694 



DIALLING. 



Theory. Art of Shadows, (Lond. 1635); Leybourn, Dialling, 

 , *"""Y" W ' Plane, Concave, Convex, Projective, Reflective, Refrac- 

 tive, &c. (second edit. Lond. 1700, fol.) 



Among the writers of the last century, we have Don 

 Bedos de Celles, Gnomonique Pratique, (Bord. 1750, 

 in 8vo.) ; Gruber, Horographia trigonometria, (Prag. 

 1718); Rivard, Gnomonique, (Paris, 1742, in 8vo.) ; 

 Casbroni Horographia Universalis, (1730); Leadbetter, 

 Mechanic Dialling ; W. Jones, Instrumental Dialling ; 

 Emerson, Dialling, (1770, 8vo.) ; Hutton's Translation 

 of Montucla's Mathematical Recreations, vol. iii. (1803); 

 Dr Brewster's edition of Ferguson's Lectures. Writers 

 on the sun dials of the ancients, are Zuzzeri, Dun ant. 

 villa scopcrtu sub doso del Tusculo ed un antico orologio a 

 Sole tra le ruince delta ritrovato, (Venez. 174-6, in 4to.); 

 George Henri Martini, A treatise concerning the Sun 

 Dials of the ancients, (in German) ; and Ernesti De So- 

 lariis. Some have composed tables, in order to abridge 

 calculations on dialling. In this class of writers may 

 be reckoned Hyppolite Saladio, Tabulae Gnomonicae 

 una cum earum usu et fabrica, (Rom. 1617, in 4to.) ; 

 Dominico Lucchini, Tratenimenti mathematici, (Rom. 

 1630, in 4to.) ; Grov. Lud. Quadri, Tavali gnomoniche, 

 (Bol. 1733, in 4to.) ; the Prince CarafFe defla Roccella, 

 Exemplar horologium solarium civilium, (Mazzareni 

 1 686, an enormous folio.) 



The theory of dialling has sometimes been treated 

 as a branch of perspective, as by Sgravesand in his 

 Essai de Perspective, (Amst. 1711, in 8vo.) ; and Dr 

 Horsley in his Tracts on the Projection of the Sphere, 

 (Oxford, 1801, in 8vo.) The subject has also been 

 treated as a branch of Analysis by Kaestner in his Gno- 

 vionica Universalis Analytica, (1751, Lip. in 4to.) ; M. 

 M. Dionis du Sejour and Godin, in Recherches Gnomo- 

 mques les regradations desplanetes el les Eclipses du So- 

 leil, (Paris, 1761, in 8vo.) 



Of late, the French mathematicians have referred 

 the theory of dialling to what they call Descriptive Geo- 

 metry ; and in this way the subject has been treated 

 by Hachette in his Cours de geometrie descriptive ; Le- 

 francoisin Journal d'EcolePolytechnique IP Cahier; and 

 Berroyer in his Gnomonique ou theorie des cadrans sola- 

 ries, given among the additions to the second edition 

 of Biot's Astronomie Physique, torn. iii. 



In the following treatise, we shall, in general, explain 

 theprinciples of this theory, and the construction of dials, 

 in a manner strictly geometrical. As, however, there 

 may be some of our readers who wish to make dials, and 

 yet are not sufficiently skilled in geometry to compre- 

 hend fully the theory, we shall give practical rules for 

 delineating the most useful kinds, employing only the 

 common problems of elementary geometry. 



The General Principles of Dialling. 



General 1 9* The principles of astronomy teach us that the earth 



principles moves in an orbit about the sun, and completes a revo- 

 ef .falling, lution in a year ; while, at the same time, it revolves 

 uniformly from west to east on its axis, which, although 

 it changes its place, is yet always parallel to a fixed 

 imaginary line, called the axis of the world. By the 

 first of these motion.., the sun appears to move round 

 the heavens, completing a revolution in the course of a 

 year ; and by the second, the sun, and all the heavenly 

 bodies, have an apparent diurnal motion about the earth 

 from east to west. 



20. The motion of the earth in its orbit is not equa- 

 ble : and hence it happens, that the apparent motion 

 •f the sun in the heavens is not quite uniform : besides, 



the plane of that motion does not coincide with the Theory. 

 plane of the diurnal motion. On these two accounts, ^~-y~~~ 

 the apparent diurnal motion of the sun differs a little 

 from uniformity, as is particularly explained in Astro- 

 nomy, p. 652. 



21. In the theory of dialling, however, we are to 

 suppose that the sun's diurnal motion is always perfect- 

 ly uniform, and that it moves throughout the day in a 

 circle parallel to the equator ; but as neither of these 

 hypotheses is strictly true, the time of the day shewn 

 by a dial will in general differ from that shewn by an 

 accurate clock. However, the difference admits of ex- 

 act estimation, and tables have been calculated which 

 shew its amount for every day throughput the year. 

 See Astronomy, p. 653, 



22. In constructing dials, it is also usual to leave the 

 effect of refraction out of consideration ; its effect might 

 indeed be exactly appreciated, and tables formed by 

 which the time indicated by the dial might be correct- 

 ed ; or the dial might even be so constructed as to give 

 the time cleared from the error. But this would be a 

 degree of refinement which may very well be over- 

 looked in the practice of what, since the invention of 

 clocks and watches, is now little more than a scientific 

 recreation. 



23. If the earth's radius had any sensible proportion 

 to its distance from the sun, that ought to be taken in- 

 to account in the construction of dials. But the earth 

 is almost a mere point, as seen from the sun; and hence 

 it happens that the diurnal motion of the sun about 

 any line on the earth's surface, which is parallel to its 

 axis, may be accounted uniform, exactly as if it were 

 performed about the axis itself. 



24. To understand the nature of a dial, let vis sup- Plate 

 pose that eEF (Fig. 3.) is" a straight rod or wire, pa- ccxxvm, 

 rallel to the axis of the earth ; or which, if produced, F 'g' 3 * 

 would pass through the pole of the heavens ; and let 



us suppose that one of its extremities terminates at e 

 in a plane, abed having any position whatever. Let 

 us farther suppose, that the wire passes through E, the 

 centre of a circle ABCD, described on some solid sub- 

 stance, and that it is perpendicular to the plane of that 

 circle : Then, as the wire passes through the poles of 

 the heavens, the circle ABCD will be parallel to the 

 terrestrial equator, and it will be in the plane of the 

 equinoctial circle in the heavens, because on the earth's 

 surface any plane whatever, parallel to the equator, may 

 be considered as coincident with it, when produced to 

 the celestial sphere. 



Now, because the axis of the earth is perpendicular 

 to the plane of the circle which the sun appears to de- 

 scribe in the heavens by his diurnal motion, and passes 

 through its centre, and that the same is almost exactly 

 true of every line parallel to the earth's axis ; when 

 the circle ABCD is illuminated by the sun, the wire 

 EF will project a shadow upon it, which will revolve 

 about E as a centre, passing over equal arcs of the cir- 

 cumference in equal intervals of time. If, therefore, 

 we suppose the circumference of the circle to be divid- 

 ed into 24 equal parts, and the points of division to be 

 numbered 1, 2, 3, 4, &c. to 12, and again 1, 2, 3, 4, &c. 

 to 12, as in the figure, and the circle to have such a 

 position, that the shadow falls upon E 12 at noon; then, 

 at one o'clock, it will have the position E 1 ; at two 

 o'clock, it will have the position E2; at three, the 

 position E 3; and so on. In short, the hour of the day, 

 from sunrise to sunset, will be indicated by the sha- 

 dow, just as it is shewn upon a watch by the motion 

 of the hour hc'ind. And as we suppose the motion of 

 1 



