TEMPERATURE GRADIENT IN AIR 



327 



in his balloon ascents, so that thus far the hypothesis is justified. But we have an 

 independent means of testing it. The form of the curve of vertices is now some- 

 what like the full lines in the following cut (Fig. 5), where is the eye, and the 

 lines RS, TU represent the boundaries of the transition stratum. It is clear, that, 

 if PM be the vertical tangent, there can be but one image of an object unless 

 its distance from O is at least twice OM. This will therefore be called the " Critical 

 distance" If the distance be greater than this there are three images : one erect, 

 seen directly through the lower uniform stratum then an inverted one, due to the 

 diminution of refractive index above the lower boundary of the transition stratum 

 and finally an erect image, due to the approximation to a stationary state towards 

 the upper boundary of that stratum. Now calculation from our assumed data gives 

 OM about six miles, so that the nearest objects affected should be about twelve 

 miles off. Scoresby says that the usual distance was from ten to fifteen miles. Thus 

 the hypothesis passes, with credit, this independent and severe test. A slight 

 reduction of the assumed thickness of the transition stratum, or of its height above 

 the ground, would make the agreement exact. 



All the phenomena described in Vince's paper of 1799, as well as a great many 

 of those figured in Scoresby's works, can easily be explained by the above assump- 

 tions. Scoresby's remarkable observation of a single inverted image of his father's 

 ship (when thirty miles off, and of course far below the horizon) requires merely a 

 more rapid diminution of density at a definite height above the sea. His figure is 

 the second in Fig. i above. But Scoresby figures, as above shown, several cases 

 in which two or more inverted images, without corresponding erect ones, were seen 

 above the ordinary direct image. The natural explanation is, of course, a series of 

 horizontal layers of upward diminishing density and without a " stationary state " 

 towards their upper bounding planes. I find that, by roughly stirring (for a very 

 short time) a trough in which weak brine below is diffusing into pure water above, we 

 can reproduce this phenomenon with great ease. In fact, when temporary equilibrium 

 sets in, the fluids are arranged in a number of successive parallel strata with some- 

 what abrupt changes of density. 



But the mathematical investigation, already spoken of, shows that it is quite 

 possible that there may be layers tending to a stationary state without any corre- 

 sponding visible images. 



This depends on the fact that, while the inverted image (due to the lower part 

 of a stratum) is always taller than the object seen directly (though not much taller 

 unless the object is about the critical distance), the numerical calculation shows 

 that the erect image is in general extremely small, and can come into notice only 



