C. GENERAL PHYSICS. 187 



the formula thus deduced theoretically to the observations 

 made by Zeuner, Weisbach, and Fliegner, it seems to result 

 that, for the atmosphere, the " co-efficient of discharge," as 

 determined by Weisbach, is equal to the " exponent of dis- 

 charge," as that term is used by Zeuner, and is represented 

 by the number 1.41. In the investigations of this latter 

 physicist, certain resistances have been taken into account, 

 such that, in general, the co-efficient and the exponent of 

 discharge will be different for different fluids. It is in 

 those cases in which the internal resistance or viscosity of 

 the fluid is that the co-efficient and the exponent of dis- 

 charge become equal. 



THE INVISIBILITY OF MINUTE BODIES. 



The invisibility of minute bodies subtending a sufficient 

 visual angle to be readily seen if properly defined, is a high- 

 ly curious and important fact. This depends upon several 

 causes that have been examined by Dr. Pigott, in a paper 

 lately read before the Royal Microscopical Society. Minute 

 bodies are often solely distinguished by the sharpness and 

 decision of their outlines. The question is, can this outline 

 be altered by the conditions of vision, or by any relation be- 

 tween the refractive index of the substance and the aperture 

 of the objective ? In examining minute globules of glass, 

 or minute spherical bubbles within a larger mass of glass, 

 we notice a very perfect picture of such objects as are be- 

 yond the globules, and the whole surrounded by a black 

 band. The field of view is found to be precisely three fifths 

 of the diameter of the bubble ; the breadth of the band 

 being the same when we look at the bubble for all object- 

 ives, whatever may be the aperture ; but when we look at 

 a solid spherule, we find that the breadth of the band in- 

 creases from nothing up, until it occupies the whole spher- 

 ule as we diminish the aperture ; the angular aperture at 

 which the black band first appears varies with the refract- 

 ive index of the sdass bead. It results from these observa- 

 tions that the aperture of the objective regulates the ap- 

 pearance or disappearance of the circular black outline of 

 minute refracting spherules, or the black bands of refracting 

 cylinders. It thus appears that the aperture of the micro- 

 scope objective must be adapted to the refractive index of 



