THE IRRIGATION AGE. 



903 



consists of the base jr r plus the shell, which is a sector of 

 a circle having a radius / and spans an arc = 2 ^ r, hence : 



S = TT r 2 + r r I = v r (r + I.) 



Problem. Find the volume and surface of a right cir- 

 cular cone when h = 7 ft. and r = 2 it. 



w r"h 3.1416X2X2X7 

 Solution, I' = = = 29.321 cub. 



ft. ; for 5 first find / \/ r + hr = V 4 + 49 = V 33 = 

 7.283, then 5 = 3.1416 X 2 (2 + 7.283) = 58.327 sq. ft. 



The frustum of a cone will be handled like that of a 

 pyramid, thus for a right circular cone : when R and r are 

 the radius of the base and top and h the height : 



h 



V = (TT R- + TT r" + V IT R' X TT r), which can be 



3 

 simplified : 



F = (R"- + r + R r.) 



3 



Problem. Find volume of a frustum of a cone, if R =. 

 4 ft., r = 3 ft. and h = 5 ft. 

 5 X 3.1416 

 Solution. I' - -(5X5 + 3X3 + 5X3.) 



V = 



5X3.1416X49 

 = 256.564 cub. ft. 



3 



6. Sphere. 



A sphere is a solid, uniformly rounded so that each point 

 in the surface has the same distance from a point within 

 called the center ; the distance from center to surface is called 

 the radius. Every section made through a sphere forms a 

 circle ; when such a section passes through the center of the 

 sphere it is called a great circle having a radius = to radius 

 of sphere. The surface area of a sphere is equal to 4 times 

 a great circle, thus if r = radius of sphere, then 5 = 4 ^ r'. 

 The volume of the sphere may be considered as the sum 

 of myriads of cones having their bases in the surface of the 

 sphere and their vertices in its center, and as the volume 

 of a cone is equal to base times 1/3 of height the volume of 

 the sphere will be equal to the area of its surface multiplied 



r 4 

 by 1/3 of the radius, or V 4 r 2 X = IT r". 



3 3 



Example. Find the surface and volume of a sphere hav- 

 ing a radius of 8 ft. 



Solution. S = 4f* = 4X 3.1416 X 8 X 8 = 804.25 

 sq. ft. 



4*7* 4X3.1416X8X8X8 



V - - = 2144.94 cub. ft. 



3 3 



If ill a cylinder the height = 2 r, its cross section be- 

 comes a square, Fig. 54; a circle of the radius r could be 

 inscribed in it and represents the cross 

 section of a sphere of the radius r, and 

 the triangle shown represents a right 

 cone having the same base and height 

 as the cylinder ; the relation of the vol- 

 umes of these 3 bodies is as 1/3, 2/, 

 and 3/3, the cone being 1/3, the sphere 

 2/3 and the cylinder 3/3 of the whole, 



4 TT r" 



thus : Cylinder = 2 v r :i , sphere 



3 



Supreme Court Decisions 



Irrigation Cases 



Fig. 54 



2,r 



and the cone = - 

 3 



It is understood that work on the irrigation project 

 between Camp Crooks, South Dakota, and Alzada, Mont., 

 on the Little Missouri river, by which 20,000 acres of 

 desert land will be reclaimed, will be started this month. 



In the city of Chicago the government of the United 

 States has established an office in charge of a gentleman 

 of the name of Carpenter, whose business it is to furnish 

 information to anyone who desires to know something 

 of irrigated lands. The full address is here given: C. F. 

 Carpenter, Settlement Agent, U. S. Reclamation Service 

 802 Federal Building, Chicago. 



POINT OF DIVERSION 



Where defendant was entitled to take water from plain- 

 tiff s ditch for irrigating purposes, it was immaterial at what 

 point upon the ditch defendant chose to divert the water, 

 though, if he selected one poiat for diverting it, he could 

 not thereafter select another point. Red-Miter Land & Canal 

 Co. v. Jones. Supreme Court of South Dakota.. 130 North- 

 western 85. 

 APPROPRIATORS 



Nonuser by an upper proprietor or appropriator of water 

 is not available to strengthen a lower appropriator's claim by 

 prescription, where such lower appropriator is not a riparian 

 owner, but takes the water for use on nonriparian lands 

 Perry v. Calkins. Supreme Court of California 113 Paci- 

 fic 136. 

 APPROPRIATION 



The bona fide intention which is required of an appropria- 

 tor to apply water to some useful purpose may comprehend 

 a use to be made by or through another person, and upon 

 lands and possessions other than those of the appropriator. 

 Nevada Ditch Co. v. Canyon & Sand Hollow Ditch Co. 

 Supreme Court of Oregon. 114 Pacific 86. 

 TRESPASS ON IRRIGATION DITCH 



Where an abutting owner used land within a highway, 

 outside of the traveled portion, for the maintenance of irriga- 

 tion ditches in such a way as not to interfere with the public 

 use, any interference with such ditches by a third person con- 

 stituted a trespass. Holm v. Montgomery. Supreme Court 

 of Washington. 113 Pacific 1115. 

 ABANDONMENT OF WATER RIGHTS 



Where, to convey water of an appropriator, it was neces- 

 sary to construct and maintain a flume across a ravine, and 

 the flume broke down, the act of the appropriator in turning 

 water into a ditch from year to year to preserve his right, 

 and in subsequently conveying an interest therein, was ad- 

 missible to negative any intention to abandon his water rights 

 at the time the flume broke down, or subsequently. Feather- 

 man v. Hennessey. Supreme Court of Montana. 113 Paci- 

 fic 751. 

 PARTIES TO SUIT ON APPROPRIATION 



An appropriator of water from a stream is a proper 

 party to a suit affecting the right of appropriation of the 

 waters of such stream : but such person is not an indispensable 

 party, and a judgment rendered in said cause would be just 

 as effective as to the rights and interest of all those who 

 were parties to said action, as between themselves, and whose 

 rights have been adjudicated, as though such other person 

 had also been made a party. Fast v. Idaho Irrigation Co., 

 Limited. Supreme Court of Idaho. 114 Pacific 38. 

 PRESCRIPTIVE RIGHT TO OVERFLOW LAND OF ANOTHER 



To acquire a prescriptive right to overflow the land of 

 another, there must have been an uninterrupted enjoyment 

 under claim of right for five years, and there must have been 

 an actual occupation by the flow of water, to the knowledge 

 of the owner of the land, and such as to occasion damage 

 and give him a right of action, and there must have been 

 such a use of land and such damage as will raise a presump- 

 tion that he would not have submitted to it unless a right 

 existed. Galbreath v. Hopkins. Supreme Court of Califor- 

 nia. 113 Pacific 174. 

 TAXATION OF WATER RIGHTS 



Where an irrigation company which owned no land con- 

 tracted to sell the water rights therein to abutting owners 

 upon condition that, when all the rights were sold, the pur- 

 chasers would own the ditch, but sold only a part of the 

 water rights, those remaining were not appurtenant to land, 

 but were separate property, and taxable under Comp. St. 1010, 

 2330, providing that the property of companies constructing 

 or owning canals, ditches, or flumes shall be assessed. Wyom- 

 ing Central Irr. Co. v. Farlow County Treasurer. Supreme 

 Court of Wyoming. 114 Pacific 635. 

 ESTABLISHMENT OF IRRIGATION DISTRICTS 



Under the following provision of section 2377, Rev. Codes, 

 to wit : "No action shall be commenced or maintained, or 

 (Continued on page 006.) 



