94 SECTIONAL ADDRESSES, 
canonical in field astronomy a few years ago are being rapidly displaced 
by new. The prismatic astrolabe is threatening to oust the theodolite ; 
and Mr. Reeves has retaliated by inventing a small attachment to the 
theodolite that does the work of the astrolabe to perfection, and makes 
a separate instrument unnecessary. Sound-ranging and flash-spotting 
may yet be turned to the arts of peace, and there is something suspiciously 
like the latter in the method proposed for connecting Egypt with Crete 
or Alaska with Siberia. Sound-ranging in air is perhaps not so likely to 
be useful to geographers as sound-ranging in water. But there is a post- 
War invention whose future is brilliant. Who would have dreamed in 
the Challenger that her modern counterpart, the Royal Research ship 
Discovery, would be equipped with deep-sounding gear on the method of 
echoes, that takes soundings in no time, or very nearly. It has become 
suddenly vastly more simple to measure the depth of the sea than the 
height of the land. There is much more sea than land, and a dispro- 
portionate part of it is very deep. Yet now for the first time we can 
begin to think of ocean contours drawn less by imagination and more by 
soundings in the new sense of the word. 
If there was twenty years ago one branch of cartography that seemed 
stereotyped and unlikely to develop, it was surely the subject of map 
projections—a subject with a large and rather unprofitable literature ; 
a science in which pure mathematics disported itself to the little advantage 
of maps; a science with a misleading title, since scarcely more than one 
of the useful projections is really a projection at all, the rest being only 
constructions ; a science in which guiding principles were hard to find. 
The most practically useful has always seemed to me the dictum of 
Sir Charles Close, that map-makers should draw the line at the root of 
minus one. The true geometrical projections had come down to us from 
antiquity, excepting that elegant small group of which the best known is 
the projection of Sir Henry James, which I think has been employed 
precisely once, by Sir Henry James himself. Mercator had constructed 
empirically in the sixteenth century the famous and much-abused projec- 
tion that Edmund Wright first put upon a strict mathematical foundation, 
though it could not be done neatly until Napier of Merchiston invented 
logarithms a few years later. Lambert had provided a whole galaxy of 
projections more than amply sufficient for the most adventurous atlas 
constructor, who nevertheless fought shy of them ; and in the middle of 
last century the Coast and Geodetic Survey popularised the useful and 
unambitious Polyconic, whose sad fate it is to be completely misrepresented 
in books that give figures—for they insist on showing as a world map what 
was especially designed for single sheets. The projections in common use 
were all, except Mercator, of little mathematical interest; and when 
exhibited, as they were, as isolated pieces of geometry, it was tedious, 
and hardly attempted, to compare their respective merits. 
But in recent years the subject has taken on a new aspect. Tissot, 
and Jordan, and especially A. EK. Young, have developed the expressions 
in infinite series—a process which sounds terrifying to those whose 
intelligences automatically shut up when they scent mathematics, but 
which is really an enormous simplification, because it reveals at once how 
much alike all these projections are in the first few terms, and precisely 
by how much they begin to diverge from one another when the sheet is 
