Oct. 1 8, 1883] 



NATURE 



599 



elevation. In like manner in defining the position of any one 

 piece of ornamentation in the vertical series it will not be suffi- 

 cient to say that it is at a certain angular distance from any one 

 point, say a door, because all the pieces in the same row are at 

 this angular distance from the door. But if these two methods 

 of stating position be combined, if the height above the ground 

 as well as the angular distance from the door be given, then a 

 definite statement may be made both of the position of the pane 

 of glass and the piece of ornamentation. Similarly with the 

 stars. Imagine a horizontal circle passing from north to south, 

 and thence to north again. A line from the zenith through any 

 body will cut this circle at some one point, and the number of 

 degrees included between that point and the north point will give 

 the angular distance from the north point, or, as it is called, the 

 azimuth. The whole of an imaginary line of bodies extending 

 from the zenith to the horizon will have the same azimuth (see 

 Fig. 3). In the same way we may imagine a whole ring of bodies 



Fig. 3. — Stars with equal altitudes and stars with equal azimuths. 



at the same height above the horizon, having the same altitude 

 (see Fig. 3), but a particular altitude and a particular azimuth 

 c in be true of only one of those bodies. It is in this way, then, 

 by a statement of the altitude and azimuth, that the position of a 

 star or other celestial body can be indicated with reference lo 

 any one particular place of observation and any one particular 

 instant of time. 



It is by thus dealing with this angular measurement that the 

 exact positions of the heavenly bodies have been determine'd. 



Fig. 4. — Tycho Brahe's altitude and azimuth instrument. 



This point has been discussed at some length, because in 

 making an historical survey it will be found, that the growth of 

 that particular knowledge of which we shall come to speak, has 

 been the growth of man's capability of getting finer and finer in 

 this angular measurement. To go back to the time of the old 

 Greeks, Hipparchus, one of the most eminent of ancient ob- 

 servers, even in his day could define the position of a heavenly 

 hody to v/i'.hin one-third of a degree. Since these 360 degrees 



into which circles are divided are each subdivided, first into 

 60 minutes, and each of these again into 60 seconds, the one- 

 third of a degree to which Hipparchus attained may be called 

 20 minutes of arc. 



Passing from his time to the middle ages, a most interesting 

 instrument then in use claims attention. Fig. 4 is a copy of a 

 photograph of the instrument. 



The model, from which the photograph has been taken, is an 

 exact copy of an instrument made by one of the most industrious 

 astronomers that ever lived, Tycho Brahe, and shows how, even 

 in the very beginning of this observational science, men got at a 

 very admirable way of making their observations, considering 

 the means they had at their disposal. First there was in this 

 instrument a quadrant of a circle (^ee Fig. 4), which served their 

 purpose just as well as a whole circle. Combined with this was 

 an arrangement somewhat resembling the "sights" on a modern 

 rifle. Remember this was before the days of telescopes. So 

 they started with these sights and a little pinhole, that they 

 might take a shot, as it were, at a heavenly body, putting the 

 eye near the pinhole, and seeing the heavenly body in a line with 

 the front sight. Then the instrument was provided with a 

 plumbline to show the vertical. This plumbline was so ar- 

 ranged that when the sight lay along it, a body in the zenith 

 would be observed, and an angle of 90 1 altitude recorded. With 

 the instrument thus set, any smaller altitude could be read along 

 the quadrant, according to the position of the line of sight 

 passing through the eye, the centre of the quadrant, and the 

 place of the heavenly body. 



To get azimuth they used a horizontal circle, shown at the 

 base, also divided into degrees and provided with a pointer. 

 By sweeping the instrument round until the azimuth was such 

 that the body was seen through the pinhole, and the altitude 

 was such that it was seen in a line with the front sight, they 

 fixed its position, as well as that instrument enabled it to 

 be done. Supposing that their circles were properly divided, it 

 was quite easy to determine a division as small as the quarter of 

 a degree. This would put Tycho Brahe in only a little better 

 position than Hipparchus. That is to say, from the time of the 

 Greeks until about the middle of the fifteenth century, the only 

 advance made with this angular measurement, was that a reading 

 of one-third was improved into a reading of one-fourth of a 

 degree. 



Another notable improvement and advance towards a finer 

 and more accurate measurement was made by Digges. He 

 introduced the diagonal scale, the principle of which is shown in 

 Fig. 5. The arrangement consists of a number of concentric 



Fig. 5. — Digges' diagonal scale. 



circles, in this case nine. The distance between the divisions of 

 the inner circle is 3 . From each of these divisions diagonal 

 lines are drawn to the outer circle in such a manner that the 

 diagonal cutting the first circle at 0° cuts the ninth circle at 3°. 

 That cutting the first circle at 3° cuts the outer circle at 6°. So 

 with the other diagonal lines. Consider the diagonal passing 

 from o" on the inner circle to 3° on the outer. If the pointer 

 cuts the scale at the former point, an observation of o* will have 

 been made ; if it cuts at the latter point, an observation of 3 will 

 have been made. But it may cut the scale at some intermediate 

 point Suppose it falls on the eighth of the nine concentric 

 circles, then the value of the observation will be 7/8ths of 3°. 

 Should the pointer fall half way between o" and 3", the reading 



