Standardization of Some of the 
 Common Tests Used in Deter- 
 mining the Acuteness of 
 Vision of School 
 Children 
 
 BY 
 
 J. M. McCALLIE 
 
 TRENTON, N. J. 
 
 A Thesis Submitted to the Faculty of the 
 
 Graduate School of the University of 
 
 Pennsylvania in Partial Fulfilment 
 
 of the Requirements for the 
 
 Degree of Doctor of 
 
 Philosophy 
 
STANDARDIZATION OF SOME OF THE COMMON 
 
 TESTS USED IN DETERMINING THE 
 
 ACUTENESS OF VISION OF SCHOOL 
 
 CHILDREN 
 
 
 J. M: McCALLIE 
 
 TRENTON, N. J. 
 
 A Thesis Submitted to the Faculty of the Graduate School 
 of the University of Pennsylvania in Partial Fulfil- 
 ment of the Requirements for the Degree of 
 Doctor of Philosophy 
 
 June, 1912. 
 
L"B 3 4 5" J 
 .M3 
 
 19/8 
 
STANDARDIZATION OF SOME OF THE COMMON 
 
 TESTS USED IN DETERMINING THE 
 
 ACUTENESS OF VISION OF SCHOOL 
 
 CHILDREN 
 
 Most, if not all of the tests, both letters and characters, 
 used for testing the acuteness of school children are based, 
 in theory, at least, upon the Snellen test letters. 
 
 Since the Snellen letters will be referred to often, a brief 
 account of their origin and structure is here given : 
 
 In 1862, Dr. Herman Snellen, professor of ophthalmolgy in the Uni- 
 versity of Utrect, Holland, and director of the Netherlands Institute for 
 Diseases of the Eyes, published an improved series of test types for 
 measuring the acuity of vision.* The principle which guided him in the 
 constmction of these test letters is based upon the fact that the normal 
 eye can just discern objects that subtend a one minute angle, the vertex 
 of the angle being* the point where the rays of light cross before falling 
 on the retina. 
 
 In order that a letter may be recognized each one its elements must 
 be discernible, hence, each of these elements must have a diameter equal 
 to the tangent of an angle of at least one minute. In constructing uni- 
 form letters in conformity with this principle, Snellen found that each 
 letter must have at least one diameter equal to the tangent of a five- 
 minute angle. Each letter is therefore made in a square which is sub- 
 divided into twenty-five equal squares, each small square being equal in 
 diameter to the tangent of a one-minute angle. Since the tangent of a 
 five-minute angle is equal to 0.001454, to obtain the longest diameter of 
 a letter to be seen at a given distance, Snellen multiplied the length of 
 the tangent of five minutes by the distance, in centimeters, of the letter 
 from the nodal point of the eye; thus, at a distance of one-hundred cen- 
 timeters the height of the letters should be 0.1454 centimeter, and each 
 stroke of the letter should be at least one-fifth of this, or 0.0291 in 
 length. 
 
 Before beginning the work a large number of test cards 
 were collected from different dealers. On some of these 
 were lines of letters of different sizes, on others, lines of 
 pictures or characters of different sizes. Under each one 
 of these lines of different sized letters, pictures, or charac- 
 ters, was printed the distance at which they were supposed 
 to be seen by the normal eye. An examination of this col- 
 
 *Snellen, H. Optotypi ad visum determinandum secundum formu- 
 
 d_ 
 D 
 scharfe.) Berlin, H. Peters. 1904. 
 
 larum y — Ed. XVII. (Probebuchstaben zur Bestimmung der Seh- 
 
 D 
 
lection of material soon disclosed the fact that there was no 
 uniformity either in the size, style, or structure of the let- 
 ters or characters or pictures, gotten out by different 
 houses, which were supposed to be seen at the same distance 
 by the normal eye. Not only was there a lack of uniform- 
 ity, but, not on a single card, could there be found a set of 
 letters or characters or pictures whose proportions were in 
 accordance with the Snellen measurements. And, not only 
 were these out of proportion, according to Snellen, but they 
 were not of the right size to be seen at the different dis- 
 tances. The letters and characters intended to be read at 
 the shorter distances were generally printed so poorly as 
 to make them useless as tests. Add to these faults the facts, 
 that these letters and characters were printed in black on 
 several shades of white or cream colored cardboard or 
 different shades of white letters on black cards, and, that 
 the finish of the cardboard varied from a glossy white or 
 black to a lustureless white or black, and it can readily be 
 seen that there could be no uniformity of results, to say 
 nothing of accuracy or the possibility of selecting any one 
 of these measures for a standard. It was evident, there- 
 fore, that if my work was to have any value, new letters 
 must be made. This was done by most accurately drawing 
 the letters according to the Snellen dimensions from which 
 new and accurate type were made, and, from which, the 
 letters used in these tests were printed, except the tests 
 made in comparing the relative visibility of the "illiterate 
 E," with the 16 ft. letters. 
 
 The picture' tests were discarded because they were not 
 and could not be constructed according to the Snellen 
 measurements, consequently the results obtained could not 
 be compared with results obtained by tests made with the 
 Snellen letters. 
 
 The tests made were divided into two parts. The first 
 had to do with the visibility of the "illiterate E," supposed 
 to be seen by the normal eye at no greater distance than 
 16 ft., as compared with the visibility of the Snellen letters 
 constructed to be seen by the normal eye at no greater dis- 
 tance than 16 ft. 
 
 The second part had to do with determining whether 
 tests made by the Snellen 12 ft., or 16 ft. letters, or a dot, 
 
supposed to be seen at 20 ft., are not as accurate as tests 
 made with letters to be seen 50 ft., 40 ft., 30 ft., or 20 ft. 
 
 The following is a detailed description of the method 
 and results obtained by comparing the visibility of the 
 "illiterate E" with the Snellen test letters of the same di- 
 mensions : 
 
 As stated above, types for the 16 ft. "illiterate E" and 
 the 16 ft. letters were not made anew. This was not neces- 
 sary because a copy of Snellen's classic work on test types 
 was found which contained the "illiterate E" and the let- 
 ters of the desired size. The letters taken from this book 
 were O, L, N, Z, B, D, T, and E, and the "illiterate E" 
 turned up, down, right, and left, (see Pig. 1) all of which 
 were supposed to be visible to the normal eye at 16 ft. 
 These were printed on white unglazed paper about the 
 thickness of ordinary book paper. 
 
 The 16 ft. letters and the 16 ft. "illiterate E," were 
 selected of one and the same size to enable comparison of 
 results to be made more readily and because the size of the 
 rooms in which the tests were made would not admit of 
 using larger letters. 
 
 Each one of these letters and "illiterate E's," were 
 carefully cut out, and pasted on white unglazed cards, 
 three and one-half by six inches, one and one-half inch 
 from the top of the card and equally distant from the sides, 
 one letter or one " illiterate E" on a single card. On the 
 back of each card was written the same letter or ' ' illiterate 
 E" that appeared on the front. This was for the purpose 
 of enabling the operator to know the letter or to tell which 
 way the "illiterate E," was turned, when presented to the 
 subject. 
 
 By having the letters on separate cards, so that only 
 one letter was in view at a time, the operator could be 
 sure that the pupil's reply was a judgment on that letter 
 and not on some other letter, as often happens when several 
 letters are shown at one time. This arrangement, also, 
 made it possible to vary the order of presentation, and, so 
 prevent the letters from being memorized. The operator 
 by this device was left free to give his entire attention to 
 the efforts put forth by the children in reading the letters. 
 By holding the cards in his hands, the operator was enabled 
 
6 
 
 to utilize the best light in the room more easily than if he 
 had used a large card hung on the wall, as is usually done 
 in such tests. 
 
 The best position for exhibiting the letters, so far as 
 light was concerned, was selected, and, beginning with this 
 position, short chalk marks were made on the floor every 
 two feet the entire length of the room, the first mark being' 
 two feet away from the position selected for best light, the 
 second four, and so on. 
 
 Everything being ready, the pupils were called one at a 
 time and told to stand with their toes to line twenty, with a 
 card held over one eye. Two or three letters were pre- 
 sented. If the pupil could not read them, he was asked to 
 step up two feet and try again. If he failed again, he was 
 asked to step up two more feet and try again. If he failed 
 at this distance — sixteen feet — he was asked to step up 
 one foot at a time, after each succeeding failure, until he 
 was able to read at least five consecutive letters correctly. 
 The letters were not exposed to view longer than two sec- 
 onds. If the correct names of five consecutive letters could 
 not be read in the time limit, the result was counted a fail- 
 ure, until a distance was found where the letters could be 
 read. If the subject could read all the letters correctly at 
 sixteen feet, this fact was indicated by placing the fraction 
 16/16 opposite his name on the record sheet. If he could 
 read the letters only at six feet, this fact was indicated by 
 the fraction 6/16. If the letters could be read at twenty- 
 four feet, this fact was represented by the fraction 24/16, 
 etc. 
 
 Having determined the greatest distance at which one 
 eye could read the letters, the same process was repeated 
 with the other eye. Immediately after each pupil was test- 
 ed with the alphabet cards he was tested with the ' ' illiterate 
 E," cards, by the same general method, except that instead 
 of naming the character the pupil was required to point in 
 the direction, up, down, right, or left, thus indicating the 
 direction of the opening of the E. In this case, as with the 
 letters, a single error was taken to indicate that the pupil's 
 vision was not sufficiently acute to read the characters at 
 that particular distance, and he was required to move to- 
 ward the cards until he reached the point at which at least 
 
five consecutive characters could be read correctly within 
 the allotted time of not more than two seconds each. 
 
 In doing this work the tests with the "illiterate E," al- 
 ways followed the test with the letters, so, if fatigue played 
 any part in the tests it would show itself in the results ob- 
 tained with the "illiterate E." 
 
 Before beginning the test each day, the operator tested 
 his own vision to see whether the light was satisfactory. 
 Tests were made only on days when the light was good. No 
 work was done on cloudy or dark days. These tests were 
 carried on in the different class-rooms, and, so far as each 
 pupil was concerned the test with the "illiterate E," and 
 the letters were made under exactly the same conditions. 
 
 470 children took the tests during the months of April 
 and May. 
 
 The results of these tests are presented in the table I. 
 This shows the number of eyes tested in grades I to VIII, 
 with the greatest distances at which the alphabet and illit- 
 erate characters could be distinguished, Four hundred and 
 seventy pupils, or 940 eyes, were tested. These pupils were 
 distributed throughout the grades as follows : 72 in the 
 first grade, 54 in the second, 39 in the third, 28 in the fourth, 
 41 in the fifth, 29 in the sixth, 130 in the seventh and 77 in 
 the eighth. The 344 pupils in grades III to VIII, inclusive, 
 were tested with both the alphabet and illiterate characters. 
 In columns headed Totals II to VIII, may be found the fig- 
 ures affording the most ready comparison of the results 
 with the alphabet characters, and illiterate cards. Thus, 
 with the alphabet characters, the largest number of eyes, 
 148, distinguished the letters at fourteen feet; the next 
 largest 128, at sixteen feet, and the next largest 114, at 
 twelve feet. Of these 688 eyes tested, 390, or 56.7 per cent., 
 distinguished the letters at from twelve to sixteen feet. 
 With the illiterate cards, however, these same eyes dis- 
 tinguished the "illiterate E" at a much greater distance, 
 in fact, 94 pupils saw the "illiterate E," at twenty- two feet. 
 This was the largest number seeing this character at any 
 distance, and the next largest number, 92, saw it at twenty- 
 four feet. The next largest number, 86, saw it at twenty 
 feet. The results of this comparative test with two 
 characters are graphically exhibited in Graph I. Curve I 
 
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 represents the results of the alphabet test and Curve II 
 represents the results of the ' ' illiterate E ' ' test. 
 
 The pupils of the first and second grades, 126 in all, 
 were tested with the "illiterate E" only, because they did 
 not all know the letters of the alphabet. Curve III repre- 
 sents the results obtained by testing these 252 eyes with the 
 illiterate cards. Curve IV combines in a single curve the 
 results of the illiterate test with the 470 pupils in all grades. 
 
 Z 4 6 8 /O fZ J4 /6 /8 ZO ZZ Z4 & 23 30 32 34 36 36 40 4244 
 Geaph 1. 
 
 The straight line a-b, running perpendicularly through 
 the curves, is the line of assumed normal vision for all of 
 the tests. If this were correct, then all of the eyes repre- 
 sented by the portion of the curves to the left of this line 
 are subnormal, and all eyes represented by that portion of 
 the curve to the right of the perpendicular are above nor- 
 mal in acuteness. 
 
 From these curves we deduce the following results : 
 
 Curve I (alphabet test) . . 
 Curve III ("illiterate E") 
 
 Eyes Normal 
 
 128 or 18.6% 
 
 27 or 3.9% 
 
 Eyes Subnormal 
 
 453 or 65.8% 
 
 56 or 8.1% 
 
10 
 
 Eyes Above Normal 
 
 Curve I (alphabet test) 107 or 15.5% 
 
 Curve III ("illiterate E") 566 or 82.2% 
 
 It is evident at a glance, that something is wrong, either 
 with the letters used or with the "illiterate E," since the 
 results were obtained under exactly the same conditions. 
 It is not possible for both results to be correct, because with 
 the "illiterate E," 8.1 per cent, of the pupils tested were 
 subnormal and 82.2 per cent, were above normal ; whereas, 
 with the alphabet test, 65.8 per cent, of the same pupils 
 were found to be subnormal and only 15.5 per cent, above 
 normal. The fact that only 3.9 per cent, of the pupils, ac- 
 cording to the illiterate test, had normal vision, and only 
 8.1 per cent, were subnormal, would warrant the suspicion 
 that something was wrong with the "illiterate E," as a 
 reliable measure for acuteness of vision. A close analysis 
 of this character will prove that the suspicion is well found- 
 ed. The structure of the "E" is shown at the right of 
 Graph I. 
 
 A pupil being tested with this character has only to de- 
 termine in which one of the four directions up, down, right, 
 or left, the opening of the character is directed, and this 
 opening can always be pointed out by observing that this 
 side of the E is always the lightest. Each of these char- 
 acters, as before stated, is constructed in a square which is 
 subdivided into twenty-five squares. The normal eye is 
 supposed to be able to discern one of these small squares 
 at the same distance at which the E, turned in different 
 directions can be recognized. It will be observed that there 
 are three of these small squares lying together unfilled on 
 the open side of this character. Four of these small 
 squares, arranged in the form of a square has twice the 
 diameter of the small square and should be discerned at 
 twice the distance or 32 feet. It would, therefore, be rea- 
 sonable to suppose that these three unfilled squares lying- 
 one above the other should be seen at about three-quarters 
 of that distance, or twenty-four feet. As a matter of fact, 
 this is exactly the distance at which they were discerned by 
 the largest number of the pupils of all grades. 
 
 This comparative test proves conclusively that sixteen 
 feet is not the distance at which the normal eye can just 
 
11 
 
 discern the "illiterate E." In fact, twenty-nine eyes were 
 found, exhibiting normal vision with the alphabet test, 
 that could interpret these characters at twice sixteen feet. 
 Many could read them farther than thirty-two feet, in fact, 
 two could do this at forty-four feet and one could make 
 them out at fifty feet. 
 
 It is evident then, that if this character is to be used 
 for testing the acuteness of vision, a new distance, at which 
 the normal eye can just see it, must be determined or the 
 size of the characters must be changed. Either or both of 
 these changes can easily be deduced from the results ob- 
 tained by these tests. 
 
 Assuming that sixteen feet is the distance at which the 
 sixteen foot letter can just be made out, by the average 
 normal eye, then, the same relative variation from this 
 normal sixteen foot distance, would be found to obtain in 
 any sized letter or characters used in a series of tests. For 
 example, if a series of tests with the sixteen foot letter, 
 should show that the eyes tested could see the letters at an 
 average distance of only twelve feet, or one-fourth less than 
 normal distance, and, if another series of tests, made on 
 the same eyes with another set of letters of any given uni- 
 form size and structure, should show that they could be 
 seen at twenty-four feet, then the distance, twenty-four 
 feet, should vary as much from the normal distance, at 
 which such letters should be seen, as twelve feet varies from 
 sixteen feet, the normal distance at which the sixteen foot 
 letters should be seen. It is evident that the distance 
 twelve feet is one-fourth less than the normal distance six- 
 teen feet, and, since the same relation must exist in the 
 series of tests which showed that the average distance at 
 which letters or characters could be seen was twenty-four 
 feet, then this distance, twenty-four feet is one fourth less 
 than, or three-fourths of the distance at which the normal 
 eye can see these letters or characters. If twenty-four feet 
 is three-fourths of this normal distance, then the distance 
 at which the normal eye should see these letters or char- 
 acters is, 4/3 of 24 ft., or 32 ft. 
 
 In the series of tests described above it was found that 
 the average distance at which the 688 eyes could just see the 
 sixteen foot letters was 13.7 ft., and the average distance 
 at which the same 688 eyes could see the "illiterate E," at 
 
12 
 
 the same time was 23.2 ft. The distance at which the nor- 
 mal eye can see the sixteen foot letters is 16/13.7 of 
 the average distance at which the letters were seen. Since 
 the same relations must exist between the normal distance 
 at which the ''illiterate E," can be seen and the average 
 distance at which it was seen, we find this normal distance 
 by taking 16/13.7 of 23.2/1 ft., the distance at which the 
 "illiterate E" could be seen. This gives 26.4 ft., which is 
 the distance at which the normal eye can see the ' ' illiterate 
 E" used in these tests, instead of sixteen feet as was given 
 by Snellen. 
 
 If it is desired to change the size of the "illiterate E," 
 so that it can just be read at sixteen feet, instead of chang- 
 ing the distance at which it can just be seen, this can be 
 readily done by making it just 16/26.4 of the size used in 
 these tests. As these tests clearly show, one or the other 
 of these changes should be made if the "illiterate E" is to 
 be used as a test. 
 
 The second part of the problem has as its object, as 
 already stated, the determination of whether the Snellen 
 12 ft., or a 16 ft. letter, or a black dot whose diameter is 
 one-fifth the greatest diameter of a Snellen 20 ft. letter, 
 might not be as reliable tests for acuteness of vision as the 
 tests made with the Snellen 20 ft., 30 ft., 40 ft., or 50 ft. 
 letters. 
 
 The vision of 200 pupils in the fifth, sixth, seventh, and 
 eighth grades of a public school were tested in arriving at 
 a solution of the second part of the problem. 
 
 The following is a description of the method used in 
 making these comparative tests : 
 
 The tests were made in a room about 90 ft. long, near 
 one end of which was a window so situated as to give an 
 excellent light, in which to exhibit the letters in making the 
 tests. A chalk mark was placed on the floor at the point 
 where the light was best. Measuring from this line, a chalk 
 mark was placed on the floor every two feet for the entire 
 remaining length of the room which was 84 ft. These marks 
 were numbered as follows : the first line, made on the floor 
 at the point of best light, was marked ; the next line, two 
 feet away, 2 ; the next line, 4 ; the next, 6, etc., up to 84. This 
 gave a clear range of vision of 84 feet. 
 
13 
 
 It was decided beforehand that the letters and dots 
 should be exhibited one at a time and that each should be 
 exposed to view not longer than two seconds. 
 
 As stated above, it was not possible to find test cards 
 printed in clear type of the right dimensions, and, it was 
 also impossible to use these test cards for testing pupils 
 with the different sized letters without some of the letters 
 being memorized, thus thwarting the purpose of the tests. 
 To overcome these difficulties, it was found not only neces- 
 sary to have new types constructed with the correct dimen- 
 sions, according to the Snellen measurements, but to de- 
 vise entirely new vision test cards. These cards serve the 
 double purpose of allowing only one letter to be seen at a 
 time, and rendering it impossible for anyone to remember 
 the order of the letters, and, beside, the tests can be made 
 with much greater ease, accuracy, and rapidity than can be 
 done with the ordinary test cards. 
 
 A set of these new test cards consists of twelve square 
 cards about 5 in. x 5 in., on which are printed forty-eight 
 letters of four sizes, one letter of each size on each card, no 
 two cards having the same letters on them. The different 
 sized letters can be seen by the normal eye at 20 ft., 30 ft., 
 40 ft., and 50 ft., respectively. These four letters, on each 
 card, are placed so 'that one appears one-half inch from each 
 margin and equally distant from the sides. And they are 
 printed in such a way that only the letter at the top of the 
 card is in a position to be read when the card is held in an 
 upright position. 
 
 A reduced copy of one of these cards is shown in Fig. 2. 
 
 The tests are made with these cards exactly as tests 
 are made with the ordinary test cards, except that the oper- 
 ator holds the cards in his hand and exhibits one letter at 
 a time, by taking the cards one at a time, from the back of 
 the pack and placing them in front. Any one of the four 
 sized letters may be used by simply giving the cards a 
 quarter or a half turn in the hands. Any possibility of re- 
 membering the order of the letters may be prevented by 
 now and then shuffling the cards. This makes it possible to 
 test pupils in their own rooms and in the presence of all 
 the pupils if desired, and obtain trustworthy results. 
 
 In making tests with the black dots which were sup- 
 posed to be seen at 20 ft., the first thing to consider was the 
 
14 
 
 T 
 
 o 
 
 w 
 
 Figure 2. Showing the four sizes of letters and their 
 arrangement on one of the twelve cards used in these tests. 
 The smallest of these letters can be seen by the normal eye 
 at 20 ft. ; the next larger, 30 ft. ; the next larger, 40 ft. ; and 
 the largest, 50 ft. 
 
15 
 
 size of the dot. According to the rule laid down by Snellen, 
 the normal eye can just discern an object whose largest di- 
 ameter is one-fifth of that of a letter which can just be dis- 
 cerned at the same distance. A letter to be just discerned 
 at 20 ft. should be 0.349 inches in height or in the largest 
 diameter, so, the size of the dot to be seen at 20 ft., should 
 be one-fifth of 0.349 inches or 0.0695 inches in diameter. 
 Accordingly, a dot as nearly this dimension as possible was 
 carefully constructed. 
 
 To enable one to make tests with the dot rapidly and to 
 add interest to the work, another set of test cards was de- 
 vised embodying the following, somewhat novel features, 
 as shown in Fig. 3, Fig. 4, Fig. 5, and Fig. 6. 
 
 It takes ten of these cards to make a set. The dot in the 
 ring is the object to be seen. There are three cards with 
 the dot in the boy's ring; three with the dot in the girl's 
 ring; three' with the dot in the bear's ring; and one with no 
 dot in either ring. All of the dots are identical in size. 
 
 The boy, girl, and bear are supposed to be playing ball, 
 and each player is supposed to be trying to catch the ball 
 in his racket. The dot is the ball and the rings are rackets. 
 
 The tests were made in this way : The pupil to be tested 
 was placed at the distance where the normal eye can just 
 see the dot. The operator shuffled the cards and then held 
 them up face toward the pupil. As the cards were taken 
 from the back of the pack and placed in front, the pupil 
 was required to tell which had the ball, by saying "boy," 
 "bear," etc., or, if he did not see the dot at all, by saying 
 "nobody has it." This method, was found to have the 
 great advantage of being easily understood by children and 
 interesting to them. Even pupils in the kindergarten may 
 be tested with these cards used as a game. 
 
 Having determined the kind of tests to be used and 
 selected the position for the best light in which to exhibit 
 the tests, and having marked off the floor as in making the 
 tests with the "illiterate E" and the 16 ft. letters, and hav- 
 ing swung a pendulum to beat seconds, the testing pro- 
 ceeded as follows : 
 
 An assistant took a set of the alphabet test cards and 
 holding them in front of him in his two hands, took a card 
 from the back and put it in front every two seconds, accord- 
 
16 
 
 Figure 3. Dot test for acuteness of vision showing one 
 position of the dot. 
 
17 
 
 Figure 4. Dot test for acuteness of vision showing- 
 absence of dot. 
 
18 
 
 Figure 5. Dot test for acnteness of vision showing 
 a second position of the dot. 
 
19 
 
 Figure 6. Dot test for acuteness of vision showing a 
 third position of the dot. 
 
20 
 
 ing to the beat of the pendulum. The cards were required to 
 be held in the proper position to receive the best light. 
 
 The operator then, instructing the assistant to show 
 the fifty foot letters, placed the subject with his toes to 
 some mark beyond the fifty foot mark, say 60 ft., and re- 
 quired him, with both eyes open, to name the letters as they 
 were presented by the assistant. If he could not correctly 
 name five letters consecutively, he was instructed to move 
 up two feet and try again. If he still failed to name cor- 
 rectly, the five letters consecutively, he was required to 
 move up two feet more and try again, and so on, until a 
 position was found where he could read the required num- 
 ber of letters consecutively. If it was found that the sub- 
 ject could read with ease all the letters while on the 60 ft. 
 line, then he was required to move back two or more feet at 
 a time until a position was found, where, at least five con- 
 secutive letters could just be read. When it was evident 
 to the operator that mistakes were due to inattention or 
 other causes than inability to see, another trial was allowed. 
 
 After the distance at which the 50 ft. letters could just 
 be seen was found, the distances at which the 30 ft. and 20 
 ft. letters could just be seen was determined in the same 
 manner. 
 
 The determination, at which the 20 ft. dot could just be 
 seen followed the test with the 20 ft. letters, and was car- 
 ried out in this way: The operator held in his hands the 
 set of ten cards, described above, and presented them in the 
 same manner as in making tests with the cards containing 
 the alphabet. However, as none of the pupils understood 
 what they were to do in this test, the method was explained 
 to each pupil or several at a time by showing them the cards 
 by saying, "Pupils the boy, girl, and bear are playing a 
 game of ball. The dot is the ball. As each new card is pre- 
 sented the dot changes position from the ring or racket of 
 any one of the players to either of the other two players, or 
 the one having the ball may keep it through one or more 
 changes. As in a real game, the ball may be lost, so, in 
 this game, and the lost ball is indicated by a card being pre- 
 sented on which no ring contains a dot. Now, you are to 
 be the umpire of the game and your duty will be to tell who 
 has the ball as the cards are changed. ' ' A few cards were 
 then presented and the pupils were required to tell who had 
 
21 
 
 the ball. When the game was understood, the pupil to be 
 tested was told to stand at the 16 ft. or 18 ft. line and try 
 seeing the dot a few times. After he saw it at this distance 
 he was required to move back two or more feet at a time 
 and try again, and so on, until a distance was found, at 
 which, the dots or blanks on five consecutive cards could 
 just be made out. This distance was recorded as the dis- 
 tance at which the dot could just be seen. 
 
 When through testing with the 20 ft. dot, the subject 
 was then tested with the 16 ft. letter and then with the 12 ft. 
 letter, exactly in the same manner as the tests were made 
 with the 50 ft., 40 ft., 30 ft., and 20 ft., letters. In passing 
 pupils through each of these seven tests consecutively, it 
 was found that results were often modified by the eyes be- 
 coming fatigued. When this was found to be the case, the 
 subject was allowed to rest for a short while. 
 
 Realizing that fatigue might modify results if each one 
 of the 200 pupils were tested first with the 50 ft. letter, then 
 the 40 ft. and so on, down to the 12 ft. letter, every other 
 pupil began his test with the 12 ft. letter, then took the 16 
 ft. letter, then the 20 ft. letter and so on, up to the 50 ft. 
 letter. By this method it can readily be seen that, what- 
 ever effects fatigue might produce, this effect would be 
 equally distributed, and consequently, it would be non- 
 effective, so far as the purpose of these tests is concerned. 
 
 These tests were conducted for each pupil in the same 
 room, and with the same kind of daylight as far as possi- 
 ble. Care was taken not to make tests on cloudy or dark 
 days. 
 
 Since the purpose of these tests was to find out how far 
 each pupil could see the different sized letters and the dot, 
 or how acute vision was, the pupils were allowed to use 
 both eyes at once. This was done because looking with the 
 two eyes is the normal way of seeing things, consequently, 
 it is believed that the results obtained more nearly repre- 
 sent the true acuteness of vision of the pupils tested, than 
 if each eye had been tested separately. Pupils wearing 
 glasses were tested with their glasses on. 
 
 Tables 2, 3, 4, 5, 6, 7 and 8, pages 23-27, show in detail 
 one phase of the results of these tests. 
 
22 
 
 Column (A) gives the number of pupils who saw the dot 
 or letters at the same greatest distance. 
 
 Column (B) hsows the greatest distances at which the 
 different groups of pupils in column (A) could see the dot 
 or letter. 
 
 Column (C) gives the combined distances at which the 
 groups of pupils in (A) could see the dot or different sized 
 letters. 
 
 In each of these tables the sum of column (A) equals 
 200, the total number of pupils tested. The sum of column 
 (C) in each table equals the total combined distance at 
 which all of the 200 pupils could see the letters or dot 
 used in the test. Therefore, it is evident that if these total 
 combined distances in each table were divided by 200, the 
 number of pupils tested, the result will be the average 
 greatest distance at which these pupils could see the letters 
 or dots with which they were being tested. The perform- 
 ance of this operation gives the following results : 
 
 The total combined distance at which the 200 pupils saw 
 the 50 ft. letters is 10,894 ft. This divided by 200 gives 
 54.47 ft. as the average distance at which the 50 ft. letters 
 were seen. 
 
23 
 
 Table 2. 
 Eesults obtained by the tests made with the 50 ft. letter 
 
 (A) 
 
 56 
 
 (B) 
 
 (C) 
 
 3 
 
 82 
 
 246 
 
 1 
 
 80 
 
 80 
 
 1 
 
 78 
 
 78 
 
 4 
 
 76 
 
 304 
 
 1 
 
 74 
 
 74 
 
 3 
 
 72 
 
 216 
 
 6 
 
 70 
 68 
 
 420 
 
 19 
 
 1418 
 
 7 
 
 476 
 
 13 
 
 66 
 
 858 
 
 10 
 
 64 
 
 640 
 
 10 
 
 62 
 
 620 
 
 16 
 
 60 
 
 960 
 
 3554 
 
 15 
 
 58 
 
 870 
 
 13 
 
 56 
 
 728 
 
 18 
 
 54 
 
 972 
 
 14 
 
 52 
 
 728 
 
 17 
 
 50 
 
 850 
 
 77 
 
 
 4148 
 
 12 
 
 48 
 
 576 
 
 1 
 
 46 
 
 46 
 
 7 
 
 44 
 
 308 
 
 3 
 
 42 
 
 126 
 
 1 
 
 40 
 
 40 
 
 24 
 
 
 1096 
 
 (A) 
 
 (B) 
 
 (C) 
 
 3 
 
 38 
 
 114 
 
 2 
 
 36 
 
 72 
 
 6 
 
 34 
 
 204 
 
 3 
 
 32 
 
 96 
 
 
 
 30 
 
 00 
 
 4 
 
 
 486 
 
 1 
 
 28 
 
 28 
 
 
 
 26 
 
 00 
 
 3 
 
 24 
 
 72 
 
 1 
 
 22 
 
 22 
 
 1 
 
 20 
 
 20 
 
 6 
 
 142 
 
 
 
 1 
 
 18 
 
 18 
 
 
 
 16 
 
 00 
 
 1 
 
 14 
 
 14 
 
 
 
 12 
 
 00 
 
 1 
 
 10 
 
 10 
 
 1 
 
 8 
 
 8 
 
 4 
 
 
 50 
 
 200 
 
 
 10894 ft. 
 
 Average distance: 54.5 ft. 
 
24 
 
 Table 3. 
 
 Results obtained by tests made with the 40 ft. letters 
 
 (A) 
 
 (B) 
 
 (C) 
 
 (A) 
 
 (B) 
 
 (C) 
 
 1 
 
 74 
 
 74 
 
 1 
 
 72 
 
 72 
 
 
 
 70 
 
 00 
 
 
 
 68 
 
 00 
 
 
 
 66 
 
 00 
 
 
 
 64 
 
 00 
 
 5 
 
 62 
 
 310 
 
 3 
 
 60 
 
 180 
 
 10 
 
 636 
 
 3 
 
 58 
 
 174 
 
 8 
 
 56 
 
 448 
 
 8 
 
 54 
 
 432 
 
 9 
 
 52 
 
 468 
 
 11 
 
 50 
 
 550 
 
 39 
 
 2072 
 
 21 
 
 48 
 
 1008 
 
 14 
 
 46 
 
 644 
 
 19 
 
 44 
 
 836 
 
 20 
 
 42 
 
 840 
 
 30 
 
 40 
 
 , 1200 
 
 104 
 
 
 4528 
 
 10 
 
 38 
 
 380 
 
 5 
 
 36 
 
 180 
 
 4 
 
 34 
 
 136 
 
 4 
 
 32 
 
 12S 
 
 6 
 
 30 
 
 ISO 
 
 5 
 
 28 
 
 140 
 
 3 
 
 26 
 
 78 
 
 2 
 
 24 
 
 48 
 
 2 
 
 22 
 
 44 
 
 
 
 20 
 
 00 
 
 2 
 
 
 310 
 
 
 
 18 
 
 00 
 
 2 
 
 16 
 
 32 
 
 
 
 14 
 
 00 
 
 1 
 
 12 
 
 12 
 
 1 
 
 10 
 
 10 
 
 1 
 
 8 
 
 8 
 
 
 
 6 
 
 
 
 
 
 4 
 
 
 
 1 
 
 3 
 
 3 
 
 6 
 
 
 65 
 
 :00 
 
 
 8625 ft. 
 
 Average distance: 43.13 ft. 
 
 29 
 
 1004 
 
25 
 
 Table 4. 
 Results obtained by tests made with the 30 ft. letters : 
 
 (A) (B) (C) (A) (B) (C) 
 
 1 60 60 2 18 36 
 
 1 58 58 1 16 16 
 
 1 56 56 2 14 28 
 
 54 00 12 00 
 
 52 00 2 10 20 
 
 50 00 8 00 
 
 2 6 12 
 
 4 00 
 
 13 3 
 
 10 115 
 
 200 6705 ft. 
 
 Average distance 33.5 ft. 
 
 3 
 
 
 174 
 
 4 
 
 48 
 
 192 
 
 5 
 
 46 
 
 230 
 
 8 
 
 44 
 
 352 
 
 9 
 
 42 
 
 378 
 
 10 
 
 40 
 
 400 
 
 36 
 
 
 1552 
 
 14 
 
 38 
 
 532 
 
 20 
 
 36 
 
 720 
 
 26 
 
 34 
 
 884 
 
 19 
 
 32 
 
 608 
 
 24 
 
 30 
 
 . 720 
 
 103 
 
 
 3464 
 
 16 
 
 28 
 
 448 
 
 10 
 
 26 
 
 260 
 
 10 
 
 24 
 
 240 
 
 6 
 
 22 
 
 132 
 
 6 
 
 20 . 
 
 120 
 
 48 
 
 
 1200 
 
26 
 
 Table 5. 
 Results obtained by making tests with the 20 ft. letters 
 
 (A) 
 4 
 7 
 6 
 
 (B) 
 34 
 32 
 
 30 
 
 (C) 
 136 
 224 
 180 
 
 17 
 
 
 540 
 
 19 
 
 28 
 
 532 
 
 21 
 
 26 
 
 546 
 
 31 
 
 24 
 
 744 
 
 35 
 
 22 
 
 770 
 
 38 
 
 20 
 
 760 
 
 144 
 
 
 3352 
 
 12 
 11 
 
 7 
 
 3 
 
 2 
 
 1 
 
 3 
 
 39 
 200 
 
 18 
 16 
 14 
 12 
 10 
 
 216 
 
 176 
 
 98 
 
 36 
 
 20 
 
 8 
 
 18 
 
 572 
 4438 ft. 
 
 Average distance: 22.2 ft. 
 
 Table 6. 
 Results obtained by making tests with the 20 ft. dots 
 
 (A) 
 
 1 
 
 2 
 5 
 
 (B) 
 
 34 
 32 
 30 
 
 (C) 
 34 
 64 
 
 150 
 
 248 
 
 12 
 
 28 
 
 336 
 
 11 
 
 26 
 
 286 
 
 30 
 
 24 
 
 720 
 
 45 
 
 22 
 
 990 
 
 37 
 
 20 
 
 740 
 
 135 
 
 
 3072 
 
 25 
 
 18 
 
 
 450 
 
 12 
 
 16 
 
 
 192 
 
 S 
 
 14 
 
 
 112 
 
 3 
 
 12 
 
 
 36 
 
 4 
 
 10 
 
 
 40 
 
 1 
 
 8 
 
 
 8 
 
 3 
 
 6 
 
 
 18 
 
 
 
 4 
 
 
 
 
 1 
 
 2 
 
 
 2 
 
 57 
 
 — 
 
 41'i 
 
 S58 
 
 200 
 
 '8 ft. 
 
 Average 
 
 distance: 
 
 20.9 ft. 
 
 
27 
 
 Table 7. 
 Results obtained by making tests with the 16 ft. letters 
 
 (A) 
 
 (B) 
 
 (C) 
 
 2 
 
 28 
 
 56 
 
 1 
 
 26 
 
 26 
 
 4 
 
 24 
 
 96 
 
 18 
 
 22 
 
 396 
 
 29 
 
 20 
 
 580 
 
 54 
 
 
 1154 
 
 59 
 
 18 
 
 1062 
 
 34 
 
 16 
 
 544 
 
 30 
 
 14 
 
 420 
 
 9 
 
 12 
 
 108 
 
 6 
 
 10 
 
 60 
 
 4 
 
 8 
 
 32 
 
 2 
 
 6 
 
 12 
 
 1 
 
 4 
 
 4 
 
 1 
 
 3 
 
 3 
 
 146 
 
 
 2245 
 
 200 3399 ft. 
 
 Average distance: 16.9 ft. 
 
 Table 8. 
 Results obtained by making tests- with the 12 ft. letters 
 
 (A) 
 
 (B) 
 
 (C) 
 
 12 
 
 18 
 
 216 
 
 36 
 
 16 
 
 576 
 
 47 
 
 14 . 
 
 658 
 
 50 
 
 12 
 
 600 
 
 145 
 
 2050 
 
 23 
 
 10 
 
 230 
 
 21 
 
 8 
 
 168 
 
 5 
 
 6 
 
 30 
 
 3 
 
 4 
 
 12 
 
 2 
 
 2 
 
 4 
 
 1 
 
 1 
 
 1 
 
 55 445 
 
 200 2495 ft. 
 
 Average distance: 12.5 ft. 
 
28 
 
 The combined distance at which the 12 ft. letters could 
 be seen was 2,495 ft. This divided by 200, equals 12.48 ft., 
 the average distance at which the 12 ft. letters were seen. 
 
 Putting these results in tabular form we have: 
 
 Table 9 
 
 Average distance at which 
 
 50 ft. 
 
 letters 
 
 could be seen 
 
 54.47 ft. 
 
 40 ft. 
 
 > > 
 
 7 7 a 7 7 
 
 43.13 ft 
 
 30 ft. 
 
 > > 
 
 )) }1 ?> 
 
 33.5 ft 
 
 20 ft. 
 
 j » 
 
 > J > > > J 
 
 22.2 ft 
 
 20 ft. 
 
 dots 
 
 > > ) 7 > > 
 
 20.9 ft. 
 
 16 ft. 
 
 letters 
 
 > > > > 7 7 
 
 16.94 ft. 
 
 12 ft. 
 
 ? ? 
 
 77 J > > 7 
 
 12.48 ft 
 
 If each one of these different sized letters and the dot 
 has the same value in making tests, then the fraction ex- 
 pressing the acuteness of vision as shown by the 50 ft. let- 
 ter test will be equal in value to the fraction representing 
 the acuteness of vision as shown by the tests made by the 
 40 ft. letter, the 30 ft. letter, and so on, to the fraction 
 representing the acuteness of vision as shown by the 12 ft. 
 letter test. In other words, the fractions representing the 
 acuteness of vision as shown by making tests with each of 
 the different sized letters and the dots will be equal in 
 value. 
 
 How nearly this proved to be true with the tests under 
 consideration is shown in Table 10. The first fraction was 
 obtained by adding the numerators of each of the 200 frac- 
 tions representing the acuteness of vision, as shown by each 
 test with the 50 ft. letter, and placing this sum over the 
 sum of all the denominators, which of course, was, in this 
 case, 200x50, because there was a fraction for each of the 
 200 pupils tested and the denominator representing the 
 acuteness of vision was always 50. 
 
 The second and all the other fractions were obtained 
 in exactly the same way, except that the denominators of the 
 respective fractions were obtained by multiplying 200 by 
 40, 30, 20, etc. 
 
29 
 
 Table 10 
 
 Fraction's showing the acuteness of vision of 200 pupils 
 when tested by the 
 
 10894 
 
 50 ft. 
 
 letters 
 
 10000 
 
 8625 
 
 40 ft. 
 
 ) 7 
 
 
 
 
 8000 
 
 
 
 6705 
 
 30 ft. 
 
 ? J 
 
 
 
 
 6000 
 
 
 
 4474 
 
 20 ft. 
 
 yy 
 
 
 
 
 4000 
 
 
 
 4186 
 
 20 ft. 
 
 rlotd 
 
 
 
 KX\J Lo 
 
 4000 
 
 
 
 3387 
 
 16 ft. 
 
 19 ft 
 
 letters 
 
 3200 
 2495 
 
 or expressed decimally 1.089 
 
 1.077 
 
 1.118 
 
 1.119 
 
 1.046 
 
 1.056 
 
 1.04 
 
 2400 
 
 Of course, if each of the 200 pnpils had tested np to 
 normal with each kind of test the fractions wonld not only 
 have been equal in value but each would have been equal to 
 one or unity. The decimal parts of the numbers in the 
 column to the right show just how much each test is away 
 from the normal. Thus the first decimal .089 means that 
 tests made with the 50 ft. letters averaged .089 of 50 ft. 
 above normal or 4.45 ft. The next decimal .077 means that 
 tests made with the 40 ft. letter yield results .077 of 40 ft. 
 or 3 ft. above normal, etc. 
 
30 
 
 If we take the decimal .077 which shows the variation of 
 the results obtained by the 40 ft. letter test, as the mean 
 variation, then the variation of each of the other decimals 
 from this mean would give a result so small that it could 
 be neglected in any ordinary tests for acuteness of vision 
 with any of the letters or dots. 
 
 These fractions not only show that the amount of vari- 
 ation of each kind of test from the mean variation is slight, 
 but that all of these variations are uniformly above normal. 
 
 The fact that each one of these tests shows but little 
 variation from the normal or from the mean variation does 
 not, within itself, necessarily mean that each is equally val- 
 uable for making tests of acuteness of vision. Grave errors 
 may exist of a plus and a minus nature, but of magnitude 
 so nearly equal as not to be disclosed by mere averages. 
 
 The exact location and the exact extent of these varia- 
 tions from the assumed normal is shown in tables 2 to 8. 
 A glance at these tables shows at once the number of pupils 
 (column A), who could see the different tests at different 
 distances. These same facts are graphically represented 
 in graphs 4, 5, and 6. These graphs not only represent the 
 number and extent of the variation from the normal, but 
 graph 4 shows the variation of these in the 12 ft., 16 ft., and 
 20 ft. letter tests both from the normal and from each other. 
 Graph 5 shows the same facts in reference to the 20 ft. let- 
 ter test and the 20 ft. dot test. Graph 6 shows these facts 
 in reference to tests made with the 30 ft., 40 ft., and 50 ft. 
 letter tests. 
 
 In each one of the graphs the line a-b represents 
 the assumed distance at which the normal eye could just 
 make out the letters or dots. 
 
 The vertical column of numbers at the left represents 
 the number of pupils who could see the tests at the differ- 
 ent distances. 
 
 The horizontal line of figures beneath the curves in- 
 creases by two's, both right and left, beginning at the base 
 of the line a-b, and shows the number of feet variation from 
 the normal, a-b, made by each group of pupils, indicated by 
 the vertical line of figures at the left. The figures to the 
 left of the base of line a-b represent the distance above 
 normal and the figures to the right, the distance below nor- 
 mal. 
 
31 
 
 Number of feet variation on either side of normal. 
 Right side is above normal, left side below normal, 
 
 Graph 4. 
 
32 
 
 Number of feet variation on either side of -normal 
 Right side is above normal, lelt helovr. 
 
 Gkaph 5. 
 
33 
 
 r-4 «) 
 
 ^ O 
 
 o c 
 
 <n o 
 
 O r4 
 
 CO ,0 
 
 V +> 
 
 0> r-* 
 
 m 
 -*- 
 
 (U +> 
 
 > v-» 
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 QO 
 
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34 
 
 If all of these seven tests had been of equal value in 
 testing normal vision and those above and below normal, 
 and, if the curves representing these results had all been 
 placed in one figure, then the apexes of each of these curves 
 would either have been- on the line a-b or some other line 
 parallel to line a-b. 
 
 Furthermore, the curve representing the results obtain- 
 ed by testing with the 50 ft. letters would have its apex 
 higher than any other curve and the distance between the 
 two ends of the curves would be greater than the distance 
 between the ends of any of the other curves. Immediately 
 under this curve with its apex on the same vertical line 
 with the apex of the 50 ft. curve and with its two ends less 
 distance apart would come the 40 ft. curve. Then would 
 follow the 30 ft., 20 ft., 16 ft. and 12 ft. curves in order, each 
 being not so high or wide as its predecessor and the sides of 
 each would be parallel with the 50 ft. curve, and, of course, 
 with each other, also. 
 
 The curve for the 20 ft. letters and the curve for the 20 
 ft. dots, theoretically, should be the same, and, of course, 
 would be represented by one and the same curve, if placed 
 in the same graph. 
 
 It was found impractical to put all of these curves in 
 one graph, so they are shown in three graphs : 4, 5 and 6. 
 
 A glance at these graphs shows at once that no two 
 curves are parallel and, consequently, the results of no two 
 tests are uniform. As a matter of fact, no two such curves 
 will ever be parallel, even if the tests used were of equal 
 value as tests, for the personal element, of both the oper- 
 ator and the subject, and the influence of environment are 
 constantly injecting themselves into and modifying the re- 
 sults, consequently, variations of these curves from each 
 other are to be expected within certain limits. We can pre- 
 scribe these limits, however, and require that results from 
 tests obtained by using any size letter and character shall 
 come within these limits. 
 
 It would be fair, it seems, in making tests with different 
 sized letters and characters to expect that the numbers who 
 could see these letters and characters further than 12y 2 % 
 of the selected normal distance should be fairly constant. 
 
 The same requirement might be made for the lower limit 
 of vision with these same tests. That is, the number un- 
 
35 
 
 able to see each test without moving nearer to the test than 
 12 1 /o% of the selected normal distance should be fairly con- 
 stant. 
 
 If this limit were not broad enough then any percentage 
 of the normal distance above or below the normal greater 
 than 12y 2 % might be taken, as 25%, 37%, or 50%, and we 
 could require that the number seeing the different tests 
 further than normal by these percentages should be fairly 
 constant, and, that the number who could not see the same 
 tests without getting nearer to them than the percentages 
 of the normal distance indicated, should also, be fairly 
 constant. Both of these methods of determining whether a 
 test is reliable or not has value. If it is desirable to deter- 
 mine how acute the vision of a pupil is who has acute vision, 
 then the upper limit method of trying out the tests will be 
 of value. If, however, it is desired to know how acute the 
 vision of a pupil is who cannot see the test as far away as 
 the normal distance, then the lower limit method will be of 
 value. But, since most pupils are supposed to have some- 
 where near normal vision, it would seem, if the correct 
 tests are used, that the number seeing these tests at normal 
 and a certain percentage above and below the normal dis- 
 tance should be fairly constant, for all the tests. This 
 might be called the mean limit of tests for acuteness of 
 vision. These methods of determining the relative value 
 of testts have been used in connection with the seven dif- 
 ferent tests under consideration and the results are shown 
 in table 11. 
 
 The (a) portion of this table represents the results ob- 
 tained by applying what has been called the " upper limit 
 test," for the given percentages above normal, to the re- 
 sults obtained from each of the seven tests. 
 
 In (b) is shown the result of applying the "lower limit 
 test," with the same percentages, to the results of the same 
 tests. 
 
 In (c), is shown the results of applying the "mean limit 
 test, ' ' with the same percentages, to the results of the same 
 tests. The uniformity of the results shown in (b) by apply- 
 ing the "lower limit test" is quite striking in the 12*4% 
 line except the numbers under the 16 ft. and the 12 ft. let- 
 ters and a close degree of uniformity in all the tests, is 
 also seen in the 25%, 37y 2 %, and 50% lines, respectively. 
 
36 
 
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37 
 
 According to these figures, either one of the tests ex- 
 cept the 12 ft. letter test could be relied upon to detect 
 vision, that is less than 50% of normal, or 37%% or 25% 
 or even 12y 2 % of normal. Since the detection of poor 
 vision, rather than the determination of how many have 
 acute vision, above normal, is the chief purpose of testing 
 the vision of school children, any of the seven tests under 
 consideration except the 12 ft. letter test would be adequate 
 for this purpose, especially is this true, if, as is usually the 
 case, only those, pupils who have vision less than 25% nor- 
 mal are given attention. 
 
 By inspection of the (c) portion of table 11 or that por- 
 tion showing the mean variation from the normal, we see 
 here, too, a rather close degree of uniformity of results. 
 This is especially marked in the figures showing variations 
 on both sides of the normal of more than 25%, and, it 
 would seem reasonable to expect that any vision test that 
 makes any pretension to reliability should show similar re- 
 sults when this test is applied. 
 
 If we now give our attention to the (a) portion of table 
 11, we see here, too, a rather close degree of uniformity in 
 all the tests for the upper limit of vision for all the per- 
 centages taken above normal. Since the application of all 
 of these tests to the tests under consideration give fairly 
 uniform results, it is reasonable, it seems, to conclude that 
 the results in general will be about as accurate with one 
 test as with another. Exceptions, however, will have to be 
 made with the 12 ft. letter tests, although the figures in the 
 tables would seem to indicate that this test is generally 
 about as good as any of the other tests. This exception 
 will have to be made in spite of these figures, because in at 
 least two cases of undoubted nearsightedness, the pupils 
 could not see the larger letters at anything like the normal 
 distance, but they could see the 12 ft. letters at about nor- 
 mal. 
 
 The variation of results of certain tests from the results 
 of other tests as shown in table 11 demands some attention. 
 
 In the (a) portion of the table it is noted that the num- 
 ber seeing the 20 ft. dots beyond the normal distance by the 
 different given percentages is smaller in every case than 
 with any of the other tests except the 16 ft. letter. From 
 the data obtained from these tests it is not possible to as- 
 
 
38 
 
 sign a reason why the 16 ft. letters were not seen as far 
 proportionately above the normal as were the twenty ft. 
 letters or any of the other letters, but it is believed that the 
 failure to see the 20 ft. dots as far as the letters, can be 
 accounted for in this way. In deciding what a letter is, 
 the element of intelligence as well as the ability to see 
 enters in as a determining factor much oftener than is the 
 case with deciding wiiether the dot is seen or not. 
 
 In seeing the dot only two things can enter into the mind 
 on which a decision is to be made, and these two things are, 
 is the dot there, or is it not there, or does the dot make a 
 sensation on the retina or does it not. The decision that is 
 made will depend almost exclusively upon pure retinal sen- 
 sation. While in the case of seeing the letter there can be 
 no doubt that the. letter is seen, that a retinal impression is 
 made, but in deciding what the letter is that is making this 
 particular impression, often, undoubtedly, involves a com- 
 plicated mental operation, in which the general shape and 
 appearance of the letter play a very important part. 
 Hence, one must expect fewer pupils to see the 20 ft. dot 
 at distances considerably above normal than will see the 
 same sized letters or letters of any size at proportional dis- 
 tances. 
 
 This expectation is borne out by the figures in (b), table 
 11. Here it is seen that the dot shows up more pupils with 
 defective vision, on the average than any of the letter tests, 
 at the percentages below normal given, except the 12 ft. 
 letter. 
 
 The figures in (c) under the 20 ft. dot column also show 
 that the letters of all sizes above the 16 ft. letters can be 
 seen better than the 20 ft. dot at the same relative distances. 
 Take, for example, the 12y 2 % variation on either side of 
 normal, there were only 90 pupils who could not read the 50 
 ft. letters, while there were 117 who could not make out 
 the dot at the same relative distance from normal. The 
 fact that the vision of the 200 pupils tested averaged 
 above normal and that more pupils saw the 20 ft. dots at 
 the average distance above normal than for any of the other 
 tests, and, since the number found with defective vision 
 was unusually small, but the dot test showed more than 
 any, one would be inclined to the belief that the dot is the 
 best of any of the tests used. One would be justified in 
 
39 
 
 coming to k this conclusion, not only because it tests vision, 
 and vision only, and the results are more in harmony with 
 what other investigators have found out about the number 
 of children who have defective vision, but, also, because of 
 the simplicity of the test and the fact that it can be used to 
 test little children, illiterates or literates with equal ease 
 and accuracy. Further evidence that the dot is a good test 
 is shown by the fact that there was not a single case of poor 
 vision detected among the 200 pupils by any of the other 
 tests that was not also detected by the dot test. This was 
 also true with the tests made with the 16 ft. and the 12 ft. 
 letter, except in the two cases mentioned above. This 
 shows undoubtedly that for certain defects of the eye the 
 12 ft. letters are not reliable. The 16 ft. letters were found 
 to be reliable for the detection of all cases of poor vision 
 that would need attention and which were detected by the 
 other tests. 
 
 The results of these tests clearly justify one in drawing 
 the following conclusions : 
 
 1. The "illiterate E" as now constructed is practically 
 useless as a test of the acuteness of vision. If it is to be 
 used as a test when constructed of the size of the 16 ft. let- 
 ter, then the distance at which it should be placed from the 
 one being tested should be, not 16 ft., but 26 ft. Or, if the 
 16 ft. distance is to be maintained then the size of the letter 
 must be reduced to 16/26 of its present size. 
 
 2. The 20 ft. dot test is thoroughly reliable for testing- 
 poor vision, normal vision, or acute vision. None of the 200 
 pupils tested seemed to have any optical trouble — myopia, 
 hyperopia, astigmatism or any other optical defect — that 
 was not detected by this test as well or better than by any 
 other test. 
 
 3. The 16 ft. letter test is reliable for all defects of suffi- 
 cient gravity to justify the teacher in recommending the 
 pupil to go to an oculist. 
 
 4. The 12 ft. letter test will detect most of the graver 
 defects of vision, but not all, therefore, it is not to be relied 
 upon. 
 
 5. The eyes of 150 of the 200 pupils, subjected to these 
 tests were tested, one eye at a time, a few weeks before. 
 
40 
 
 Every pupil, with four exceptions, who had vision 25% or 
 more below normal, as shown by this one-eye-at-a-time test, 
 could with two eyes make a better showing. Not only was 
 this true of pupils having poor vision, but it was equally 
 true of all other pupils. This can be taken as an indication, 
 not only, that binocular vision is better than monocular 
 vision, but it accounts for the fact that the pupils in these 
 tests averaged above normal in vision. 
 
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