TJie Hclmholtz Theory of the Microscope. By J. TV. Gordon. 393 

 r . The total light produced by r\ in unit time must therefore 

 stand to the total light similarly produced by e in the ratio ~ < 



r * 



From this we infer at once that the radiating surfaces of the two 

 lamps must bear the same proportion to one another, and if the 

 lamps be, as here showD, radiant spheres, their diameters will be 

 as r € : r simply. We may therefore write 



^=M, (1) 



r 



the magnifying power of this system, since we have already seen 

 that the proportion is the same in fig. 81 between the lamp-board 

 and its image as between these conjugate lamps. 



"We have tacitly assumed in this demonstration that both lamps 

 are burning in the same luminiferous medium. This is of course 

 no longer necessarily the case when we substitute focussed images 

 for lamps, since a focussed image may be formed in any transparent 

 medium. We must then consider what difference it would make 

 to the foregoing proof if we were to assume a more sluggish medium 

 behind the aperture than in front of it, say glass with a refractive 

 index of 1 • 5 behind and air in front. 



The problem so presented is not a difficult problem except in 

 the sense that it is usually discussed with the most unpleasant 

 array of mathematical symbols. Helmholtz does not himself 

 discuss it, but assumes the result reached by Kirchhoff, and more 

 commonly connected with the name of Clausius.* It is very easily 

 investigated by the help of analogies, of which many familiar 

 examples present themselves to the mind. Perhaps nothing can 

 be more familiar than the common eight-day clock — not a superior 

 article provided with dead-beat escapement, but one in which there 

 is a strong reaction between the scape wheel and the pallets. 

 There we have an example of energy consumed in producing 

 oscillatory movements, and it is familiar knowledge that the 

 capacity of the weight to impart energy to the pendulum, depends 

 in part upon the mass of the weight, and in part also on the 

 mobility of the pendulum. Increase the weight and you will 

 quicken the beat of the clock, although the clock-maker has done 

 his ineffectual best to make the period of the pendulum inde- 

 pendent of the driving power. Shorten the pendulum, so rendering 

 it more mobile, and you may, if you shorten it enough, enable the 

 driving power to discharge its eight days' supply of energy through 

 that very active pendulum in eight minutes. 



* Helmholtz quotes Kirchhoff probably from memory, certainly without giving 

 any reference to his paper. But it may almost certainly be identified with the paper 

 on the relation between the power of bodies to emit aud to absorb heat and light, 

 which appears in Pogg. Ann., cix. (1860) p. 275. For Clausius' exposition of the 

 law, see his Meckanische Warmtheorie, 8th Memoir, or in English, Hirst's trane- 

 tion of Clausius on Heat, p. 2tf0. 



