494 REPORT — 1889. 



This is the condition that the relative retardation of the rays from the centre and 

 from the margin of the aperture shall amount to ^X. If 2r is to be equal to the 

 aperture of the pupil,/ would have to he about 66 feet. At this focus and with 

 this aperture the image formed without a lens would be at least as well-defined as 

 that received upon the retina. 



In some recent experiments / was about 9 feet, and 2r about ^^ inch. The 

 specimens exhibited were taken upon gelatine plates, and represent a weather-cock 

 seen against the sky. The amount of detail is not materially less than that 

 observable by direct vision in the case of ordinary eyes. Theoretically, it should 

 correspond to that obtained when the eye is limited to an aperture of jj inch. If 

 the pictures are held at the ordinary distance of say a foot from the eye, the object 

 is seen under a magnification of nine times, and there is, of course, a corresponding 

 loss of apparent sharpness. 



As the focal length increases, the brightness (B) of the image in a properly 

 proportioned pin-hole camera diminishes. For 



But modern plates are so sensitive that there would be no difficulty in working 

 with an aperture equal to that of the pupil, other than that incurred in providing 

 a focal length of 66 feet with the necessary exclusion of foreign light. 



3. On Boscoviclis Theory. 

 By Sir William Thomson, B.G.L., LL.T)., F.R.S. 



Without accepting Boscovich's fundamental doctrine that the ultimate atoms of 

 matter are points endowed each with inertia and with mutual attractions or repul- 

 sions dependent on mutual distances, and that all the properties of matter are due 

 to equilibrium of these forces, and to motions, or changes of motion produced by 

 them when they are not balanced, we can learn something towards an understand- 

 ing of the real molecular structure of matter, and of some of its thermodynamic 

 properties, by consideration of the static and kinetic problems which it suggests. 

 Hooke's exhibition of the forms of crystals by piles of globes. Navier's and Poisson's 

 theory of the elasticity of solids. Maxwell's and Clausius' work in the kinetic 

 theory of gases, and Tait's more recent work on the same subject — all develop- 

 ments of Boscovicli's theory pure and simple — amply justify this statement. 



Boscovich made it an essential in his theory that at the smallest distances there 

 is repulsion, and at greater distances attraction ; ending with infinite repul- 

 sion at infinitely small distance, and with attraction according to Newtonian 

 law for all distances for which this law has been proved. He suggested numerous 

 transitions from attraction to repulsion, which he illustrated graphically by a curve 

 — the celebrated Boscovich curve — to explain cohesion, mutual pressure between 

 bodies in contact, chemical affinity, and all possible properties of matter — except 

 heat, which he regarded as a sulphureous essence or virtue. It seems now wonder- 

 ful that, after so clearly stating his fundamental postulate which included inertia, 

 he did not see inter-molecular motion as a necessary consequence of it, and so dis- 

 cover the kinetic theory of heat for solids, liquids, and gases ; and that he only used 

 his inertia of the atoms to explain the known phenomena of the inertia of palpable 

 masses, or assemblages of very large numbers of atoms. 



It is also wonderful how much towards explaining the crystallography and 

 elasticity of solids, and the thermo-elastic properties of solids, liquids, and gases, 

 we find without assuming more than one transition from attraction to repulsion. 

 Suppose, for instance, the mutual force between two atoms to be repulsive when 

 the distance between them is <Z ; zero when it is equal Z ; and attractive when it 

 is >Z ; and consider the equilibrium of groups of atoms under these conditions. 



A group of two would be in equilibrium at distance Z, and only at this distance. 

 This equilibrium is stable. 



A group of three would be in stable equilibrium at the corners of an equilateral 

 triangle, of sides Z ; and only in this configuration. There is no other configuration 



