6s6 PHILOSOPHICAL TRANSACTIONS. [ANNO 1785. 



that seem to be capable of great certainty, ihey being no less than an actual 

 survey of the boundaries of our sidereal system, which I have plainly per- 

 ceived, as far as I have yet gone round it, every where terminated, and in most 

 places very narrowly too, it will be proper to show the length of my sounding 

 line, if I may so call it, that it may appear whether it was sufficiently long for 

 the purpose. In the most crowded part of the milky way I have had fields of 

 view that contained no less than 588 stars, and these were continued for many 

 minutes, so that in one quarter of an hour's time there passed no less than 

 ] l6000 stars through the field of view of my telescope.* Now, if we com- 

 pute the length of the visual ray by putting s = 588, and the diameter of the 

 field of view 15', we shall find n = ^/b 2 s = 4Q8 ; so that it appears the length 

 of what has been called the sounding line, or n — 1, was probably not less than 

 497 times the distance of Sirius from the sun. The same gage calculated by 

 the '2d arrangement of stars gives */ <p* — 1 = 1.41421 ; 



-—*—- = tangent of 31° 28' 55*.77 ; 7 = b = 280.6o; V ** ~ ' = d = 



.81649 ; iB*s = 231634097 = n s + iri 2 + $n ; where n = 284.8 nearly; and 

 idn — 1 = 464, the visual ray. 



It may seem inaccurate that we should found an argument on the stars being 

 equally scattered, when in all probability there may not be two of them in the 

 heavens, whose mutual distance shall be equal to that of any other two given 

 stars ; but it should be considered, that when we take all the stars collectively, 

 there will be a mean distance which may be assumed as the general one ; and an 

 argument founded on such a supposition will have in its favour the greatest pro- 

 bability of not being far short of truth. What will render the supposition of an 

 equal distribution of the stars, with regard to the gages, still less exposed to ob- 

 jections is, that whenever the stars happened either to be uncommonly crowded 

 or deficient in number, so as very suddenly to pass over from one extreme to the 

 other, the gages were reduced to other forms, such as the border gage, the dis- 

 tance gage, &c. which terms, and the use of such gages, there will hereafter be 

 an opportunity of explaining. And none of those kinds of gages have been ad- 

 mitted in this table, which consists only of such as have been taken in places 

 where the stars apparently seemed to be, in general, pretty evenly scattered ; 

 and to increase and decrease in number by a certain gradual progression. Nor 

 has any part of the heavens containing a cluster of stars been put in the gages ; 



* The breadth of my sweep was 2° 26', to which must be added 15' for two semi-diameters of 

 the field. Then, putting It) I = a, the number of fields in 15 minutes of time; .7S54 = b, the 

 proportion of a circle to 1, its circumscribed square; <p = sine of 74° 22', the polar distance of the 

 middle of the sweep reduced to the present time; and 588 = s, the number of stars in a field of 



view, we have — = H6u70 stars. — Orig. 



