THE IRRIGATION AGE. 



863 



can be cut into 5 triangles by diago- 

 nals and the area of the figure will 

 be the sum of the triangles. Another 

 method can be used, indicated by 

 dotted lines where the figure appears 

 ,j cut into 4 triangles and 3 trapezoids, 

 *' all right angled. The advantage of 

 the latter method is that the line AB 

 serves as height for all the figures, 

 and if the dimensions CC', DD', EE', 

 FF', GG', and the dimensions on AB 

 as AC, CD', D'E', E'B, BF', F'G' 

 and G'A are either given or observed, 

 CC'XAC 

 the area of the polygon = 



2 



CC'+DD' DD' + EE' EE' X BE' 



-f - -X CD' X - -X D'E' + - - + 



222 



BF' X FF' FF'+GG' AC' X GG' 



- X F'G' + - ; this can be 



22 2 



simplified as follows : 



Area = Y* [CC X AC" + CD' (CC 4- DD') + D'E' 

 (DD' + EE') + BE' X E'E + BF' X FF' + F'G' (FF' 4- 

 GG') 4- AG' X GG'.] 



4. Regular Polygons. A regular polygon is a figure in 

 which all the sides and all the angles are equal. The area of 

 a regular polygon is easily found by 

 cutting the same into triangles from 

 the center point. Thus in Fig. 43 

 the regular heptagon is divided into 

 7 equal triangles by connecting the 

 corners to the center O ; then each 

 360 



central angle = = 51 25' 43". 



7 



Draw OM perpendicular to AG; this 

 bisects central angle so angle AOM 

 = 25 42' 51.5" = say 25 43'; let 

 the side AG 12 ft., then AM = 

 h 



6 ft. ; let OM = h then = cotg 



6 



25 43', and h 6 cotg 25 43' = 6 X 2.0763 = 12.4578 ft; 

 area of triangle AOG 6 X 12.4578 = 74.7468 sq. ft, and 

 area of heptagon = 7 X 74.7468 = 523.2276 sq. ft. 



Supreme Court Decisions 



Irrigation Cases 



5. The Circle. The circumference of a circle is 3.1416 

 times the diameter or, if r is the radius 2 ^ r. If the circle 

 is considered a polygon with a very large number of sides, 

 and the ends of these sides all con- 

 nected to the center O, see Fig. 44, then 

 the circle is cut up into a large number of 

 equal triangles, all having the same height, 

 which is the radius, and the sum of the 

 base lines making the circle line, if the 

 bases of triangle = a the area of circle = 

 ar ar ar 



- -| (- - -|- ... in which the 



222 

 Fig. 44. r r 



factor may be set out ; thus : A 

 2 2 



(o + o + o + ....) but the sum a + a + a + = cir- 

 cumference 2 TT r, hence by substitution we get : 



r 

 A = (27r r) ; this can be simplified to : A = r 2 which, 



2 



expressed in words means: The area of a circle is equal to 

 the square of the radius multiplied by 3.1416. 

 (Continued on page 869.) 



Will pay for the IRRIGATION AGE 

 I.OO one year and the PRIMER OF 

 IRRIGATION. 



PERCOLATING WATERS 



Injunction lies where one by means of a well in the high- 

 way wrongfully diverts percolating water from an abutting 

 owner of the fee. Bonetti v. Ruts. Court of Appeal, Second 

 District, California. 113 Pacific 118. 

 SUIT BY LOWER PROPRIETOR 



Where a lower riparian proprietor diverts on his own 

 land only such water as the upper proprietor permits to flow 

 down to him, the nonuser of water by the upper proprietor 

 is not available to strengthen a claim of appropriation by 

 the lower riparian proprietor by prescription. Perry v. Cal- 

 kins. Supreme Court of California. 113 Pacific 136. 

 WATEB RIGHTS 



A reservation in a grant of land for an irrigation ditch 

 of the right to use water therefrom, to the extent of grantors' 

 "interest," etnitled the grantors to flow through the ditch 

 and to divert therefrom on land retained a quantity of water 

 represented by stock in a water supply company, but the 

 amount could not be increased by subsequent purchase of 

 other stock. Ruhnke v. Aubert. Supreme Court of Oregon. 

 113 Pacific 38. 

 RESERVOIR SITES 



Filing upon a reservoir site by a company and subse- 

 quent approval thereof by the Secretary of the Interior, 

 whether valid or voidable, segregated the land from the pub- 

 lic domain for private use, so that no legal entry of it could 

 be made by another before a judicial, legislative, or executive 

 determination restoring the site to the public demand. O'Reilly 

 v. Noxon. Supreme Court of Colorado. 113 Pacific 486. 

 DAMAGE BY FLOW 



Where water, wrongfully collected and discharged by 

 defendant, flowed down and spread over plaintiff's field sown 

 to grain and actually damaged him, there was an invasion 

 of plaintiff's property rights, authorizing the recovery of 

 nominal damages and the granting of an injunction, and evi- 

 dence of any specific amount of damage was unnecessary. 

 Galbreath v. Hopkins. Supreme Court of California. 113 

 Pacific 174. 

 PRESCRIPTIVE RIGHT 



No right to water in a stream can be acquired by pre- 

 scription, where the lower riparian proprietor has taken the 

 water out of the stream at a point on his own land, and 

 uses only such water as the upper riparian proprietor has 

 permitted to pass down to the lower owner ; such use not be- 

 ing adverse in the sense required to give a right by pre- 

 scription. Perry v. Calkins. Supreme Court of California. 

 113 Pacific 136. 

 DEED AND WATER RIGHT 



A deed of land by one having the right to divert water 

 as a stockholder in a water supply company, including 28% 

 "inches of water stock," gave the grantee the right to divert 

 28 2 /3 inches of water from a ditch from which the grantor 

 ' had a right to take water as an easement appurtenant to 

 land, including that conveyed, and gave the grantee the right 

 to use such water anywhere on his land. Ruhnke v. Aubert. 

 Supreme Court of Oregon. 113 Pacific 38. 



HEAD GATE 



Where a ditch having priority had appliances for divert- 

 ing water from the river, the character of such appliances 

 is only material on the question of the volume of water 

 diverted through the ditch, and where there was ample testi- 

 mony to show the amount of water diverted, the mere ab- 

 sence of such a head gate as the statute requires does not 

 affect the rights of the parties in an action for diverting 

 water and settling rights. Johnson v. Sterling Irr. Co. Su- 

 preme Court of Colorado. 113 Pacific 496. 

 INDEPENDENT USE OF INCREASED FLOW 



If defendant Irrigation Company had, by turning addi- 

 tional streams into its canal or by some form of work, 

 prevented loss by seepage, evaporation, or the like, and 

 thereby increased its natural flow, it might claim the addi- 

 tional waters as salvage, and not within prior irrigation con- 

 (Continued on page 873.) 



