The following formula by Benoit is also sometimes used for the determination of high temperatures. (d) r=1+.002445 t +.000000572 t2. In this formula t is the temperature in degrees centigrade. When, as is frequently the case, it is more convenient to measure the length of a wire than its resistance, we may adopt Matthiesen's formula, viz. : (e) 1=1, (1+.00000851 t +.0000000035 t2). [where 1 = length of wire and t = temperature]: or use the uncorrected scale of the platinum thermometer (J) 1=1(1+.00000886 t). These being almost the only data we possess for the calculation of the temperature of a hot wire, the question of their accuracy is of some importance. The formulæ may be best compared by plotting, side by side, the curves which represent them (see figure 2). In the figure, resistance is substituted for length in formulæ e and f by making use of the measurements given in the second paragraph of this paper. The following table affords a further comparison of the six formulæ. In the columns a to ƒ are given the temperatures calculated by the various formulæ, at which the resistance of the wire, compared with its resistance at 0° as unity, is given in the column marked r. The curves marked Siemens b and c were identical so far as the methods employed are concerned, but the platinum used contained some slight impurities. To this the disparity of the results was due. Dr. Siemens found that even such impurities as are usually contained in commercial platinum affected both the resistance of the cold metal, and the law of the change of resistance with the temperature. Benoit's formula (d) depends for its accuracy upon the determination of the boiling points of mercury, sulphur, cadmium, and zine; for which températures he adopted the values given by De Ville and Troost.1 M. Ed. Becquerel opposed those values at the time of their publication, and later researches have confirmed him, at least so far as cadmium and zinc are concerned, in think 1 De Ville and Troost, Annales de Chimie, Ser. 3, T. 58. ing them entirely too high. In the following table the results of De Ville and Troost are compared with the more probable values of other physicists. The substitution of these other values in Benoit's formula places it more at variance than ever with the work of Siemens and of Matthiesen; a variation probably due to the difference of behavior noticed by Siemens in the case of different specimens of platinum. This brief discussion of the above mentioned results suffices we think to show that, 1. The formulæ are based for the most part, if even a fair degree of accuracy be claimed, upon unwarrantable assumptions, -such as the constancy of the specific heats of copper and platinum, the constancy of the coëfficient of expansion of the latter metal, and upon the accuracy of certain determinations of the boiling points of the metals Zn, Cd, etc. 2. That aside from the inaccuracy of those data, the variation of different specimens of platinum renders the use of any formula for the calculation of the temperature of the metal from its electric resistance applicable only to the individual wire for which the law of change of resistance had been determined or at best to a wire identical chemically and physically with the former. 3. That from the data at command we are not in position to calculate the temperature of an incandescent platinum wire, either from its expansion or change of resistance, further than to find an expression of the temperature in terms of the length or of the resistance of the wire. 4. That owing to the great variations shown by different specimens of platinum as regards resistance, the determination of the expansion is to be preferred whenever practicable to the measurement of the conductivity. THE STEREOSCOPE, AND VISION BY OPTIC Divergence. [ABSTRACT.1] C. R LET a and a' be corresponding foreground points, b and b' corresponding background points on a stereograph card, symmetrically situated with regard to a median line from C to B. Rays from a and a' are deviated by lenticular prisms into the eyes, R and L, as if they came from A; likewise b and b', as if from B. Let i RL distance between optic centres. = Let D=CA apparent distance of point of sight, Suppose prisms and stereograph removed and a binocular camera substituted. Let i RL distance between two cameras. Let D=CA distance of point to which they are directed. The formula then gives the absolute distance of the object photographed. If a=0, D= ∞; if a <0, D < 0. Both these conditions imply that there is no point of sight at any finite distance in front. Hence, if distinct vision in the stereoscope is possible when the visual axes are parallel or divergent, the mathematical theory of the stereoscope, as usually accepted and taught, is incorrect. To test this, measurements of the foreground interval, aa', were made on 166 stereographs. It was found to vary between 60mm and 95mm, the mean being 72.9mm. The mean interocular distance, i, for adults, is about 64mm. Hence, if the rays, aR and a' L, enter the eyes without transmission through prisms, and binocular fusion of retinal images is attained, this shows that axial divergence also is attained, if we assume average stereographs 1 Printed in full in Am. Jour. Sci., Nov. and Dec., 1881; also in Transactions of N. Y. Academy of Sciences, Nov. and Dec., 1881, and abstract in London Philosophical Magazino, Dec., 1881. and average separation between the eyes. My own eyes, though perfectly normal, have been thus diverged 7°, an extent that is easily noticeable. Many other persons have been found to possess the same power in less degree. To ascertain whether divergence is unconsciously practised in using the stereoscope, thirty pairs of lenticular prisms were examined. The mean focal length was 18.3cm. Parallel rays, 64mm apart, were transmitted at points opposite R and L, the screen being 18.3cm distant. The mean interval between points of light caught on the screen was found to be 79.12mm. Hence, if the stereographic interval aa' exceed 79.12mm, optic divergence is necessary, assuming the average stereoscope and average interocular distance. This interval is not infrequently exceeded, though it is greater than the average stereographic interval, 72.9mm. It was found that the mean value of the angle, a, on the assumptions just made, was 1° 57', which corresponds to 1.88mm as the distance of the point of sight. A variety of elements are to be considered in estimating the distance of an object of sight. The relation between the visual axes, being only one of these, is not alone sufficient. Its value depends largely upon our recognition of the degree of muscular strain induced in rotating the eyeballs. Rotation inward is habitually associated with approach of the object of sight, rotation outward with its recession. In like manner, contraction of the ciliary muscle is associated with nearness, relaxation with remoteness, of the object to which the focal adjustment has to be adapted. Axial adjustment and focal adjustment are consensually adapted to the same point of sight in normal binocular vision and conduce to the same judgment of distance, which increases in accuracy as the object is nearer. The value of each is greatest near the minimum limit of distinct vision, which is also about the distance at which stereographs are usually held when regarded. At this distance, 25cm in normal vision, the optic angle, a, is about 15°. In average vision through the stereoscope, since a is about 2°, while the apparent distance of the card, as magnified by the lens, is less than 25cm, the focal and axial adjustments are not consensually accordant, and the judgment of distance is vitiated by this conflict between important elements which thus tend to produce widely different impressions. The discordance increases as |