642 



SCIENCE, 



[N. S. YoL. IX. No. 221. 



read with profit by thousands, for it states 

 that " to find the great-circle courses from 

 the azimuth tables you have only to regard 

 the latitude of the port bound to as declina- 

 tion, and the difierence of longitude, turned 

 into time, as the hour-angle. The latitude 

 of the ship you take from the top of the page 

 as usual. ' ' But the author goes on to remark 

 that, as Burwood's solar azimuth tables ex- 

 tend only to twenty-three degrees of decli- 

 nation, this ready-made method is only ap- 

 plicable when the place of destination is 

 within the tropics. 



It may be of value, therefore, to point out 

 that the solar-azimuth tables are universally 

 applicable for finding great-circle courses, 

 because all great circles pass into the trop- 

 ics, and, if the problem of finding the 

 courses is with reference to a great-circle 

 track between a point of departure and a 

 point of destination, both lying outside of 

 the tropics, it is only necessary to find a 

 point lying on the prolongation of the 

 great-circle arc beyond the point of actual 

 destination and within the tropics, and treat 

 this point as the place of destination in 

 finding the courses. 



The longitude of the selected point within 

 the tropics may be found without any cal- 

 culation by simply prolonging the straight 

 line representing the great circle upon a 

 gnomonic chart. By this combination of 

 the gnomonic chart and the azimuth tables 

 the courses upon a great circle track may 

 be determined with very great facility. 



To illustrate, take the problem of finding 

 the initial course on a voyage by the great 

 circle route from Bergen, in latitude 60° N. 

 and longitude 5° E. , to the Strait of Belle 

 Isle, in latitude 52° 1' 2" N. and longitude 

 55° W. On a copy of a gnomonic chart, 

 such as Godfray's, draw a straight line 

 between the geographical positions above 

 stated and extend it beyond the latter into 

 the tropics. It will be found to intersect 

 the 20th degree parallel of latitude in longi- 



tude 90° W., or 95° from the meridian of 

 the point of departure. Entering the azi- 

 muth table at latitude 60°, under declina- 

 tion 20°, and opposite hour-angle 95° or 

 6h. 20m., we find the required course to be 

 N. 75° 31' W. 



G. W. LiTTLEHALES. 



SOME NEW AMERICAN FOSSIL FISSES.* 



The following new occurrences of fossil 

 fishes were reported : (1) A species of 

 Cladodns, scarcely distinguishable from C. 

 striatus Ag. in the Gorniferous Limestone of 

 Ohio. (2) TJielodus-like scales from same 

 horizon. (3) A pair of naturally associated 

 pectoral spines of Macluer acanthus from the 

 Hamilton, near Buffalo, ]Sr. Y. (4) A pty- 

 chopterygian pectoral fin from Naples Shale 

 of the same locality. (5) Two new species 

 of Diplodus from Upper Devonian near Chi- 

 cago, 111. (6) Teeth of Phcebodus from 

 Keokuk Limestone of Iowa and Permian 

 of Nebraska. (7) Largest known spine of 

 Stethacanthus (length over 35 cm.) from 

 Keokuk Group, Iowa. (8) A complete 

 fin, spines and shagreen scales of a 

 new and very large species of Acanthodes, a 

 genus not hitherto met with in the United 

 States, from Coal Measures of Mazon Creek, 

 111. (9) PhoUdophorus americmius sp. now., 

 also belonging to a genus new to this coun- 

 try, founded on very perfect material dis- 

 covered by N. H. Darton, of the U. S. 

 Geological Survey, in the Jura of the Black 

 Hills, South Dakota. 



Photographs of the new Jurassic fishes 

 were exhibited and their specific characters 

 summarized as follows : Gracefully fusi- 

 form, upwards of 15 cm. long, the head 

 forming about one-fourth the total length 

 and slightly less than maximum depth of 

 trunk ; dorsal arising behind pelvic fins ; 

 scales not serrated, thin, smooth, nearly 

 rhomboidal, overlapping; flank series not 



* Abstract of a paper read before the Boston So- 

 ciety of Natural History, March 15, 1899. 



