548 



NATURE 



{April 6, 1893 



The lines whose focus is Pj are curves of equal latitude, and those 

 whose focus is Sj are Sumner lines. Suppose systems of both 

 kinds of lines to be drawn, the figure will be divided into small 

 quadrilaterals, and the eye, aided by a scale with small divisions, 

 would approximately determine the point within any quadri- 

 lateral at which the values of c and s are given, intermediate 

 between those of the bounding sides. It is difficult to estimate 

 the error to which this determination would be liable, but sup- 

 posing the linear dimensions of a quadrilateral at a distance of 

 10 inches from Pj were comparable with the tenth of an inch 

 and that an error of one-hundreth of an inch were committed in 

 the direction -L'' to PiZj, this would mean an error of 3 or 4 

 minutes in the measured value of the hour angle. This error 

 would be important, but not large enough to condemn the 

 method, and the estimate shows that the scale of the diagram 

 should be as large as is practicable. 



If we confine the diagram to points in north latitudes c may 

 be taken to range between 30° and 90°, though it would ob- 

 viously be desirable also to draw a few lines for which c is 

 >90°. The range of 2 may be taken between 10° and 80°. 

 The distance between the foci is, as we have seen, tan \ p and 

 the distance between the directrices is readily proved to be 

 cot \p. The consideration which determines the scale on which 

 the curves should be drawn is that the Sumner for which 2 = 80° 

 should appear in the diagram as far as it may be required. 



The curves in each diagram are different from those 

 in every other for different values of p ; for although 

 it might at first appear that since the distance from 

 the focus to the directrix is the same for 180° - / as 

 it is for p some saving would be effected, the indications of 

 the same curves in the two cases are different, and the Sumners 

 are placed differently in regard to the parallels of latitude. In 

 the case of the sun a diagram for every ten minutes change in 

 declination would probably be necessary, and this would mean 

 an enormous amount of work. Diagrams for a few of the 

 best stars could, however, be constructed on this principle and 

 would be extremely useful. 



It will have been noticed that the angle Z^SiPj is equal to the 

 angle ZSP in the spherical figure, but the azimuth is not repre- 

 sented in the plane figure. The following properties of the 

 plane curves may therefore be stated : — 



(i) The angle at which SiZj cuts the sumner at Z^ is equal to 

 the angle at which P^Zj cuts the parallel of latitude. 



(2) If a tangent at Z^ be drawn to either curve, say the 

 sumner, to cut S^P^ in T and perpendiculars be drawn from T to 

 ZjPi, ZiSj meetmg them in M and N, then 



cos (azimuth) = q: 



TM 

 TN 



according as T falls between Sj and Pj or not. From this result 

 a graphical determination of the azimuth is easily obtained. 



4. If we take ZjPj for base line the curves to be drawn are 

 curves of altitude and polar distance. This method of represen- 

 tation is tempting as the angles at Pj and Z^ are then the hour 

 angle and azimuth. Moreover it would be a very convenient 

 way of producing the diagrams to arrange them for consecutive 

 values of the colatitude. Unfortunately there are serious objec- 

 tions. Suppose the common directrix of the polar distance lines 

 cuts PjZi produced in X, then when the sun is in the southern 

 hemisphere these lines are hyperbolas on the remote side of the 

 directrix from Pj and they diverge rapidly for consecutive values 

 of/ > 90° ; so much so that, when the colatitude is between 30° 

 and 40°, it is impossible to represent them on a scale which would 

 be of any value. For places in the tropics there would not be 

 the same objection, and diagrams drawn on this principle would 

 be convenient in those regions. 



There is another difficulty. In winter, in northern latitudes, 

 the azimuth and hour angle may be together greater than 

 two right angles or, what is equivalent, p + z may be >i8o°. 

 In that case the construction we are going upon fails, although 

 it is possible to meet the difficulty. 



The point is interesting, and admits of the following explana- 

 tion : — In the figure P is the north pole, Z the place of observa- 

 tion, AB the diurnal path of the sun. If C be the middle point 

 of PZ, then all points above the plane through the centre O 

 perpendicular to OC may appear in the plane diagram supposed 

 large enough. Again a plane KL perpendicular to OZ corres- 

 ponding to a = 80° limits the area in which observations may be 

 taken. If, therefore, the sun were observed between F and G 



NO. 1223. VOL. 47] 



he would be out of the diagram, and this means that p + e 

 >i8o°. 



The difficulty may be overcome by solving graphically another 

 triangle Sj^P^Z^ corresponding to S^PZ in the spherical figure 

 where S^ is diametrically opposite to S. For, if SZP-t-SPZ 

 > 180° then S^PZ-fS^PZ< 180°. Hence, if we interchange 

 Zj and Pj in the diagram 'and pick out the intersection of the 

 curves 180° -2 and 180°-/ we shall thereby find graphically the 

 supplements of the hour angle and azimuth. 



5. To these modes of representation may be added stereo- 

 graphic projection on the plane of the equator which admits of 

 lines of equal latitude and Sumner lines being represented by 



systems of circles and of two angles of the spherical triangle 

 being represented in the corresponding plane figure. 



6. The object of all such methods is to facilitate the drawing 

 of lines of position on a Mercator's chart, and as the hour angle 

 must be determined with the greatest possible precision, the 

 diagram should be on a large scale with hour angle lines drawn 

 upon it at suitable intervals. 



With this in mind the most practical of the foregoing methods 

 would seem to be the first, viz. that in which there is a single 

 diagram, cut into sections, not necessarily on the same scale, but 

 large enough to admit of the hour angle lines and perhaps alsfi 

 azimuth lines being drawn upon it. 



ANTHROPOLOGICAL USES OF THE CAMERA. 



A N interesting paper on the anthropological uses of the 

 "^ camera was lately read by Mr. E. F. im Thurn before 

 the Anthropological Institute of Great Britain and Ireland, 

 and is now reprinted in the Institute's "Journal." 



Mr. im Thurn points out that primitive phases of life are fast 

 fading from the world in this age of restless travel and explora- 

 tion, and urges that it should be recognised as almost the duty 

 of educated travellers in the less known parts of the world to 

 put on permanent record, before it is too late, such of these 

 phases as they may observe. It is certainly, however, he says, 

 not a sufficiently recognised fact that such records, usually made 

 in writing, might be infinitely helped out by the camera. 



As illustrating the small use of the camera for this special pur- 

 pose, Mr. im Thurn calls attention to the almost universal bad- 

 ness of illustrations of living primitive folk in books of anthro- 

 pology and travel, when these illustrations are not merely what 

 maybe called physiological pictures. Of old the book illus- 

 trator, if, as was usual, he was not himself the traveller, drew 

 as pictures of primitive folk, merely the men and women that 

 surrounded him, drew figures of men and women of his own 

 stage of civilisation, and merely added to these such salient 

 features as he was able, from the traveller's tales, to fancy that 

 his supposed primitive subjects had. So in 1599 the imaginative 

 artist of Nuremberg who drew the pictures for the rare Latin 

 abbreviation of Sir Walter Raleigh's " Disco verie of Guiana" 

 gave to the world his impressions of the "Amazons," the 

 "Headless Men," and the "Men who dwelt on trees" which 

 are typical of the pictures of "savages" which adorn the 

 travellers' books up to nearly the present century. 



Mr. im Thurn refers also to the beautifully executed illustra- 

 tions by Bartolozzi in Stedman's "Dutch Guiana," in which, 

 in place of natives, are shown, with the necessary change of 

 dress, simply Europeans of more than average beauty of form. 

 There were doubtless exceptions to the misrepresentation of 

 primitive folk, and the greatest of these exceptions known to 

 Mr. im Thurn is the beautiful series of drawings by Catlin of 

 North American Redmen. But Catlin enjoyed the unusual 

 advantage not only of considerable technical skill as an artist. 



