Theory of Shadow

Generally, the opposite nature of brightness is supposed to be darkness i.e. shadow. For the formation of shadow, source of light; object and screen are required. We can see forming shadow, but we can not see the some rules of nature that governs the shadow. As for example- F=MA, This is the famous equation from the Newton's second law of motion. It shows the relationship among applied force F, mass of body M and acceleration produced on body A. This even helps to formulate the much famous equation E=MC². In the same way, 'Theory of shadow' also shows the relationship among the different factors. From the close observation, when the symmetrical point source is taken, object distance; area of object and shadow distance are interrelated to the nature and size of shadow. 'Theory of Shadow' focuses on how these different factors are interconnected, how do they rule the formation of shadow and finally give the whole conclusion in the beauty of equation. For this work, experimental; mathematical and geometrical procedures are being applied while in each and every trial, The 'Theory of Shadow' is found to be exactly proved.Key words: Point source; Area of object; Object distance; Area of shadow; Shadow distanceThe Himalayan PhysicsVol.1, No.1, May, 2010Page: 101-105Uploaded Date: 29 July, 2011

Angular relations between equivalent planes and distances between equivalent points in symmetrical point groups

A fundamental problem arising out of the study of symmetrical point groups can be formulated as follows: Let N points in threedimensional space be connected two and two in every possible way by straight lines: what relations must exist between the lengths of these lines if the points are equivalent members of a symmetrical point group ?The methods of projection used in crystallography (e.g. the stereographic projection) at once show that the points may be considered to be the images of straight lines or planes. The problem formulated above has therefore a direct application to descriptive crystallography and can in this connexion be stated as follows:A complex of N planes is determined by the points of intersection of the normals with the surface of a unit sphere, i.e. by their poles. What now must the angular relations between the planes be if all are equivalent, that is to say, belong to one and the same simple form ?

II. Mathematical contributions to the theory of evolution. II. Skew variation in homogeneous material

In the deduction of the normal curve of frequency from the symmetrical point binomial, three conditions are usually assumed to be true:— ( a .) The chances of any “contributory cause” giving its unit of deviation in excess or in defect are presumed to be equal. ( b .) The number of “contributory causes” are supposed to be indefinitely great.