VOL. LXXIV.] PHILOSOPHICAL TRANSACTIONS. 465 



parts by 6oths, which has been delivered down to us from the ancients, and 

 gradually extended by similar sub-divisions by the moderns, among various uses, 

 serves for trigonometrical and other mathematical operations, by adapting to 

 those divisions of the arc, certain lines expressed in equal parts of the radius, as 

 chords, sines, tangents, &c. " But among all the improvements in this useful 

 branch of science, I have long wished to see a set of tables of sines, tangents, 

 secants, &c. constructed to the arcs of the quadrant as divided into the like 

 equal parts of the radius as those lines themselves. In this natural way, the 

 arcs would not be expressed by divisions of 6oths, in degrees, minutes, &c, 

 but by the common decimal scale of numbers ; and the real lengths of the 

 arcs, expressed in such common numbers, would then stand opposite their 

 respective sines, tangents, &c. The uses of such an alteration would be many 

 and great, and are too obvious and important to need pointing out or enforcing. 

 I have therefore had for a long time a great desire to commence this arduous 

 task ; but continual interruptions have hitherto prevented me from making any 

 considerable progress in so desirable an undertaking. But I am not without 

 hopes that some future occasion may prove more propitious to my ardent wishes. 

 It is not however to be expected, that this work can be accomplished by the 

 labours of one person only ; it will require rather the united endeavours of 

 many." But as this paper will be found in Dr. Hutton's works collected, any 

 further account of it in this place may be spared. 



VII. On the Means of discovering the Distance, Magnitude, &c. of the Fixed 

 Stars, in consequence of the Diminution of the Velocity of their Light, in 

 case such a Diminution should be found to take place in any of them, and such 

 other Data should be procured from Observations, as would be further necessary 

 for that Purpose. By the Rev. John Michell, B. D., F. R. S. p. 35. 



1 . The very great number of stars that have been discovered to be double, 

 triple, &c. particularly by Mr. Herschel, if we apply the doctrine of chances, as 

 was done in Mr. M.'s " Inquiry into the probable Parallax, &c. of the Fixed 

 Stars," published in the Philos. Trans, for 1767, (abridg. vol. 12, p. 423,) can- 

 not leave a doubt with any one, who is properly aware of the force of those argu- 

 ments, that by far the greatest part, if not all of them, are systems of stars so 

 near to each other, as probably to be liable to be affected sensibly by their 

 mutual gravitation; and it is therefore not unlikely, that the periods of the 

 revolutions of some of these about their principles (the smaller ones being, on 

 this hypothesis, to be considered as satellites to the others) may some time or 

 other be discovered. 



2. Now, the apparent diameter of any central body, round which any other 

 body revolves, together with their apparent distance from each other, and the 



VOL. XV. 3 O 



