aluminum. The internal cone piece is 12.4 cm. in diameter. The face on which the prongs ride is notched out to admit a prong of the star-wheel. As the internal cone piece revolves clockwise (as viewed in the figure), a steel roller at the rear edge of the notch engages the finger on the rear riding prong; this prong moves down into the notch, and the drum makes one-fifth of a revolution. On the inner side of the internal cone piece is mounted a cam which operates, by means of a lever and connecting rod, the aluminum shutter H. The sliding external cone piece is held out of contact with the internal piece by means of a spring; it is thrown into contact by means of a bell crank, which is operated by a wire cable running down through pulleys to the base of the apparatus, where it passes through a hole to a lever attached on the outside of the case. The latter lever greatly reduces the amount of pull necessary to throw the clutch in gear; it is operated by a cord passing through pulleys to the operator's table.

The power unit is a 1/6 h.p. 110 a.c. motor of 1140 r.p.m. The shaft of the motor K is coupled to the shaft of the worm-gear speed-reducer J, the speed being thus reduced to approximately 30 г.p.m. The sprockets on the speed-reducer and on the external cone piece of the clutch are related as 2 to 3, so that the upper sprocket and external cone piece make one revolution in three seconds. When the internal cone piece is in gear, the star-wheel and drum are in motion. one second and at rest two seconds during each of these 3-sec. intervals. The shutter H is closed while the drum is in motion and open while it is at rest. The motor and speedreducer are enclosed in a felt-padded box; the sound produced by them is thus so reduced as not to interfere with auditory stimuli or verbal responses. The clutch, drum, and cardholder mechanisms are practically noiseless.

The card-holders are 26 x 13.6 cm. They are constructed of two horizontal strips of 16-gauge tin, bent into U-shape to afford slots for the cards, and two vertical strips of 3/64 in. galvanized iron, whose ends are bent into hinges to receive 3/32 in. steel axles. These axles bear hooks by which wire loops secure them in the hinges.

The window before which the shutter H is placed is 26 x 13 cm. The chain of card-holders passes behind this window through vertical hardwood guides. Either half of the window may be closed by means of the 1/32 in. steel drop-doors G, contained in metal guides, which are operated by means of cords passing through pulleys.

The wooden case is 2.6 m. in height and 45 cm. in width. The front is vertical, but the rear slopes from a depth of 46 cm. at the base to 31 cm. at the top. The sides and back are constructed of 7/8 in. pine: the front of 3/8 in. laminated panel stock. Hinged doors at D, F, and I afford access to the mechanism. The height of the case as given permits of a chain of as many as 32 card-holders; if only one half of the window is used, the apparatus therefore has a capacity of 64 exposures of a 13 x 13 cm. area.

The mode of operation is as follows. The cards on which the figures to be used are mounted are placed in the slots of the card-holders, access for this purpose being through door F. The operator, seated at his table, controls the apparatus by means of a switch which starts and stops the motor, and three cords, of which one operates the clutch and the others the two drop-doors G. If two vertical series of figures have been placed on the cards (as shown in the illustration), one of the drop-doors (e.g., the left) is raised and the other lowered. The motor is then started; a slight pull on the control-cord throws the clutch in gear and sets the drum and shutter mechanism in motion. The series on the left having been completed, the left door may be dropped and the right raised. The drum and shutter mechanism may be stopped at any instant by releasing the clutch.

The writer has coined the name bradyscope as being more appropriate for this apparatus, in view of the slow ate of presentation, than the term tachistoscope which was applied to the earlier forms of the apparatus. The rate and manner of presentation are well adapted to any experiments in which the subject's responses to visual objects of relatively large area must be recorded in writing, either by the subject himself or by the experimenter.2

2 The Robert D. Simpson Company of Columbus, Ohio, is prepared to duplicate the apparatus.

TWO DEVICES FOR AIDING CALCULATION

BY HERBERT A. TOOPS

Ohio State University

I. A STANDARD DEVIATION DEVICE

The device shown in the accompanying figure (A) has been found very useful in obtaining the frequencies of frequency distributions and in obtaining averages and standard deviations.

Twenty-five piano wires each 7 inches long are stretched between two parallel steel L-bars. The successive wires are I inch apart. On each of these wires are hung 50 brass checks, 7/8 inch in diameter, similar to the brass checks attached to door keys in hotels. Each check takes the place of a tally mark in obtaining a frequency distribution. On the front faces the 50 checks of the o-wire are labeled with a large o; similarly the 50 checks of the no. I wire are all marked I on their front faces, and so on.

If the scores of the distribution all lie between 0 and 24 one may pay attention only to the numbers on the faces of the brass checks when making the distribution.

In case the inclusive range of the variable is more than 25, that is, outside the range of o to 24, it is necessary to revolve the wooden bar at the top until the fourth face, which is covered with a slate preparation, is visible, whereupon the desired classes may be written thereon in chalk, the checks being now distributed by reference to the classes just written.

The checks being all at the rear of the several wires, one merely pulls forward on the wire a brass check whenever one wishes to make a tally mark corresponding to a frequency of the distribution. Since the separate checks are separated from each other on the wire by a small washer, about 1/32 inch thick, it is very easy to introduce the fingernail behind.

the check and slide it forward along the wire. A completed distribution is shown in the forward side of the picture. Part of the distribution is hidden in the picture by the front frame of the device. It will be noted that class-II has the modal frequency.

The distribution having thus been made, one turns the device around in order to observe the back face of the checks last plotted on each of the several wires of the distribution and now plainly visible from the rear side of the machine. The back face of the twenty-third check of the 10-column, or wire, is shown in the inset diagram of the figure. The top one of the three figures of the check indicates the number of the check; that is, 23 indicates that there are 23 checks in this column in the distribution, thus saving us the necessity of counting them as we should have to do for tally marks. On the next check in the 10-column the top entry would be 24; then on the following one, 25 and so on. That is, we may now copy the frequency distribution by merely copying the top figures showing on all the successive checks respectively. If we are not interested in the distribution itself we may add the top figure on all successive ones of the 25 checks showing and thus obtain N, the total number of cases.

The second figure showing on any check is the step times the frequency, that is, the EX component. By adding the second figure showing on all the successive 25 checks we obtain EX. In the inset the figure 230 means step-10 times the frequency 23 = 230. This operation therefore saves the operation of multiplying steps by frequencies, needed both in the computation of the average and the standard deviation.

The third figure showing on any one check is the square of the step multiplied by its frequency; that is, the EX2 component. Thus on the inset, 2300 is the product of the square of step-10 times the frequency 23. The sum of all such entries on the 25 checks showing gives us 2X2. Thus this step saves the operation of multiplying the square of the step by the frequency. The peculiar advantage of the machine is that the counting of frequencies in the successive steps and the extensions of the steps and their squares by