VOL. IX.] PHILOSOPHICAL TRANSACTIONS. 18^ 



Divers Rural cmd Economical Inquiries, recommended to Observation and Trial. 



N° 111, p. 240. 



Of no use at the present time. 



Extract of a Letter of Dr. J. TVallis, to M. Hevelius, from Oxford, December 

 31, 1673; gratulatory for his Organographia ; and particularly concerning 

 Divisions by Diagonals, lately inserted in Mr. Hook's Animadversions on the 

 first Part of the Machina Ccelestis of Hevelius ; but so faultily there printed, 

 that it teas thought fit, at the Author s desire, to be here done more correctly. 

 Translated from the Latin. N° 111, p. 243. 



After returning thanks to M. Hevelius for the present of his book Organo- 

 graphia, or description of his astronomical apparatus, and some handsome com- 

 pliments in commendation of the book, the instruments, and of the ingenious 

 astronomical labours of the author. Dr. Wallis then adverts to some certain 

 parts of it, particularly the divisions on instruments by diagonals. Without 

 dwelling on particulars, says Dr. Wallis, I may yet briefly mention one thing, 

 viz. the divisions by diagonal lines, intersecting the concentric circles on the 

 limb of the instrument. You retain that method of dividing, long since used, 

 and very deservedly, and also those concentric circles disposed at equal distances 

 from each other. But although this might occasion certain small, and even 

 larger errors on broad limbs of instruments; yet in your instruments, which are 

 so large, and the limbs so narrow, as you justly observe, this cannot cause any 

 difference at all that can be sensible. 



On this occasion I shall here subjoin what formerly, about the year 165O or 

 1651, occurred to me on this matter; and which I now find among my 

 memorandums. Namely, if it be required thus to divide the broad limb of a 

 smaller instrument ; to determine by trigonometrical calculation, at what dis- 

 tances the concentric circles ought to be drawn, so that the angles may be equal 

 among themselves, which are determined by the transverse intersections with 

 those circles. 



The Division of the Arc on the Limh of a Quadrant, or other such like Instrument, 

 by Concentric Circles, and a right Diagonal Line. 



Let the breadth of the limb RL = / (fig. 6, pi. 7); the radius of the inner 

 circle AR = r ; that of the exterior AZ = AL = / -f- r = z; containing the 

 angle R AZ = A, to be divided into any number of equal parts, the number of 



late Dr. Black of Edinburgh, and among other ingredients was found to hold in solution siliceous 

 earth. 



