2. Chronic cutaneous affections, especially of the scalp. 3. Severe injuries of the bones of the head; convulsions. 4. Impediment of speech. 5. Want of due capacity of the chest, and any other indication of a liability to a pulmonic disease. 6. Impaired or inadequate efficiency of one or both of the superior extremities on account of fractures, especially of the clavicle, contraction of a joint, deformity, etc. 7. Lateral deviation of the spine from the normal midline of more than 2 inches (scoliosis); curvature of the spine of any degree in which function is interfered with, or in which there is noticeable deformity when the applicant is dressed (scoliosis, kyphosis, or lordosis). 8. Hernia. 9. A varicose state of the veins of the scrotum or spermatic cord (when large), hydrocele, hemorrhoids, fistulas. 10. Impaired or inadequate efficiency of one or both of the inferior extremities on account of varicose veins, fractures, malformation (flat feet, etc.), lameness, contraction, unequal length, bunions, overlying or supernumerary toes, etc. 11. Ulcers or unsound cicatrices of ulcers likely to break out afresh. The requirements of the following tables of physical proportions are minimum for growing youths and are for the guidance of medical officers in connection with the other data of the examination, a consideration of all of which will determine the candidate's physical eligibility. Mere fulfillment of the requirements of the standard tables does not determine eligibility, while, on the other hand, no departure below the standard should be allowed unless upon the unanimous recommendation of the medical examining board for excellent reasons, clearly stated in each case. The physical requirements should be those of the age at the birthday nearest the time of the examination. Fractions greater than one-half inch will be considered as an additional inch of height, but candidates must be at least 64 inches in height. See the following table of physical proportions: Table of physical proportions for height, weight, and chest measurement. Following is a list of the places at which the examination is held: Fort Ethan Allen, Vt. Army Building, 39 Whitehall Street, New Army Medical School, Washington, D. C. Fort Bliss, Tex. Carlstrom Field, near Arcadia, Fla. Fort Douglas, Salt Lake City, Utah. Jackson Barracks, New Orleans, La. Fort Keogh, Miles City, Mont. Fort Leavenworth, Kans. Letterman General Hospital, Presidio of Fort Rosecrans, Calif. Fort St. Michael, Alaska. Fort Wm. H. Seward, Alaska. Fort Snelling, Minn. MENTAL EXAMINATION. The examination takes place as follows, viz: First day.-History, 9 a. m. to 1 p. m., 4 hours. Second day.-Algebra, 9 a. m. to 1 p. m., 4 hours. English grammar, composition and literature, 1.30 to 5.30 p. m., 4 hours. Third day.-Geometry, 9 a. m. to 1 p. m., 4 hours. Algebra. Candidates will be required to pass a satisfactory examination in that portion of algebra which includes the following range of subjects: Definitions and notation; the fundamental laws; the fundamental operations, viz: Addition, subtraction, multiplication, and division; factoring; highest common factor; lowest common multiple; fractions, simple and complex; simple, or linear, equations with one unknown quantity; simultaneous simple, or linear equations with two or more unknown quantities; graphical representation and solution of linear equations with two unknowns; involution, including the formation of the squares and cubes of polynomials; binomial theorem with positive integral exponents; evolution, including the extraction of the square and cube roots of polynomials and of numbers; theory of exponents; radicals, including reduction and fundamental operations, rationalization, equations involving radicals; operations with imaginary numbers; quadratic equations; equations of quadratic form; simultaneous quadratic equations; ratio and proportion; arithmetical and geometrical progressions. Candidates will be required to solve problems involving any of the principles or methods contained in the foregoing subjects. The following sets of questions were used at recent examinations: MARCH, 1917. No. 1.--(a) Simplify 2r3 (x−3a)—2 [2r1—a2 (r2—a2)]—3a [r3—2x {a2+r (a−x)}+a3]. (Wt. 10.) (b) Find the lowest common multiple of r3-6x2+5x+12, r3-5x+2r+8 and 13-42+x+6. No. 2. (a) Simplify (Wt. 10.) "[VA]" (b) Rationalize the denominator of 2√ No. 4. (a) Find the values for m for which the equation 2mx2+(5m+2)x+(4m+1)=0 has its two roots (Wt. 12.) equal. Find the roots for these values of m. (b) Arrange in order of magnitude 319,52 and 3√3. No. 5. A coach due at B 12 hours after it leaves A, after traveling from A as many hours as it travels miles (Wt. 12.) per hour, has an accident; it keeps on, however, at a rate of one mile per hour less than its former rate and arrives at B 3 hours late. Find the distance from A to B. 11 No. 8.-A and B ran a race to a post and back. A returning meets B 30 yards from the post and beats him (Wt. 12.) by 1 minute. If on arriving at the starting place A had immediately returned to meet B, he would have run the distance to the post before meeting him. Find the distance run, and the rates of A and B. No. 9.--(a) Write the formula for the rth term of (1+y)n. Two boys run in opposite directions around a rectangular field, the area of which is 1 acre (4,840 One No. 6.-A broker bought a number of $100 shares, when they were a certain per cent below par, for $8,500. (Wt. 12.) He afterwards sold all but 20, when they were the same per cent above par, for $3,200. How many shares did he buy, and what did he pay for each share? No. 7.—(a) Solve graphically the equations (4x+5y=24 (Wt. 10.) 13x-2y=-5 (b) Solve these same equations algebraically. (c) Explain why the answers may not be exactly the same in the two cases. Which answers are correct? No. 8.-Find for what values of k the roots of the equation 10+6kr+k2-4-0 are (1) equal; (2) real and (Wt. 12.) unequal; (3) imaginary. What are the equal roots when k has such values that they will be equal? No. 9.-Define an arithmetical progression. (Wt. 10.) When a train arrives at the top of a long slope the last car is detached and begins to descend, passing over 3 feet in the first second, 3 times 3 feet in the second second, 5 times 3 feet in the third second and so on. At the end of 2 minutes it reaches the bottom of the slope. What space did the car pass over in the last second? (b) If A runs around a circular track in 40 seconds, how fast must B go in order that they may meet every 18 seconds when going in opposite directions. 12 No. 5.-Two passengers together have 400 pounds of baggage and are charged, for the excess above the (Wt. 10.) weight allowed free, 40 cents and 60 cents, respectively. If the baggage had belonged to one ol them, he would have been charged $1.50. How much baggage is one passenger allowed without charge? (b) The sides of two rectangles, one of which is within the other, are parallel and at equal distances apart. How far apart are the sides if the outer rectangle is 10 centimeters by 14 centime ters and is twice as large as the inner one. (Answer required to 3 decimal places. Test your answer.) No. 7. (a) Deduce the formulæ giving the roots of the quadratic equation ar+br+c=0. Under what (Wt. 12.) conditions will these roots be 1° equal, 2° real and unequal, 3° numerically equal with con trary signs? (b) For what values of k will the equation 14kr+4=0 have equal roots? Find these equal roots. No. 8. (a) Write down the general or rth term in the expansion of (1+y)" by the binomial formula. (Wt. 10.) (b) Find the middle terms of (2a-3-27a5)15. is a geometrical progression and find No. 9.-(a) Prove that the repeating decimal 20.202020 20 MARCH, 1920. No. 1. (a) Simplify [8a-3{a-(b−a)}]—4[a—2{a−2(a−b)}+b]. (Wt. 12.) (b) Find the highest common factor of x-ax3—a2x2-a3x-2a1 and 3x3-7ar2+3a2x-2a3. No. 2.-Simplify (Wt. 10.) No. 4.-(a) Show that the sum of any fraction and its reciprocal is greater than 2. (Wt. 10.) (b) Simplify a-mb-n C-1 No. 5. A grocer mixes three kinds of coffee. He can sell a mixture containing 2 pounds of the first kind, 9 (Wt. 12.) pounds of the second, and 5 pounds of the third, at 18 cents per pound; or one composed of 6 pounds of the first, 6 pounds of the second, and 9 pounds of the third, at 19 cents per pound; or one composed of 5 pounds of the first, 2 pounds of the second, and 18 pounds of the third, at 22 cents per pound. Find the number of cents in the cost of a pound of cach kind. No. 7.-(a) For what values of m will the equation 2mx2+(5m+2)x+(4m+1)=0 have its roots 1°. real and (Wt. 12.) equal, 2°. real and unequal, 3o, imaginary? No. 8. (Wt. 12.) No. 9. (b) When the roots are equal, what are their values? (a) Write the general or rth term of (a + b)n. (b) Expand and simplify (1) Two circles with their centers on the same diameter of a third circle are tangent to each other ex(Wt. 12.) ternally and to the third circle internally. What must be the radii of the two circles in order that the sum of their areas be three-fourths that of the outer circle? How will the sum of the circumferences of the inner circles compare with the circumference of the outer circle? No. 2.--Examine the following statements and say what you can as to the truth or falsity of each (i. e, for (Wt. 12.) what values of 1, if any, the statement is true): (1) 3(2x+7)+x=7(x+3). (2) 3-[r-2(3x-4)]=(x+2)24r-13. |