i. e. nearly 5 times the limiting value. There is little doubt that this satellite should be visible under good atmospheric conditions. The coincidence method of measurement is liable to these types of error:— (a) Line thickness parallax. (b) Malfocus parallax. (e) Colour parallax. (d) Intensity and visual threshold parallax. (a) Line thickness parallax.-In the case of indices which are attached to scales which lie side by side (e. g. scale and vernier), the accuracy is not so noticeably affected by line thickness as by a difference in thickness of the lines on the two scales. But even in the latter case the inaccuracy is small compared with that introduced into interpolation measurements by thick lines. (This will be considered later.) (b) Malfocus parallax.-This is the error familiar to astronomers when two points under observation differ in position in the direction of the line of sight, or when two scales which are being placed in coincidence with one another are in different planes relative to the eye, i. e. one scale being nearer to the observer than the other scale. The avoidance of error due to these causes is, as a rule, simple, and practical details are well known. It should be noticed, however, that when both eyes are being used together during observations, it is usually one eye-called by oculists the master eye by means of which the settings are made. It is known, however, that in certain individuals neither eye is master, but one eye is sometimes used for setting and, on other occasions, the other eye. This selection takes place without the observer being aware that any change is taking place. Errors may be introduced from this cause if the two scales do not lie in the same plane. (c) Colour parallax.-Donders pointed out that the eye suffers from chromatic difference of magnification; Gullstrand estimates that violet images are 3 per cent. smaller than red ones. I have confirmed this value *, and find that since the fovea is approximately 0.6 mm. to the temporal side of the optical centre of the retina, the foci for different coloured rays fall approximately along a straight line which *Hartridge, Journ. Physiol. lii. p. 176 (1918). The cuts the optic axis 115 mm. in front of the retina. centres of the aberration disks formed on the retina by rays of different colour do not therefore coincide, but the blue disks fall relative to those of the yellow on the nasal side and red disks on the temporal. To this is due the phenomenon of chromatic stereoscopy described by Donders. The relative displacements of the centres of red and blue images on the retina is approximately 0.02 mm. That is an apparent displacement of about 03 mm. in a scale illuminated by monochromatic red light in reference to a scale lit by pure. blue-violet light placed side by side with it at, say, 250 min. distance from the eye of the observer. Two examples will be given : Case 1. Suppose that first one eye and then the other be used for measurement, an error of 0.6 mm. might occur if the scales were illuminated by pure red and blue light respectively. Scales tinted red and blue would suffer smaller apparent relative displacements, because these would not reflect pure spectral colours differing greatly in refrangibility, but only mixed rays the mean refrangibility of which would be less. A smaller but still noticeable error should occur if, say, one scale be of gold and the other of silver (a common arrangement for a scale and its vernier). Case 2. Suppose that the length of an object part blue and part red is being measured at 250 mm. from the eye; then an error in the length of 0.3 mm. might result. A number of other examples might be given, but errors of this nature can be avoided by avoiding coloured scales, making corresponding scales of similar metals, and measuring all coloured objects under monochromatic light of specified wave-length. (d) Intensity and visual threshold parallax.-It has been found by experiment that the measurements of the mean wave-length of absorption bands are influenced (a) by the relative brightness of the illumination on the two sides of the bands (the band appears to be shifted towards the darker side), and (b) by the relative sensitive ess of the two parts of the retina on which the images of the edges fall * (the band appears to be shifted to that side falling on the less sensitive half of the retina). Since the image on the retina, even of a mathematical line, * Hartridge, Proc. Roy. Soc. B. lxxxvi. p. 128 (1913). Phil. Mag. S. 6. Vol. 46. No. 271. July 1923. F is a diffuse one, such a line must show similar though probably smaller shifts under the influence of these two factors. Suppose, for example, that a scale, consisting of black lines on a white ground, be discoloured by a localised dark stain, then if the edge of the stain happens to coincide with one of the lines, so that on one side of the line the ground is darker than it is on the other, then it would be expected that measurements made in reference to such a line would be inclined towards the darker side. These effects of intensity are probably negligible under ordinary circumstances. It would, however, appear best in practice to avoid any possible errors due to them by the use of clean scales. The retinal factor is not so readily disposed of. It would seem best in practice either to examine the scales with their ends alternatively to the right and left, or to perform coincidence settings alternatively with the scales on which the determinations are being made and with another set as nearly like them as possible which can be examined with their ends alternatively to right and left. The four cases just considered apply to the unaided eye, and, with suitable modification in the actual values of the errors, to the eye when looking through an optical instrument which has an exit pupil large in comparison with the pupil of the eye (e. g. a Galilean telescopic system or a magnifying-glass). When the exit pupil of the instrument is small in comparison with the pupil of the eye, it is found that three sources of error may occur in instruments which employ the coincidence method of measurement: i. The first is well known, namely, when two objects to focussed for white light, rays from the violet part of the spectrum would be brought to a focus in front of the retina, whereas rays from the red end of the spectrum would be brought to a focus behind the retina. If the exit pupil of the instrument accurately coincided with the optical axis of the eye, no deflexion of these images relative to one another would result; but if the exit pupil of the instrument was to the left side of the optical axis of the eye, then it would be found that violet images would be displaced to the left and red images to the right, and vice versa. Supposing, then, the spectrum has its violet end on the left and its red end on the right, the difference in wave-length of the red and violet lines would appear to be exaggerated so that the violet line would appear to have too small a wave-length and the red line one that was too large. Alternatively, if the exit pupil of the instrument were to the right of the optic axis of the eye, the reverse conditions would hold good, and the converse would be the case. It was found in the case of a direct reading spectroscope by Zeiss that an error of approximately 50 A.U. in the wave-length measurements of the violet helium line (X=4713) could be introduced by causing the rays from the instrument to pass through the extreme right or left-hand edge of the pupil. iii. In cases where an instrument with split field is being used, it is found that a relative shift of the two fields can occur if the exit pupils of the rays which have illuminated the two fields do not accurately coincide with one another, and if the eye suffers from spherical aberration (as is almost always the case). For example, supposing the upper of two fields to have its exit pupil to the right of the exit pupil in the lower of the two fields, and supposing that the exit pupil of the upper field passes through the periphery of the lens system of the eye (which is usually found to suffer from spherical under correction), then the images in the upper field will be found to be displaced to the right in relationship with images occurring in the lower field, and therefore errors will be introduced. This method is used in a large number of instruments, e. g. the chemical burette and the slide-rule. SECTION IV. Interpolation Methods of Measurement. This method depends on the visual subdivision of a space bounded by two lines. Suppose, for example, that the position of a line is being measured by means of a millimetre scale; the millimetre is subdivided by the eye into tenths and possibly hundredths, and the number of such tenths or hundredths added on to the whole number of millimetre divisions which the object is found to measure. The accuracy with which such a subdivision can be effected has been made the subject of measurement. In Table III. are given the mean values of ten measurements of certain distances; in the first column as adjusted by interpolation by the eye, and in the second column as actually measured by means of the vernier. In the third column are given the differences between these two methods of measurement. TABLE III. Showing Errors in Judging the Subdivisions of a 1 mm. Scale into Tenths at 25 cm. from the Eye. An observation of this column will show that the whole reading in millimetres is very accurately judged, this depending on the coincidence of two lines; but the readings on other parts of the scale will be found to show considerable inaccuracy; e. g. the bisection of the space is judged inaccurately by 2, the subdivision into the first tenth is judged inaccurately to 6 μ, and 4 μ for the two ends of the division respectively, other values giving errors which vary between |