From the above data we obtain the accompanying photographic light-curve compared to Münch's visual light curve (dotted lines). It is to be remarked that the amplitude of the photographic curve is much larger than that of the visual, both curves indicating a large deformation of the descending branch. DOMINION OBSERVATORY, OTTAWA. ON A CURIOUS EFFECT OBTAINED BY SUPERPOSING TWO PHOTOGRAPHS OF STAR FIELDS, FROM WHICH AND ACCURATE METHOD OF MEASURING SMALL DISTANCES CAN BE DEVISED BY F. HENROTEAU The two accompanying star field photographs have been obtained with a wide angle camera attached to the large equatorial telescope of the Dominion Observatory by Mr. Henderson and myself (exposures five hours). As is seen, they cover two different regions having however a large part in common; the first one has its center near the star 17 Vulpeculæ (20h 2m; +23° 19′) and the second one near the star 8 Cygni (19h 28m; +34° 14′). When we try to superpose the common regions we obtain a strange figure which seems to indicate a distribution in concentric circles or spirals. A slight shift of one photograph with respect to the other makes the common center of these spirals move a great amount; the center of the spirials for two different respective positions of the two plates is shown clearly on the accompanying plates representing two superpositions. The displacement of the spiral's center is nearly perpendicular to the direction of the shift of one plate with respect to the other, and is usually a great many times larger than this shift. The explanation of such a distribution in seemingly concentric spirals is simple. The two photographs of the common field of stars are indeed projective representations, where the distance separating any two points of one representation very nearly equals the distance separating the two corresponding points of the other. To be concrete, let A and A1 be two corresponding points on the two photographs, similarly for B and B1. Let us put A over A1, since A B is nearly equal to A1B1, B1B will be nearly perpendicular to AB, irrespective where B is. It is easy to see then that all the BB's, for If we now shift the second photograph in the direction B1B and of the amount B'B, so that B1 falls on B, it is readily seen that the center of the apparent.spirals will move from A to B. We will have a much simpler case if instead of considering two different projective representations, we consider them identical, but the second one turned through a certain small angle with respect to the first. The apparent spirals will then become apparent concentric circles, and it is easy to prove that for a certain linear displacement a of one plane with respect to the other, the apparent displacement of the centre will be b-a/2 cosec w/2. If w is very small, b will be many times greater than a, easily 100 times, or even more, without however having much greater uncertainty in the determination of the position of the center of the apparent concentric circles. The displacement of b is nearly perpendicular to the displacement a, (forming an angle w/2 with this perpendicular direction). Two plates constructed like this (identical projections) having each a well defined reference point or line, could then be used for measuring small displacements (letting them slide along a straight rule) and might by measuring the displacement of the center of the circles, replace with advantage the actual gauges or screw measuring engines. An apparatus based on the above principle would be simple, and easy to construct, and possibly much cheaper than devices now in use. It might assist greatly in measuring radial velocities, parallaxes and other small quantities encountered in astronomy, physics or engineering. My thanks are due to Mr. Steadworthy, photographer at the Dominion Observatory, for his skilful treatment of the adjoining combined photographs. |