eters, 5,000 diameters, and still it is to us a mathemati cal point without dimensions. How much more, therefore, is it without dimensions to the naked eye! And yet it is perfectly visible. The only sense in which science recognizes a minimum visibile is the smallest space or object which can be seen as a surface or as a magnitude the smallest distance within which two points or two lines may approach each other and yet be perceived as two points or two lines. In this sense it is a legitimate inquiry; for there is here a real limit, which depends on the perfection of the eye as an instrument and the fineness of the organization of the retina.

We can best make this point clear by showing a similar property, but far less perfect, in the lower sense of touch. There is also a minimum tactile.

Experiment. Take a pair of dividers; stick on each point a mustard-seed shot, so that the impression on the skin shall not be too pungent. Now try, on another person whose eyes are shut, the least distance apart at which two distinct impressions can be perceived. It will be found that, on the middle of the back, it is about 3 inches; on the arm or back of the hand, it is about to inch; on the palm, about 1 inch; on the finger-tips, about or inch; and on the tip of the tongue, about inch, or less.

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Now, sight is a very refined tact, and the retina is specially organized for an extreme minimum tactile. There is no doubt that the size of the cones of the central spot determines the minimum visibile. If the images of two points fall on the same retinal cone, they will make but one impression, and therefore be seen as one; but if they are far enough apart to impress two cones, then they will be seen as two points. So also

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of an object: if its image on the retina be sufficient to cover two or more cones of the central spot, then it will be seen as a magnitude. Taking the diameter of central-spot cones to be (which is the diameter given by some), the smallest distance between two points which ought to be visible at five inches distance is Too of an inch. This is found to be about the fact in good eyes.

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2. Blind Spot. This is the spot where the optic nerve enters the ball of the eye. Objects whose images fall on this spot are wholly invisible. It is for this reason that the point of entrance is always placed out of the axis, about inch on the nasal side. For, if it were in the axis, of course the image of the object we looked at would fall on this spot, and the object would consequently disappear from view. The structural cause of the blindness of this spot we have already explained on page 59. It is the absence of the bacillary layer. The existence of the blind spot may be easily proved by experiments which any one can repeat.

Experiment 1.-Make two conspicuous marks, A and B, a few inches apart. Then shut the left eye, and

while looking steadily with the right eye at the left object, A, bring the paper gradually nearer and nearer: at a certain point of approach B will disappear utterly. Continue to bring the paper nearer, still looking steadily at A: at a certain nearer point B will reappear. The explanation is as follows: At first, when the paper is at considerable distance, say 18 inches, the image of A is, of course, on the central spot, for the axis of the eye is directed toward this point; but the image of B falls a little to the internal or nasal side of the central spot,

FIG. 25.

viz., between the central spot and the blind spot. Now, as the paper comes nearer, the eye turns more and more in order to regard A, the image of B travels slowly over the retina noseward until it reaches the blind spot, and the object disappears. As the paper still approaches, the image of B continues to travel in the same direction until it crosses over the blind spot to the other side, when the object immediately reappears.

The accompanying diagram, Fig. 25, illustrates this phenomenon. Let A and B represent the two objects, and R and I the positions of the right and left eyes respectively. The right is drawn, but the left, being shut, is not drawn, but only its position indicated by the dot. The central spot is represented by c, in the axis A c, and the blind spot by o, where the optic nerve enters. It is obvious that the image a of the object A will be always on c, and the place of the image of B is on the intersection .b of the line B b with the retina.

RA

R 3

R2

R'

Now, as the eye approaches the objects A and B, it is seen that the image b of B travels toward the blind spot, o. At the second position of the eye, R', it has not reached it. At the third position, R", it is upon it.

At the fourth position, R''', it has already crossed over and is now on the other side. At the third position, R", the object B disappears from view.

The distance at which the disappearance takes place will, of course, depend on the distance between the objects A and B. If these are 3 inches apart, then the disappearance on approach from a greater distance takes place at about 1 foot, and the reappearance at about 10 inches. If the objects be 1 foot apart, then the disappearance takes place at 48 inches, and the reappearance at 38 inches.

Experiment 2.-Place a small piece of money on the table. Shutting the left eye, look steadily with the right at a spot on the table a little to the left of the piece, and move the piece slowly to the right while the point of sight remains fixed; or else, the piece of money remaining stationary, move the point of sight slowly to the left. At a certain distance from the point of sight the piece will disappear from view. Beyond this distance it will reappear.

Experiment 3.—The experiment may be varied in many ways. If, when the object B has disappeared from view in the previous experiments, we open the left eye and shut the right, and look across the nose at the object B, then A will disappear. Thus we may make them disappear alternately. If, finally, we squint or cross the eyes in such wise that the right eye shall look at the left object A, and the left eye at the right object B (the two, A and B, had best be similar in this case), then B will fall on the blind spot of the right eye and A on the blind spot of the left eye, and they will both disappear; but a combined image of A and B on the central spots of the two eyes will be seen in the middle. This, however, is a phenomenon of bin

ocular vision, and will be explained farther on (see page 107).

Experiment 4.-Any object, if not too large, may be made to disappear by causing its image to fall on the blind spot. For example: From where I now sit writing the door is distant about 10 feet. I shut my left eye and look at the door-knob. I now slowly remove the point of sight and make it travel to the left, but at the same level; when it reaches about 3 feet to the left, the door-knob disappears; when it reaches 4 feet, it reappears. Precisely in the same way a bright star or planet, like Venus or Jupiter, or even the moon, may be made to disappear completely from sight.

Size of the Blind Spot.-As every point in the retina has its representative in the visual field, it is evident that the size of the invisible spot is determined by the size of the blind retinal spot. We may, therefore, measure the latter by the former. I have made many experiments to determine the size of the invisible spot. At the distance of 34 feet (42 inches) I find the invisible spot 12 inches from the point of sight, and 3 inches in diameter; i. e., a circle of 3 inches will entirely disappear at that distance. Taking the nodal point of the lenses or the point of ray-crossing at of an inch in front of the retina (it is a very little less), an invisible spot of 3 inches at a distance of 3 feet would require a blind retinal spot of a little more than inch in diameter. At 36 feet distance the invisible area would be 3 feet; it would cover a man sitting on the ground. At 100 yards distance the invisible area would cover a circle of 8 feet diameter. In a word, the angular diameter of the invisible spot is a little more than 4°. Helmholtz makes it a little larger than this.

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