£84 PHILOSOPHICAL TRANSACTIONS. [ANNO 1800. 



The difficulty of ascertaining the greatest opening of the eye, arises from the 

 impossibility of measuring it at the time of its extreme dilatation, which can only 

 happen when every thing is completely dark; but, if the variation of a is not 

 easily to be ascertained, we have, on the other hand, no difficulty to determine 

 the quantity of light admitted through a telescope, which must depend on the 

 diameter of the object-glass, or mirror; for its aperture a may at all times be had 



a 2 l 



by measurement. It follows therefore, that the expression — will always be accu- 

 rate for the quantity of light admitted be the eye; and that — will be sufficiently so 

 for the telescope. For it must be remembered, that the aperture of the eye is also 

 concerned in viewing with telescopes; and that consequently, whenever the pencil 

 of light transmitted to the eye by optical instruments exceeds the aperture of the 

 pupil, much light must be lost. In that case, the expression a 2 / will fail ; and 

 therefore in general, if m by the magnifying power, - ought not to exceed a. 

 As I have defined the brightness of an object to the eye of an observer at a 



a 1 1 



distance, to be expressed by — , it will be necessary to answer some objections that 

 may be made to this theory. Optical writers have proved, that an object is equally 

 bright at all distances. It may therefore be maintained against me, that since a 

 wall illuminated by the sun will appear equally bright, at whatever distance the ob- 

 server be placed that views it, the sun also, at the distance of Saturn, or still farther 

 from us, must be as bright as it is in its present situation. Nay it may be urged, 

 that in a telescope, the different distance of stars can be of no account with regard 

 to their brightness, and that we must consequently be able to see stars which are 

 many thousands of times farther than Sirius from us; in short, that a star must 

 be infinitely distant not to be seen any longer. Now, objections such as these, 

 ' which seem to be the immediate consequence of what has been demonstrated by 

 mathematicians, and which yet apparently contradict what I assert in this paper, 

 deserve to be thoroughly answered. It may be remembered, that I have dis- 

 tinguished brightness into 3 different kinds. Two of these, which have been dis- 

 criminated by intrinsic and absolute brightness, are, in common language, left 

 without distinction. In order to show that they are so, I might bring a variety of 

 examples from common conversation; but taking this for granted, it may be shown 

 that all the objections I have brought against my theory have their foundation in 

 this ambiguity. The demonstrations of opticians, with regard to what I call in- 

 trinsic brightness, will not oppose what I affirm of absolute brightness; and I shall 

 have nothing further to do than to show that what mathematicians have said, must 

 be understood to refer entirely to the intrinsic brightness, or illumination of the 

 picture of objects on the retina of the eye: from which it will clearly follow, that 

 their doctrine and mine are perfectly reconcileable; and that they can be at variance 

 only when the ambiguity of the word brightness is overlooked, and objections, such 

 as I have made, are raised where the word brightness is used as absolute, when we 

 should have kept it to the only meaning it can bear in the mathematicians' theorem. 



