OCTI IBEE 24, [918 



X. ITU RE 



'55 



numbers, bul Mi - to treal them as 



— ol hybrid varieties produced b; much natural 

 crossing, in the first instance between the 

 botanical spt < ies from « hit h 1 ultivated 



apple has arisen, and, later, between the varieties result- 

 ing from the earlier hybridisation. The main pro 

 is to deti 1 mine thi 



on ill'- resulting fruit-tree, and, in particular, wl 

 it is -imi>l\ 1n.1h.1ni1.il in nature and regulated by the 



morpholog) ol thi 1 system, or whethei there is a 



definite physiological influence, the nature of which 



ed l'\ the character of the seedling. If 



tin latter i- .1 factor, the problem is, ol course, 



lordinarih complicated, but there pened up 



possibiliti. • di velopments in the culture 



of fruit. Further work on this important subject will 

 be awaited with int< 



.•1 NEW GR 1/7//' METHOD IX N IUTH 1/ 

 [STRONOMY. 



AMU departure "I some little interest has been 

 ■i|\ taken in America in the publication b) 

 the United States Hydrographic Dep a new 



, or diagram, foi finding readilj bj 1 simple 

 graphii process houi angle 01 azimuth at sea. So fai 

 as azimuth is concerned, a diagram ol this nature, 

 known as Weir's \zimuth Diagram, has been in us.- 

 for mam years, bul in that cas< the hour angle is 

 madi datum, whereas in the new diagram 



the altitude takes the placi of houi angle a~ argu- 

 ment; and, as an altitude can be observed at sea with 

 much less trouble than houi I duced 



from chronometi 1 tim< , some labour is saved b\ its 

 substitution. 



Th. construction of the diagram, which is due to 

 tin inventivi Mr. G. V\ Littlehales, of the 



U.S. Hydrographic Department, is based upi 

 function of the angle very generally employed by 

 navigators, but not much known ..nNi.li- nautical 

 s, called th havi rsine. A formula very generalh 

 employed in spherical trigonometry for finding an 

 angle "I a triangli from thre< sides given is 

 , A sin ■ 

 2 sin 



lh. practical application ol this formula was ver; 

 much simplified about a centurj ago b} the intro- 

 duction into the nautical text-books ..1 a new table 

 which gave the value of the logarithm of thi square 

 of the sine of one-half the angle, and was then 

 called the "sine squan" table. A little later, since 



sin-' — = i(i - cos A) = i vets A, 



2 



the name of haversine, or half versine, suggested 

 itself for the new function of the angle, and as such 

 n i- generally know n to-da; 



The particular formula on which the diagram is 

 based was proposed about ten years since, and is as 

 follows : 



hav(a)=hav(£~f) + {hav(*+f)-hav(i5 -c)j hav A. 

 If the -ides h.c be regarded . a, A being 



variables, this expression takes the form 



■ that is, of the equation to a straight line. 



I hi- formula suggested to thi inventoi thi 

 of a square chart, with sides graduated according to 

 the values of a series of natural haversines, by means 

 of which, having given the altitude and declination 

 of a body and the latitude of place, hour angle and 

 azimuth might be found by simple inspei tion. Upon 

 such a chart, by drawing a stn through tw > 



Mi. 2556. VOL. I02" 



puims read i I) determined, a connection would be 

 established, in om ca een the hour angle and 



zenith distance, in the othei between azimuth and 

 polar distance, so that, om ol a pair being given, 

 the value of the other could bi tak. n approximatel) 

 from the chat t. 



/ he I riangle oj Position in ' ; ■ momy. 



lh. diagram which follows exhibits on thi plane 



of the hoi izon v hal i know n as thi " ti iangle of 

 position," in which 



IV., the co-latitude .... lal 

 PX, the polai distani 1 =90° ±de< 

 /.\ . the zenith distan 1 tit. 01 



ZPX, the houi angl : - JX 



PZX, thi azimuth '/.. 



The general formula adapted to this triangle gives 

 for hour angle 



hav c- hav (/ ~ < )=;hav i/ + i,i - hav {p~c)'i hav H, 

 the polar distance- |/>) and co-latitude (c) being con- 

 sidered as constants. 



The small diagram given below will perhaps servi 

 to explain the process adopted. The side is only 3 in. 

 in I. ngth, compared with 2 ft. in that issued for prac- 

 tical use. In the actual chart, again, a system of 

 "grillage," by means of lines drawn at short intervals 

 parallel to the sides of the chart, enables the value 

 of an angle to be read off to the fraction of a degree 

 at sight, whereas in the small diagram the graduations 

 of the sides an equal, and the points marked indicate 

 the angles corresponding with successive values of the 

 hayersines at intervals of 0-I2**. 



ti] 



&* £ = 



41*25' 60* 75*3l' 90* 104*29 120* 133*55 169* 

 (2"45"40') (4*) (5*2"4*) (6") (6"57*56*) (8*) {i't<Ci<f) (I2*) 



//.. n Angle mil/ Zenith Distance. 



Example i. At a place in lat. 6o°, when the sun is 

 on the equator, find zenith distance at 4I1. p.m., hour 

 angle at setting, and at the end of twilight. 



Rule.- On left-hand margin mark the point corre- 

 sponding with (p~c), t.r. of meridian zenith distance 

 at upper transit, and on right-hand margin the 

 poinl for (p+c), or meridian zenith distance at lower 



