334 JllathtmaikalandPhihfophkal Corrc'poiiScnce. 



Another metliod of obtaining the value of * is by means of a table of artificial fines, as 

 follows : — Let r be the logarithmic radius, a, b, and c the common logarithms of a, b, and f, 

 and d = r — I c. Find an artificial fine, and its correfpondent coGne, f and s, in the tables, 



fo that — — may be = , , each of which quantities will then be = x. The demon- 



(Iration becomes obvious by confidering, that if one of three quantities be equal to the fum 

 of the other two, their fquare-roots are the fides of a right-angled triangle. 



Noarly a fimilar anfwer was given to this queftion by Analyticus. 



NEW MATHEMATICAL QUESTIONS. 



Question XI. By TV. Simpson. 



IF H, t, be the heights of any two fignals above the horizon of an obfer^'er. A, the 

 angle which they fubtend, and a, the fame angle reduced to the plane of the horizon, then 

 ivill cof. A — cof. a X cof. H X cof. h + fine H X fine /;•. Required the demonftration. 



Question XII. By JF. C. of Gtamvich. 



ON the id of May 1797, the fun's declination being 15" 9', it was obferved that his 

 altitude, azimuth, and the latitude of the place were all equal. Required the hour and 

 place where the obfer»'ation was made. 



%* I SHOULD "be glacf to give a defcription and drawing of Mr. Varley's machine 

 for producing perpetual motion, as requeft'cd by Mr. Notlcm of VVifbech, if an attentive 

 jjerufal of the fpecification enrolled in Cliancery had flicwn me any thing tending to improve 

 the theory or prafticc of mechanics. The defcription in the periodical work he mentions 

 is not fufficlently clear to fhew the whole of what the writer meant to explain, and I found 

 the original equally imperfeft. Mr. Varley's notion, obfcured by fome extraneous and 

 unimportant circumftances, appears to be, that if an exhaufted cylinder be fixed to one 

 part of the periphery of a wheel, and a pillon fitted therein, the prefilire of the atmofphere 

 on this lad, fuppofed alfo to be attached to the wheel by a ijpring and chain 'parallel to a 

 tangent), will tend to drive it into the vacuum, and, if prevented by the fliortnefs of the 

 chain, will draw the wlieel round. It is obvious to any perfon moderately acquainted with 

 ftatics, that the prelRirts on his wheel muft counterbalance each otter, and cannot produce 

 motion. 



It has always been eafy to fliew the fallacy of fchemes for perpetual motiinn in tl\e par- 

 ticular inftances ; but I have met with no clear enunciation of this projeft fo ge"Ueral as to 

 include every poffible fchcmc, and evince its own abfurdity. The difficulty of performing 

 this fecms to arife from a want of direct and concife demonflrations of the fundamiNital 

 principle of the lever, and of the equal preflure of fluids in all dire^ons. 



6 ^ THE 



