L C L C 765 single (or onefold) condition is a surface ; the locus of the points satisfying tvo conditions (or a twofold condition) is a curve in space, which is in general a twisted curve or curve of double curvature. LOCUST. In its general acceptation this term is strictly applicable only to certain insects of the order Orthoptera, family Acrydiidx (see INSECTS) ; and it is advisable to reiterate that according to modern classifica tion the family Locustidx is now viewed in a sense that does not admit of what are popularly termed " locusts " being included therein. We universally associate with the term the idea of a very destructive insect ; therefore many orthopterous species that cannot be considered true locusts have had the term applied to them ; in North America it has even embraced certain Hemiptera-IIomoptera, belonging to the C icadidx, and in some parts of England cockchafers are so designated. In a more narrow definition of the term we are wont to associate with the destructive propensities the attribute of migration, and it therefore becomes necessary that a true locust should be a migratory species of the family Acrydiidx. Moreover, the term has yet a slightly different signification as viewed from the Old or New World. In Europe by a locust is meant an insect of large size, the smaller allied species being ordinarily known as "grasshoppers," hence the notorious "llocky Mountain locust " of North America is to Eastern ideas rather a grasshopper than a locust. In Europe, and a greater part of the Old World, the best known migratory locust is that which is scientifically termed Pachytylus migratorius, to which is attached an allied (but apparently distinct) species known as P. cmerascens. Another locust found in Europe and neigh bouring districts is Ccdoptenus italicus, and still another, Acrydium peregrinum, has once or twice occurred in Europe (even in England in 1869), though it can only be considered a straggler, its home (even in a migratory sense) being more properly Africa and Asia. These practically include all the locusts of the Old World, though a migra tory species of South Africa known as Pachytylus pardcdinus (presumed to be distinct from P. migratorins) should be mentioned. The Rocky Mountain locust of North America is Ccdoptenus spretus, and in that continent there occurs an Acrydium (A. americanum) so closely allied to A. peregrinum as to be scarcely distinct therefrom, though there it does not manifest migratory tendencies. In the West Indies and Central America the absolutely true A. 2^regrimim is also reported to occur. As to general biology, a few words will suffice. The females excavate holes in the earth in which the eggs are deposited regularly arranged in a long cylindrical mass en veloped in a glutinous secretion. The young larvse hatch, and immediately commence their destructive career. As these insects are " hemimetabolic " (see INSECTS), there is no quiescent stage ; they go on increasing rapidly in size, and as they approach the perfect state the rudiments of the wings begin to appear. Naturally in this stage they are incapable of flight, but their locomotive powers are never theless otherwise extensive, and their capacity for mischief very considerable, for their voracity is great. Once winged and perfect these powers become infinitely more disastrous, redoubled by the development of the migratory instinct. The laws regulating this instinct are not yet perfectly understood. Food and temperature have a great deal to do with it, and there is a tendency for the flights to take a particular direction, varied by the physical circumstances of the breeding districts. So likewise it is certain that each species has its area of constant location in which it always exists, and its area of extraordinary migration to the extremes of which it only occasionally extends. Per haps the most feasible of the suggestions as to the causes of the migratory impulse is that locusts naturally breed in dry sandy districts in which food is scarce, and are thus impelled to wander in order to procure the necessaries of life ; but against this it has been argued that swarms bred in a highly productive district in which they have tem porarily settled will seek the barren home of their ancestors. Another ingenious suggestion is that migration is intimately connected with a dry condition of the atmosphere, urging them to move on until compelled to stop for food or procreative purposes. The distance particular swarms may travel depends upon a variety of circumstances, such as the strength of impulse, the quantity of food, and many other causes. Certain it is that 1000 miles may, in particular cases, be taken as a moderate estimate; probably it is often very much less, certainly sometimes very much more. As a rule the progress is only gradual, and this adds vastly to the devastating effects, which may be likened to those caused by a foreign army levying black-mail upon the inhabitants of an invaded country through which it is marching. When an extensive swarm temporarily settles in a district, all vegetation rapidly disappears, and then hunger urges them on another stage. Such is their voracity that it has been tolerably well ascertained that the large Old World species, although undoubtedly phytophagous, are often compelled by hunger to attack at least dry ani mal substances, and even cannibalism has been asserted as an outcome of the failure of all other kinds of food. The length of a single flight must depend upon circumstances. From certain individual peculiarities in the examples of Acrydium peregrinum that were taken in England in 1869, it has been asserted that they must of necessity have come direct by sea from the west coast of Africa ; and what is probably the same species has been seen in the Atlantic at least 1200 miles from land, in swarms completely covering the ship, and obscuring the air; thus, although it is no doubt usual for the swarms to rest during the night, it undoubtedly happens in certain cases that flight must be sustained for several days and nights together. The height at which swarms fly, when their horizontal course is not liable to be altered by mountains, has been very variously estimated at from 40 to 200 feet, or even in a particular case to 500 feet. A " dropping from the clouds " is a common expression used by observers when describing the apparition of a swarm. The extent of swarms, and the number of individuals in a swarm, are matters that must of necessity be purely speculative. That the sun may sometimes be utterly obscured, and the noise made hy the rustling of the wings be deafening, is confirmed by a multitude of observers. We prefer to decline the attempt to grapple with so vast a subject, not unnaturally so when one observer says of a particular swarm that, when driven out to sea and drowned, the dead bodies washed up formed a bank 50 miles long and 3 or 4 feet high. No special periodicity appears to have governed these flights (which, it is necessary to state, happily do not occur to an alarming extent every year), still an American writer (Mr Thomas) makes the interesting remark that the interim between the years of superlatively extra ordinary appearance is both in Europe and America "very nearly a multiple of 11." In Europe the best known and ordinarily most destructive species is Pachytylus migratorius (fig. 1), and it is to it that the numerous records of devastations in Europe mainly refer, but it is probably not less destructive in many parts of Africa and Asia. Eastern Europe, and especially the plains of southern Russia, appear to be more especi ally liable to its attacks. That the arid steppes of Central Asia are the home of this insect appears probable; still much on this point is enveloped in uncertainty. In any case the area of permanent dis tribution, according to Koppen (who published an elaborate memoir on the subject in 1871), is enormous, and that of occasional distri bution is still greater. The former area extends from the parallel of 40" N. in Portugal, rising to 48 in France and Switzerland, and
