the frequencies have been done once for all by the checkmaker, the proper sums and extensions being permanently impressed into the brass checks.

We now have the value of N, 2X, and 2X2. We may substitute these in the usual formulæ for the mean and standard deviation:

in which Ix is the class interval; Fox is the face-value of

the zero-step.

The machine contains 1250 checks no two of which are identical. This results in a fairly expensive machine; but it simplifies the work to such an extent that any clerical worker can satisfactorily obtain distributions, averages and standard deviations.

Face I of the bar at the rear of the machine is shown in the picture. On face 2 of the bar, found by revolving the bar in its slide sockets, are found the numbers 25 to 49 inclusive; and on face 3 the numbers 50 to 74 inclusive. The first three faces have been found very useful in tabulating the errors made on individual examination questions in tests given in the objective type, where there are no more than 75 items. This range will include the majority of mid-term and final examinations. By tallying the failures, item by item, one may thus readily determine the degree of difficulty of the several items of mid-term examinations and save up those difficult items, where the difficulty is intrinsic and not due to the wording of the item, for use as final examination questions. Such final questions will yield an excellent dispersion of the students and so improve the academic marks by making the number of 'border line cases' small.

After completion of one distribution the machine is 'set back to zero' by tilting upward the front until the checks rush down hill by gravity to the rear side of the machine.

II. AN INTERCORRELATION DEVICE

A method whereby intercorrelations can profitably be computed by reducing the plotting paper to polar form has been published. By increasing the curvature of the ordinates in this form it is possible to make the center of a number of concentric charts lie within 27 inches of the bottom of the charts; consequently the charts may be arranged in a circle on the top of a rotating table 54 inches in diameter. This allows the worker to sit comfortably on a chair and to have successive charts rotate around to his position.

The figure (B) shows II charts thumb-tacked in a circle about the top of a soft pine rotating table. The table 2 is adjustable for height and for angle-tilt to suit the worker's height and convenience.

A movable bar, pivoted at the center of the table, contains a slide which may be set at any Y-score, o to 17 inclusive, of person A of test 1. The successive tally-marks of A on the correlation charts 712, 713, 714,, Tin, will always occur in the same horizontal row.

Let us

Subject A.

1 Toops, H. A., Solving intercorrelations by polar coördinates. 1922, 5, 60-75.

This JOURNAL,

2 Such a table may be readily constructed from a discarded drawing stand at a cost of about $10.00 for table and work. The charts used in this method may be obtained from the author.

3 Toops, H. A., Computing intercorrelations of tests on the adding machine. J. Appl. Psychol., 1922, 6, 172-184.

The reader calls out to the tally-marker, 'Set slide on 6.' The tally-marker sets the slide at 6; all tally-marks on the successive correlation charts will now appear opposite the slide in the 6th row. The reader now calls three scores, '8, 9, 4.' The tally-marker moves the table and brings the 712 chart with Column-8 showing just to the left of the bar and puts a tally-mark opposite the slide; then brings the 9-column of the r1s chart to the bar and enters a tally opposite the slide; and similarly the 4-column of the r14 chart. After each tally he calls out his entry to the reader for verification and correction in case of error. As soon as he has called out the series 8, 9, 4,' the reader gives the new series '10, 2, 8,' whereupon the procedure is repeated. With practice the table may be stopped almost exactly at the right column, since the table is light and has little inertia. If not stopped at exactly the right place, the bar is movable and is quickly brought to the right place by the right hand which is used to prevent turning of the bar as the left hand rotates the table.

Practice rapidly improves one's ability with the device. The table below gives the number of minutes required by two persons to plot 10 correlation coefficients of 364 cases each; i.e., 3640 tally-marks, with the increase in practice observed up to 200 coefficients.

4 Allen, W. S., A Study in Latin Prognosis. Teachers Coll. Contrib. to Educ., no. 135, 1923, 10-11. The writer wishes to express his thanks to Mr. Allen for the collection of the data here presented.

It will be noted that the limit of improvement has not yet been reached but that the efficiency after having plotted 200 correlation coefficients, in about 70 hours, was 22.8 tallymarks plotted per minute. The initial efficiency was 14.6 tally-marks per minute, the time including the time required to align the papers and plot the correlations, two people working together in the process. This means the time of one person for roughly 140 hours was required to plot the 200 correlations of 364 cases each. Inasmuch as the work can be done by relatively unskilled clerical workers the saving is obvious. It is to be hoped that other workers will publish figures showing the efficiency of other methods, subdivided. according to time required for plotting, for making extensions, and for making all final computations.

A NON-ELECTRICAL ROTATION-TABLE FOR

LABORATORY ANIMALS 1

BY F. S. FEARING

Department of Psychology

AND

F. W. WEYMOUTH

Department of Physiology, Stanford University

The interest in problems connected with the responses to stimulation of the non-acoustic labyrinth has turned the attention of investigators in this field to the development of rotation apparatus. The apparatus described in the present paper was developed in connection with a program of research on labyrinthine functions in the pigeon being carried out in the Department of Anatomy at Stanford University. These investigations called for a rotation-table which would be constant as to (a) the rate of rotation and the number of revolutions, and (b) the rate of acceleration and retardation.

In the investigations in which this table was used a nonelectrical form of motive power was deemed advantageous. Maxwell 2 has described such a table, certain features of which we have retained. Our most important modification concerns the method of imparting an initial impulse to the table.

3

References to the accompanying figure will make clear the following description. The starting mechanism consists of weight A which communicates the initial impulse to the table by way of the cord B at post C. By pulling down the trigger

1 The construction of this apparatus was made possible by a grant from the Research Committee, Stanford University, with supplementary funds from the Department of Psychology.

* Maxwell, S. S., Burke, U. L., & Reston, C. The effect of repeated rotation on the duration of after-nystagmus in the rabbit. Amer. J. Physiol., 1922, 58, 432.

3 Our apparatus was built by Mr. Sidney W. Borrow, mechanician, Physics Department, Stanford University.