Ml 



IRRIGATION. 



IRRIGATION. 



HI 



By trial (or by semi-tentative methods, described in many older books 

 of algebra) itjnay be found that a cube root of -10 + 9</3 V~l > 

 i + VsV-T: whenoer-2, o= >/' Hence one root (2 r) is 4 ; the 

 woood and third (-r + o V 3 and -F-o >/),> -2 + 3and -2-3, 

 or 1 and -5. 



But the beat method of obtaining the roots is by having recourse to 

 a registry of the roots of cubic equations which is in the hands of every 

 tyro, namely, the table* of sines and cosines, by which also the theorem 

 of Bombelli will be eetabliahed, namely, that the difficulty of the irre- 

 ducible case answers to that of the trisectiun of an angle in geometry. 

 It is proposed then, by means of trigonometry, to calculate the values 

 of(3). Assume v = r cos. t, w=rsin.8, or find rand 8 from 



tan.8=- 



in which that sign must be given to r, which gives r cos. 8 the sign 

 of v. Then, by De Moivre's theorem [NEGATIVE AND IMPOSSIBLE 

 QUANTITIES], 



(cos. 8 + sin. 8 V~)'=cos. J 8 sin. J8 V 3 ^" 



in which, by substituting 8 + 860 or 8 + 720 for 8, the equation tan. 

 8 = v-f-w is still satisfied, and while the first side of the preceding 

 equation is not altered in appearance, the different values of the cube 

 root appear on the second side. From this we readily find that the 

 expression (8) is no other than 2 V r . cos. $8 ; the three values of which, 

 obtained as just noted, are 



2 Vr.cos. J8, 2 V- . coe. (120+J8), 2 tyr . cos. 240 + \ 8) 

 which may be thus written : 



2 */r . cos. J8,-2Vr . cos. (60-J8),-2Vr . cos. (60 + J.) 



Thus, in the preceding example, which gives v = 10, w = 9 V", we 

 find r = 100 + 243 = 343=7*; whence ljr= - V7- And tan. 8= -ft 

 V3, whence 8 is found to be (57 19' 16"), one-third of which is 

 -(19 C' 25"), and this, with 79 6' 25" and 40 53' 35", are the angles 

 on which the required values depend. The cosines of these angles, 

 severally multiplied by 2 V7, 2 V7, and 2 v/7 , give results as near to 

 5, 1, and 4 (the values found), as the unavoidable errors in the last 

 places of logarithmic results, and the preceding rejection of fractions of 

 seconds, will permit. 



IRRIGATION. Of all the substances which concur in the vegetation 

 and growth of plants water is the most essential ; without moisture 

 the seed cannot germinate, nor can the plant receive nourishment. 

 Hence in warm climates, where rains are periodical, and where the 

 soil is dried and parched by a continued evaporation, no verdure exists, 

 except where springs or rivers supply the waste of moisture. The 

 wanner the climate, and the more rapid the evaporation, the more 

 luxuriant is the vegetation, provided there be an abundant supply of 

 water. This circumstance has suggested the plan of diverting streams 

 and conducting them in channels to fertilise as great an extent of land 

 as possible. In China and in India, as well as in Egypt, ingenious 

 modes of watering lands have been adopted from the most remote ages. 

 No expense hss been thought too great to secure a supply of water, 

 and to distribute it in the most advantageous manner. It seems that 

 where there is great heat in the air, water alone will supply the neces- 

 sary food for the growth of plants. It is probable that the component 

 parts of the atmosphere are more easily separated, and made to enter 

 into new combinations with those of water, in a high temperature than 

 in a lower ; or that the leaves and green parts of vegetable? imbibe 

 water in a state of solution in air, and in this state it is more easily 

 decomposed. Atmospheric air and water contain all the principal 

 elements of vegetables, namely, oxygen, hydrogen, carbon, and nitrogen ; 

 the remainder are cither found in the soil or diffused through the 

 water. 



Water has also an imjwrtant office to perform, if we admit the prin- 

 ciple discovered by Macaire, that plant* reject through their roots 

 those portions of the sap which are the residue of its elaboration, and 

 which are of no further use to the plant, but rather injurious if they 

 are again imbibed by the root*. Plants may perhaps require a removal 

 of their excrement!, as tiimU do when tied up in stalls, or confined 

 in a small space ; and the percolation of water through the soil may be 

 the means which nature has provided for this purpose. Hence we can 

 readily suppose that the mere washing of the roots has a In 

 effect, and to this in a great measure must be ascribed the fertilising 

 fleets of pure and soft running water. But besides this washing of 

 rooU, there is the constant feeding of them, which is the more probable 

 explanation of the fertilising influence of that constant current of 

 water among them which is produced in drained and in irrigated land. 



If water stagnates and is evaporated, and the noxious matter held in 

 solution remains in the soil, all the advantage of irrigation is lost, and 

 the better kinds of grasses are succeeded by rushes and coarse aquatic 

 plants, as may be seen in all manihy spots. The circulation of the 

 water therefore appears to be as necessary as its presence ; and, pro- 

 Tided there be a sufficient supply of water of a proper quality, the 

 more porous is the soil, and especially the subsoil, the more vigorous 

 is the vegetation. It is on this principle alone that we can rationally 



account for the great advantage of irrigation in those climates where 

 rain is abundant, and where the soil, which is most benefited by having 

 a supply of water running through it, is of a nature to require artificial 

 draining as an indispensable preliminary to being made fertile by 

 irrigation. By keeping these principles in view great light will be 

 thrown on the practical part of irrigation, which, having been long 

 established by experience before these principles were thought of, 

 dejwnda not on their correctness, but only confirms their truth. 



The whole art of irrigation may be deduced from two dimple 

 rules, which are, first, to give a sufficient supply of water during all 

 the time the plants are growing, and secondly, never to allow it 

 to accumulate so long as to stagnate. We shall see hereafter 

 one apparent exception to this last rule, but it will be readily 

 explained. 



The supply of water must come from natural lakes and rivers, or 

 from artificial wells and ponds, in which it is collected in sufficient 

 quantity to disperse it over a certain surface. As the water must flow 

 over the land, or in channels through it, the supply must be above the 

 level of the land to be irrigated. This is generally the principal object 

 to be considered. If no water can be conducted to a reservoir above 

 the level of the land, it cannot be irrigated. But there must also 

 be a ready exit for the water, and therefore the land must not be so 

 low as the natural level of the common receptacle of the waters, 

 whether it be a lake or the sea, to which they run. The taking of 

 the level is therefore the first step towards an attempt to irrigate any 

 lands. 



Along the banks of running streams nature points out the declivity. 

 A channel, which receives the water at a point higher than that to 

 which the river flows; may be dug with a much smaller declivity than 

 that of the bed of the river, and made to carry the water much higher 

 than the natural banks. It may thence be distributed so as to descend 

 slowly and water a considerable extent of ground in its way to rejoin 

 the stream. This is by far the most common mode of irrigation ; and 

 the shape, size, and direction of the channels are regulated by the 

 nature of the surface and other circumstances, which vary in almost 

 every situation. A few examples will give to those who are not 

 acquainted with the best modes of irrigating land a pretty accurate 

 notion of the system. 



We shall suppose a river to run with a rapid current between high 

 banks. At some point of its course a portion of the water is diverted 

 into a canal dug along the bank, with a very small declivity. The 

 water in this canal will flow with less rapidity than the river, keeping 

 nearly the same level as that part of the river where it has its origin. 

 Thus the water may be carried over lands which are situated con- 

 siderably above the bed of the river farther down. All the lauds 

 between this canal and the river may be irrigated if there is a suftirinit 

 supply of water. The canal may be carried to a considerable distance 

 from the river. The size of the canal and its declivity depend on the 

 quantity of water which may be made to flow into it. A dam is often 

 constructed across a river, in order that as much of its water as is 

 possible may be diverted, and the original channel is often laid quite 

 dry, to take advantage of all the water at the time when it is 

 advantageous to irrigate the land. To have an entire command of the 

 water there ore flood-gates on the main channel and on the leaser 

 branches. By opening or shutting these the water may be stopped or 

 made to flow as may be required. It must be remembered, that to 

 carry water to a considerable distance, and in great quantity, a larger 

 channel and more rapid declivity are required ; and it is a matter of 

 calculation whether it is most advantageous to bring a smaller quantity 

 to a higher point, or a greater abundance somewhat lower. Having a 

 certain command of water, it may be carried from the main channel by 

 smaller branches to different points, so as to irrigate the whole equally. 

 These branches should be nearly horizontal, that the water may over- 

 flow the sides of them, and be equally distributed over the land 

 immediately below. Every branch which brings water over the land 

 should have a corresponding channel below to carry it off; for the 

 water must never be allowed to stop and stagnate. When it bos run 

 15 or 20 feet, according to the declivity, over the land situated below 

 the feeder, or the channel which brings the Water, it should be col- 

 lected into a drain to be carried off, unless it can be used to irrigate 

 lands which lie still lower. Finally it runs back into the river from 

 which it was taken, at a lower point of its course. 



When there is a considerable fall and a sufficient supply of water, a 

 series of channels may be made, so situated below each other, that the 

 second collects the water which the first has supplied, and in its turn 

 becomes a feeder to irrigate the lower parts of the declivity : a third 

 channel receives the water and distributee it lower down, until the 

 last pours it into the river. This is called catch mirk, because the 

 water is caught from one channel to another. This method is only 

 appliraMc where there is a considerable fall of water and a 

 declivity towards the river. But it must be borne in mind that the 

 water is deteriorated for the purpose of irrigation, when it has passed 

 over the land, and that it is not advantageous to let it flow over * 

 great extent when a fresh supply can be obtained : but where only a 

 small portion of water can be commanded, that must be made the most 

 of ; and it will irrigate three or four portions of land in succession 

 without there being any rery marked difference in the effect : beyond 

 this it rapidly loses its fertilising qualities. This is not owing to the 



