balance Sheet. (g) Multiplication Proof Sheet. IX. Improved schedules and result slips. (a) Record Margin Schedule. (To secure secrecy.) (c) The General Sorter Result Slip. By sex, etc., and 12 (d) The Age Result Slip. (e) The Place of Birth Result Slip. (f) The Parent Nativity Result Slip. (g) The Occupation Tally Scheme, and Result Slips. Actually used for 22,000 details. (h) Correlated Result Slips. (i) The Children and Children Living Result Slip. () The Chip System Result Slip. (k) The Adding Machine Result Slip. (7) The Punch Schedule. For electrical tabulation. (m) The Enumerator's Punch Schedule. X. Other machines, etc., used in mechanical tabulation and addition. (a) Sorting Boxes. (b) Proof Boxes. (c) Proof Wires. (e) Position Cards. (7) Eyelet Sets, and Eyelets. As has been stated, none of these machines can be used advantageously unless the "scheme" is prepared and the ways to utilize the machine explained to the clerks. Then they mean much more for the same money, or the same for much less money. How much more or how much less depends entirely upon the nature of the work to be done, and no general rule can be given, and no special rule, unless that particular work has been done covering the same details as that for which an estimate of cost is desired; so much depends, also, upon the facility or availability of different clerks that no estimate can be guaranteed to be realized practically. Machine tabulation requires "grasp" and "consecutivity" in the clerk that is the ability to "grasp " instructions and the brain power to apply them in "consecutive " order as laid down in the scheme. The instructions should be written, in type writer work, or printed. Machine clerks should be as expert in horizontal as in perpendicular addition. Machine tabulators are not obliged to bend over to their work, there is a certain fascination in running a machine, there is more physical than brain tire; for these reasons, |