4S6 



NATURE 



[March 21, 1895 



It will be ncticedihit when 



i5>2(tan / ± tan S) sin i' cosec- ij', 

 the aboTe corsf uction fails, and .r may be then considered as 

 twice the abscissa of the point on the circle whose radius is 

 2{tan / T tan S) sin i' cosec" 15', 



By making a diagram on ruled paper, the distance between 

 the lines being taken as unit, the diBBcully of measuring x and k 

 is more or less overcome. 



A portion of such a diagram is represented in the annexed 

 6gure, c D being a portion of the curve 



V = tan -T sin i' cosec- 15' 

 described with c as origin, y being for convenience reckon ed 

 negatively 



As an example of its use. suppose it were required to find 

 the reduction for latitude 17' N., declination 9° S., and hour- 

 angle I2m. By using a pair of dividers the sum of the ordi- 

 nates of the curve c D corresponding to 9 and 17 is found to be 



7, and a radius vector of length 12 meets the circle of radius 7 

 at a point whose abscissa is 10. The required reduction is 

 therefore 10'. 



Again, i being now expressed in minutes of arc (5) and (6) 

 may be written 



h — - ^(tan / T tan 8) sin 1' cosec- 15' 

 60 



©■" 



an /T tan 8) sin i' cosec- 15'. 



So that h and i are the lengths of the arcs of a circle and its 

 involute respectively, corresponding to the angle at the centre 

 who5e circular measure is -jujfxt in the case of the Sun, and 

 I 035^", 60 in the case of the Moon. Now for the former body 

 T'will not in general exceed 20, and for the latter 38, so that 

 we may assume for graphical purposes that in the case of the 

 Sun tu is the number of degrees in an angle of circular measure 

 ?i»/6o, and in ihe case of the Moon iv it the number of degrees 

 in an angle of circular measure I '035zi//6o. 



Thus in both cases h is approximately the arc of a circle of 

 radius 



(Ian /^lan 8) sin I'cosec" 15' 

 intercepted between the diameter and the radios which makes 

 an angle w degrees with it. 



Having obtained h, x may he found as in the general case, or 

 by drawing a tangent to meet the involute, as in the figure. 



In the preceding example, suppose the .ship to be steaming 

 south 20 knots, the ileclination decreasing 160' per lom. Here 

 » 5B - 36- By laying off at an angle of 36°, the intercepted 



NO. 1325. VOL. 51] 



arc bd is found to be about 43, and by drawing the tangent at 

 * the intercepted arc of the involute is about I •3. The hour 

 angle and reduction for the maximum altitude are therefore 

 4m. -3 and i''3 respectively. 



The graphical method considered above will be found to 

 give results which, although approximate, are sufficiently 

 accurate for purposes of navigation ; in fact, il Ihe diagram 

 be constructed on a large scale, the reduction may be easily 

 obtained within fifteen seconds of the truth. 



H.M.S. Ha-j/ke, Mediterranean. J. White. 



Table of Elements. 



IN OROtH OP ATOMIC W»GMT^. 



20" 





c/ 



V 



W 



Argon and the Periodic Systenu. 



The annexed engraving is a copy, on a small .scale, of a large 

 diagram which I have used with advantage for some years in 

 dealing with Ihe periodic classi- 

 fication of the elements. It 

 may prove of some little interest 

 to your readers who are actively 

 discussing the probable position 

 of "argon," on the assumption 

 that this remarkable substance 

 is an element. 



To the left of the illustration 

 is a scale of equal parts, and 

 the dots indicate the atomic 

 weights of Ihe elements the sym- 

 bols of which are placed farther 

 to Ihe right. The latter are ar- 

 ranged in zig zag fashion so as 

 to exhibit the periodic rise and 

 fall in gercral properties, ob- 

 served in each set of seven 

 elements. A certain analogy 

 may be traced between these 

 periods and the loops into 

 which a suspended cord of 

 somewhat unequal weight can 

 be thrown when set in vibra- 

 tion. Each small loop pictures 

 for us a small period ; and, just 

 as Ihe alternate loops are those 

 which are in the same phase at 

 any given moment, so the alter- 

 nate periods of Ihe elements are 

 those between which Ihe closest 

 resemblances can be traced. 



The members of Mendeleef's 

 eighth group, or the " triplets," 

 as they are sometimes called, 

 viz. Fe, Ni, and Co, with atomic 

 weights from 56 to 59 : ku, Rh 

 and Pd, 102 to 106 : Os, Irand 

 I't, 191 to 195, seem to form 

 another system of elements 

 which — to pursue the analogy of 

 the vibr.iting cord — is related to 

 that of the other elements some- 

 what as a given note to its 

 octave. On carrying the eye 

 along Ihe curves it will be seen 

 that Ihe atomic weights of trip- 

 lets occur nearly opposite to the 

 points of maximum displacement 

 of three of the greater loops. 

 We know very little as yet about 

 the elements Ihe atomic weights 

 of which lie between 140 and 

 180, hence we cannot recognise 

 the triplets Ihe .atomic weights 

 of which should be near to 150; 

 and a similar remark applies to 

 the elements above 210. But 

 the distribution of the triplets 

 throughout Ihe whole of Ihe best- 

 known elements is so nearly 

 regular that it is diflicult to avoid 

 Ihe inference that Mrc/- elements 



should also be found in the symmetrical position between 19 

 and 23, i.e. between fluorine and sodium. And further, that 



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Tl. 



