488 



SCIENCH. 



[Vol. I., No. 17. 



unhappily, died slaortly after the end of the jour- 

 ney from the effects of exposure. There is a 

 provoking lack of appreciation of geographical 

 form, and a want of understanding of geologi- 

 cal structure, that deprives the observations of 

 much value ; and the pen-drawings that illus- 

 trate the book in good number are extremely 

 rough. Perseverance and euergj' are, how- 

 ever, apparent enough in the success of the 

 expedition ; and the itinerary notes as to roads, 

 supplies, and water, have a great value forthose 

 who may have to repeat the author's journej' 

 in this desert country. The partj- entered 

 from the southern coast at Gwadar ; and, after 

 traversing for some two hundred miles a barren 

 region of flat valleys or plains abruptlj' broken 

 bj' mountain ranges, thej' reached the desert 

 interior basin, into whose depressions the 

 Mashkel flows from the south ; the Halmand and 

 others, from the north-east and north ; and 

 several smaller temporary streams, from the 

 surrounding or dividing ranges, forming salt 

 plains or marshes (hamun) at the lowest points. 

 This district is absolutelj' barren, and verj' flat, 

 broken only by sand-ridges, or occasional rockj' 

 peaks that rise like islands over the level plain. 

 The largest central depression, known as the 

 God-i-zirreh, is a drj' salt waste about seventy 

 miles long east and west, and twenty miles 

 wide, surrounded bj' a barren sandj' desert ; 

 and the passage across the southern margin of 

 this desolate tract, hitherto unexplored, to a 

 point named Shah Godar, exposed the explo- 

 rers to great hardships . Water was found there 

 onlj' bj' digging in the sand of a dry stream- 

 channel (175-185). This was their farthest 

 station ; and from it thej' returned eastward to 

 Jacobabad, in Sind. The jjeople were found 

 avaricious and untrustworthy' : their towns 



were of the most forlorn description. The 

 difficulty of learning local names was not small. 

 The instructions' given bj' a local official to a 

 guide who was to accompany Maegregor were 

 overheard b^- him : ' This sahib will ask j-ou 

 the name of everj' hill, everj^ river, and every 

 hut you see.' — ' What for? ' — ' Heaven oulj^ 

 knows ! These sahibs alwaj^s do that : they ask 

 the name of everj' thing, and then write it 

 down. ' — ' But how am 1 to name all the hills ? ' 

 — ' Call them anj- thing j'ou like, and he will 

 write it.' It seems, that while the people have 

 names for the ravines that thej' follow, and for 

 the stopping-places on them, thej^ generally 

 have no names for hills and ranges ; nor have 

 they anj' idea of the connection of mountains 

 with each other, or of anj- system of drainage. 

 Sand-hills are verj' numerous on the deserts ; 

 and, on the plain north of the Mashkel hamun, 

 a peculiar form was noticed, provoking one 

 of the few pieces of careful description in 

 the book (p. 157). The examples were very 

 numerous, and all closelj' alike ; their form was 

 crescentic, and the largest were sixty feet high 

 at the middle of the curve, descending to the 

 general level at the horns ; the outer slope is 

 30°, and the inner 45° with a still steeper 

 inclination at the outer side of the top of the 

 ridge ; thej' stand on a perfectl}- level plain, 

 with the curve to the north or windward, and 

 horns to the south. One would ' afl^brd co\-er 

 enough for a regiment or two.' The author 

 imagines that some obstruction like a bush 

 formed the nucleus about which the sand origi- 

 nally gathered. ■ A sketch-map accompanies 

 the volume ; but there is often an unfortunate 

 disagreement in spelling between it and the 

 text. Table of contents and index are 

 lacking. 



WEEKLY SUMMARY OF THE PE OGRESS OF SCIENCE. 



MATHEMATICS. 



Strain of an isotropic solid. — Mr. Stearn has 

 given a very brief method for obtaining the ex- 

 pression for the internal energy per unit volume 

 of a strained isotropic solid. — (Quart, j own. math., 

 Feb. ) T. c. [967 



Elliptic functions. — Mr. Glaisher has given a 

 series of integrals of functions depending upon elliptic 

 functions. The paper is of such a character that it 

 is impossible, in this place, to do more than refer to 

 it. It may, liowever, be remarked that the set of 

 integrals obtained constitutes a valuable addition to 

 the known elliptic function formulae. A continua- 

 tion of the investigations may be inferred from tbe 

 manner in whicli the autlior has introduced the pres- 

 ent article. — (Quart, journ. viath., Feb.) T. c. [968 



Spherical triangle. — Professor W. W. Johnson 



remarks, that in the proof of the addition theorem 

 in elliptic functions by means of a spherical triangle 

 whose sides are ^, V, and /U, where ip = am u,ip = am v, 

 /i = am («. -t- v), and k is the ratio of the sines of the 

 angles to the sines of tlie opposite sides, it is usual 

 to state that the angle opposite to tlie side ," is ob- 

 tuse, so that its cosine is — A|U, if tlie other angles are 

 acute, so that their cosines are A^ and Aip. This may 

 be shown to be a consequence of the assumption 

 that k is less than tinity. The present note aims to 

 show that the restriction, k < 1, may be removed, in 

 accordance with which A/i is always positive ; proving 

 directly, that, in all cases, the cosine of tlie angle in 

 question is —A/i. It is further shown, in orfler to 

 complete the proof, that the triangle from whicli the 

 formulae are derived is possible for all real values 

 of u and «, as well as k. — (Quart, journ. math., Feb.) 

 T. c. [969 



