424 PHILOSOPHICAL TRAKSACTIONS. [anNO 1 767. 



the fixed stars, is owing to their immense distance, yet it may not perhaps be 

 disagreeable to see that this distance is further confirmed by other circumstances; 

 for let us suppose them to be, at a medium, equal in magnitude and natural 

 brightness to the sun, to which they seem in all respects to be analogous. And, 

 having laid this down as a foundation to build on, let us inquire what would be 

 the parallax of the sun, if he were to be removed so far from us, as to make the 

 quantity of the light, which we should then receive from him, no more than 

 equal to that of the fixed stars. To do this with accuracy, it would be proper 

 to compare the quantity of light, at present received from him, with that of the 

 fixed stars, by some such methods, as are made use of by M. Bouguer, in his 

 Traite d'Optiqiie; but as the present purpose does not require any such exactness, 

 Mr. M. deduces it in a more gross way, from facts already well known. He 

 assumes Saturn then in oppt^sition, exclusively of his ring, and when the earth 

 and he are at their mean distances from the sun, as equal, or nearly equal in 

 light, to the most luminous fixed star. Now the mean distance of Saturn from 

 the sun being equal to about 2082 of the sun's semidiameters, the density of 

 the sun's light at Saturn, will consequently be less than at his own surface, in 

 the proportion of the square of 2082 (or 4334724) to 1. If Saturn therefore 

 was to reflect all the light that falls on him, he would be less luminous in the 

 same proportion: but, besides this difference in his brightness, his appdrent dia- 

 meter, in opposition, is at most but 105th part of that of the sun, and conse- 

 quently the quantity of light, which we receive from him, must again be dimi- 

 nished in the proportion of the square of 105 (or 1 102.')) to 1. If we multiply 

 these two numbers together, we shall have the whole of the light of the sun to 

 that of Saturn (on the supposition of his reflecting all the light that falls on him) 

 as the square of nearly 22O000 (or 48,400,000,000) to 1 ; and removing the 

 sun to 220000 times his present distance, he would still appear at least as bright 

 as Saturn, and his whole parallax on the diameter of the earth's orbit would be 

 less than 2 seconds. This must consequently be assumed for the parallax of the 

 brightest of the fixed stars, on the supposition that their light does not exceed 

 that of Saturn. 



By a like computation we shall find, that the distance at which the sun would 

 afford us as much light as we receive from Jupiter, is not less than 46000 times 

 his present distance, and his whole parallax, in that case, on the diameter of the 

 earth's orbit, would not be more than 9 seconds, the light of Jupiter and Saturn, 

 as seen from the earth, being in the ratio of about 22 to 1, when they are both 

 in opposition, and supposing them to reflect equally in proportion to the whole 

 of the light that falls on them. 



But if Jupiter and Saturn, instead of reflecting the whole of the light that 

 falls on them, should in fact reflect only a part of it, as for example, only a 4th 



