VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 133 



XXV 11. A General Theory for the Mensuration of the Angle subtended by Two 

 Objects, of which One is observed by Rays after Two Refections from Plane 

 Surfaces, and the other by Rays coming Directly to the Spectator's Eye. By 

 George Atwood, M. A., F. R. S. p. 3Q5. 



The actual determination of an angle implies 2 observations, one taken at each 

 extremity of the arc by which that angle is measured. When fixed astronomical 

 quadrants or other sectors are used for the practical estimation of angles, one of 

 these observations is previously made by directing the axis of the telescope or 

 line of collimation to some fixed point in the heavens, the index being then 

 coincident with the initial point on the arc of the sector: after this adjustment, 

 one observation only is necessary to ascertain the angular distance between that 

 point and any other celestial object in the plane of the sector. This method 

 however is evidently impracticable, unless the instrument can be steadily fixed ; 

 for which reason astronomical quadrants become useless at sea ; and from the 

 difficulties which attend placing them in their due position and adjustment on 

 firm ground, they are almost wholly confined to regular observatories. 



Mr. Hadley, by an ingenious application of optical principles, contrived to 

 bring both extremities of the arc measured into the field of the spectator's view 

 at the same time ; by which improvement, angles are taken at sea, as well as on 

 land, with an unfixed instrument, to a degree of accuracy sufficient for nautical 

 and other purposes, when the utmost exactness is not required. Mr. Hadley's 

 invention is a particular case of a very extensive theory, as yet but little attended 

 to. According to his method, which is well known, the 2 reflecting surfaces 

 used in the observation are perpendicular to the plane of motion ; the direction 



the author was convinced that evaporation had no share whatever in producing the remarkable cold 

 which was observed. The title of the paper is thus expressed : " Experiments and Observations on 

 a remarkable Cold which accompanies the separation of Hoar-frost from a Clear Air ;" and the fol- 

 lowing are the general conclusions which, in die author's opinion, the experiments establish : — 

 " That when bodies attract hoar-frost from a clear air, there is a cold produced at their surfaces ; and 

 that this cold does not originate from any peculiar qualities of bodies on which the hoar-frost settles, 

 any further than as some bodies are capable of attracting from die air more or less of it in a given 

 time.'' And again, " That the disposition of the air of thus parting with hoar-frost, and the cold 

 which accompanies that separation, has a constant dependance on die general serenity of the atmos- 

 phere, and is always interrupted on the sky being overcast with clouds or fogginess, especially near 

 the place of observation." 



After stating these conclusions, the audior observes : " That the nature or essence of the thing we 

 call heat is so far removed beyond die immediate reach of our senses, that we need not wonder, 

 though new facts relating to it come into view, and even though they cannot immediately be traced 

 up to any general laws hidierto established. That if, on mature consideration, the present phenomena 

 cannot be accounted for in this way, they ought, on that very account, to challenge our attention the 

 more, as opening to us die necessity of enlarging our stock of principles, and inviting us forward to 

 so desirable a work." 



