Manual / Guide
Early Post leaflet for its Hemmi-made Mannheim rules (ISRM files it under the early model 1447, the sibling of the Hemmi 30/32 pocket rules). Describes the parts, locating numbers, and the operations; recommends freeing a tight slide with paraffin oil, paraffin wax or sandpaper. Undated (pre-Teledyne). 6 pp.
A MANNHEIM TYPE SLIDE RULE (WITH A, B, C, D, Cl, K, S, T, L SCALES) A simple and accurate device for solving quickly mathematical problems involving multiplication, division, proportion, percentage, squares and square roots, cubes and cube roots, diameters and areas, reciprocals, logarithms and exponents, trigonometric formulae, and all sorts of combinations of these operations. The art of operating a slide rule is easy and can be learned readily by anyone. Any person called upon to do much numerical calculation will find it profitable to invest the small amount of time necessary to learn this art. The slide rule will save hours of mental strain for those en- gaged in business or engineering calculations. Problems are worked (name- ly, the various — operations of mul- tiplication, division, — taking square roots, “ ~ on are carried out) by comparing of the scales with other. Since there are n scales (marked A, B, C, D, ¢ K, S, L, T,) it is easily seen there are numerous combin: taking two scales at a time manipulation of the slide rule sists in moving the slider along body and in sliding the cursor to or left over the face of body and It is important for the hair line o cursor to be placed exactly at right to the direction in which the scales setting of the hair line may be checked centering it upon the reading A-| (at the lef or right end of the A scale): if the hair line properly adjusted, it will also center upon mark D-I. Any two readings (such as A-I and D-I) - which center upon the hair line when in proper ad-. — justment are said to be in register. The purpose o the cursor is to enable one to read easily the figure on any one scale which lie in register with readings on any other scale. If the slider is too tight in the dy | ‘grooves, it may be freed by using a little talcum powder, | foil of paraffin, paraffin wax, or sandpaper. , It will be easy to learn the operations of the slide rule, if the following instructions be read carefully. The first point is to learn how to locate given numbers on the various scales. After explaining how to read numbers on the scales, we give a deseri tion of each scale, and then explain how to make calculations wi the slide rule. : Used by Students, Teachers, Architects, Engineers, Merchants, Salesmen, Purchasing Agents, Manu- facturers, Accountants, Chemists, and Estimators. DESCRIPTION OF THE SLIDE RULE The Mannheim type slide rule consists of three parts, a ruler, a slider, and a runner. The ruler (also called the -body or the stock) carries three scales marked A, D, and K. The slider fits into and slides in grooves on the top side of the i The slider can be reversed in the body and carries on one side the B, Ci, and C scales, the re- verse side bearing the S, L, and T scales. The runner (also called indicator or cursor) consists of a lens carrying a hair line and set in a | frame which slides to the right or left over the face of the rule. ¢ \ com, so THE FREDERICK POST * ci Hi ia aati tatoo te tabatatatat Pitetetetededete tet fadantonduntinlititin Cc pert seeetiee eee TT TUTTE 0 T i: iH T ie abi LJ ity I eee yooh A RE ‘ Am , fri frin ! 6 Fig. A. Rule with Slide chosen shy ¢3 2 3 Di rN 2 o¥ 125 Fig. I. c} ih es et get eg ye | h Oe et Sa SE de Se SiR a a SB y 1% Fig. II. SECC Cc 1 2 3 5 6 7, 18 is) 1 is 6 |9 A Fig. II. ex 125 j LOCATION OF NUMBERS ON THE SCALES \ 1. Experience proves that the beginner's first step is to learn how to locate numbers on the various scales. We cannot emphasize too strongly the necessity of learning how to read the scales. The various scales are not calibrated uniformly (except the L scale), and the marks on the scales do not measute lengths—they represent numbers. Since the reading of all the scales is done in much the | same manner, it will be sufficient to illustrate the procedure with one scale. We use the C (and exactly similar D) scale for our example. ? i 2. The C and D scales consist of ningymain divisions, Fig. 1, of steadily decreasing lengths as one proceeds to the right. The first line of each of these divisions is numbered: beginning at the left with | (called the left index), then 2, 3, 4, 5, 6, 7, 8, 9, and finally | (which stands for 10, and is called the right index). 3. Dropping down to Fig II, we see that each of these main divisions is\ divided into 10 secondary | |» divisions. Between the main divisions | and 2, the secondary|divisions are numbered from | to 9 in | smaller figures. The secondary divisions between the main divisions 2 and 3, 3 and 4, and so on are | not numbered, but they can and must be counted as |, 2, 3)... . 9. | 4. Dropping down to Fig Ill, we see that the secondary divisions are again subdivided into 7 tertiary divisions. The secondary subdivisions between | and 2 are each divided into i0 tertiary ; parts. The shorter secondary divisions between main 2 and 3 and between main 3 and 4 are. divided only into 5 tertiary parts. The still shorter secondary divisions between the main divisions - beyond 4 are divided into two tertiary parts (of course, to ayoid crowding the scale with marks). |B. To locate a three digit number (say) on the C or D scale, one proceeds as follows: In the first place certain technical terms must be explained. The first significant digit of a number is | | the first digit appearing on the left which is not zero: thus| | is the first significant digit in all | (the numbers, 125, 12.5, 1.25, 0.125 and 0.0125 etc. One locates on a slide \tule only the sequence of numbers, 1-2-5; the decimal point has nothing to do with locating the jaumber. As an example, let us locate this sequence 1-2-5 on the C scale. § t ¢ 4 a Step |. The first significant digit (1 for the number 125) \locates, Fig,\|1, the number as lying between the main divisions | and 2. A Step 2. The second significant digit (2 for the number 125) locates, Fig. II, the number between { ih secondary divisions 2 and 3 of the main division | to 2. step 3. The third significant digit (5 for the number 125) locates the number as on the fifth of | he ten tertiary divisions of the secondary range 2 to 3 of the main division | to 2. Had the | | PAT PEND. ff i : B. { cl Fiddle ai tatabtat Matatiteie : f cans Cc an 2 3 5 orn | epeeetpeets Leetnyite pi tudtauhalt fe eee ARAMA : h Slide set to right with MADE IN U, S.A. justo sieve vcolvivtuveatouint av vis 0 feieoationbvntetntoalavdtaielativoitntoentevstosedturetoneetaventsoeat | NAMA NAA ARMA AAA ANA AA ARRAY ANNA RAR AARRR AEE ; | Aa BS ESL A Uda Ll LU AM TTT TY ET UU i i) lil TE ON, BA, PR SBS PRS TTS BP PPT Lu 0 PE f g the 6 scales, A, B, C, D, Cl and K. 5 § 7 8 9 1 ie 6 5 7 8 9 1 pia IN DIVISIONS DARY DIVISIONS DMPLETE SCALE number been 1257, we should then have located it 7/10 of the tertiary division between 1250 and 1260, this last shift being made by estimating the 7/10 by eye since there are no fourth order divisions. : The above procedure is to be followed for any number on the scale, except that it should be | noted that the tertiary divisions toward the right end of the scale represent fifths (between main 2-3 and main 3-4) and halves (between main 4 and the right index). For example, the number | 463 lies, first on the main division between 4 and 5 second on the secondary division between 460 ey 470, and third 3/5 of the first tertiary division between 460 and 465, this 3/5 being estimated y eye. 6. The decimal point is ignored in operating the slide rule. At the end of a calculation, the decimal point is located by estimating the answer from rounding off the factors and divisors. One quickly learns how to carry out such estimations. There is a method of keeping account of the decimal point in slide rule calculations: this method depends upon the theory of logarithms, but is universally ignored even by those who |have a working knowledge of its use. , ? ifs DESCRIPTION OF THE SCALES ae i) 7. The C and D scales, which are exactly alike, are calibrated in proportion to the logarithms ot the actual numbers which are marked on these scales. It may be a satisfaction to the reader to } understand the theory of logarithms, but will not be necessary in using the slide rule. The C-D combination is used for multiplying, dividing, and in ratio and proportion. — 8. The Cl or reciprocal scale is calibrated in the same way as the C and D scales except that it reads from right to left, namely, is the C scale reversed in direction. The Cl scale may be used \in reading off the reciprocal of a number as well as in multiplication and division. | 9. Scales A and B, which are alike, are logarithmic scales just half as long a the C and D scales. | If the left half of the A (and B) scale represents numbers from | to 10, the right half represents ' numbers 10 times as large, namely, from 10 to 100. Again, if the left half represents numbers from 100 to 1000, the right half represents numbers from 1,000 to 10,000 and so on. These scales may be used in finding squares and square roots. i 10. The K scale is a logarithmic scale 1/3 as long as the C scale. The second third of the scale represents numbers 10 times as large| as those of the first third. The right third of the K scale represents numbers 100 times as large as the first third, and 10 times as large as the second third of the scale.. Thus the first, second, and third scales may represent numbers | to 10, 10 to 100, and 100 to 1,000 respectively. j MADE IN U.S.A. , wil WJ ptlsfrttatatababatitatsPatati tata Ielity A MMs sc eabaitntscrineia tide osc. Bi 7 8 o ' : index of C scale set\ over 2 on D acale. § 11. The S scale (on the opposite side of the slider from the B, Cl, and C scales) is used in finding the sines of angles. | 12.° The T scale (on the same side of the slider as the S scale) is used in finding the tangents | of angles. 13. The L scale is uniformly calibrated, and is used in combinations with the C and D scales in finding the logarithms of numbers. \ SLIDE RULE OPERATIONS ’ 14. Multiplication. Use the C-D combination. To multiply two numbers, locate one factor on the “ 4) Descale, set the index (either the left or right end) of the C scale in register with this factor on ‘} the D scale, locate the other factor .on C, then in register with this reading on C the product will be found on the D scale. j For example, in Fig. B, the left index of C is set on the number 2 of the D scale. If the cursor be moved over to 3 on C, then under this number and in register with it the product 6 of 2x3 will be found on D. In register with C-4 and on D will be found the product 8 of 2x4. In register “|, with C-5 and on D will be found the product 10 of 2x5. How about 2x9 (say)? A glance at Fig. B shows that C-9 is off the D scale. In this and similar examples, the slider is to be pulled to the left in the ruler until the right index of C is in register with the first factor appearing on D (in the present example 2), and then the answer is again to be read on D in register with the second factor as read on C sin, “= 15. Division. Use the -C-D combination. Division is the inverse of multiplication. Locate the divisor on the C scale and set this reading in register with the dividend on the D scale: the quotient will be found on the D scale in register with the index of the C scale (with whichever index of C, left or right, that appears on the D scale). As an example, note that the divisor C-3 of Fig. B is in register with the dividend 6 on D, and that the quotient 2 lies on D in register with the left index of C. Note that with this setting of the slide rule, any number on the D scale divided by the number in register on C, gives 2 as quotient. 16, Squares and Square Roots. Use the A-D combination of scales. To find the square of any number, locate this number on the D scale, set the hair-line of the cursor upon this number, | end read its square in register on the A scale. To find the square root of any number, use the scales in reverse order. Thus, locate the given number whose square root is to be found upon the A scale (use the left half of A if this number has an odd number of digits, the right half if the number of digits is even), set the cursor upon is number, and read its square root in register on the D scale. 7 ie Cubes and Cube Roots. Use the D-K combination of scales, To find the cube of any number, locate this number on the D scale, set the cursor on this number, and read its cube in register on itie K scale. | To find the cube root of any number, use the D-K combination in the reverse order. Thus, locate ig the given number whose cube root is desired upon the K scale (use the left third of K if the A.) number has |, 4, 7, etc. digits, namely if its number of digits \is | plus @ multiple of 3; use the ti mile third of K if the number of digits is 2 plus a multiple) of 3, such as 2, 5, 8, etc. digits; _, and use the right third of K if the number of digits is an exact multiple of 3, such as 3, 6, 9, etc. digits), set the cursor upon this number, and read its cube root jn register on| D. t heal Proportion. Use the C-D combination of scales. Problems of proportion| arise, for example, in 4 | the conversion of yards to feet, dollars to pounds, gallons to cubic feet, and so on. As an ex- fi: ample of such use of the slide rule, let us set the rule for the yard-to-foot conversion. Place the ef index (either right or left) of the C scale upon the number 3 of the D Scale. Note the number e corresponding number of feet. n the D scale, and in register s. of yards and fraction thereof on C, and read in register on D Conversely, locate the number of feet in any given distance u is number will be found on C this distance expressed in ya Reciprocals. Use the CI-D combination of scales. To find) the reciprocal of any number, locate this number on the D scale and set the cursor upon this reading: the reciprocal of this r will be found in register on the Cl scale. Alternatively, lo¢ate the number on the Cl scale, set the cursor upon this number, and read its reciprocal in register on the D scale. af 20._ Further Uses of the Cl Scale. Ualtipticetion by use of the D-Cl eehdbidation: To multiply | two numbers together, locate one factor on the D scale, the other on the Cl scale, set these two factors in register by use of the cursor, and read their product on D in register with the index of “+ the Cl scale. Since either the left or right index of Cl will always be found upon the scale, this A method of multiplication never requires the reversal of the slider which is frequently necessary - when multiplying by use of the C-D combination (as in Par. 14). i Ve Hath ee Observe that this method of multiplication permits finding the product of three factors with one setting of the slider. As an example, let us calculate the volume of a wall 15.5 feet long, 8 feet high, and 0.55 feet thick. Solution: Set the cursor at 155 on D; draw the slider until 8 on Cl coin- | aig with the hair-line; move the cursor to 55 on C; read the product 68.2 cubic feet in register | on Division by use of the D-Cl combination: To divide one number by another, locate the dividend on D, set the cursor on this number, draw the slider until its (right or left) index comes into register with the hair-line, locate the divisor on Cl and set the cursor on this number, the quotient lies in register on the D scale. J 21. Sine of an Angle. Use the A-S combination of scales. Turn the slider over in the body so that — the * L, T scales are on top. Set the indices of the S scale in exact register with those of the A scale. } To find the sine of any angle (greater than about 30'), locate this angle on the S scale, its sine will be found in register on the A scale. Note that the left half of the A scale covers the angle range, 30' to 5°45’, and that the sines of angles in this range have one zero after the decimal — point (for example, sin 4°30' is 0.0785); whereas the second half of the A scale covers the angle » range, 5°45' to 90°, and that for sines of angles in this range the significant digits begin immediate- — ly after the decimal point (for example, sin 35° is 0.574). | Given the sine of an angle, to find the angle, use the scales A and S in the reverse order. Thus, spat the numerical value of the sin on the A scale, and read off the angle in register on the scale. Alternative Methods. Use the B-S combination of scales. Place the slider in the ruler with the B-CI-C face up. | To find the sine of an angle, locate the angle on the S scale, draw the slider over until this | angle comes into register with the celluloid reading edge on the back side of the ruler, turn the ruler over without disturbing this setting, and read the required sine on the B scale in register with the right index of the A scale. Given the sine of an angle, to find the angle: locate the given sine on the B scale, draw the slider over until this number comes into register with the right index of the A scale, turn the ruler over without disturbing this setting, and read off the required angle on the S scale in register with the reading edge on the back of the ruler. oy 4 22. Tangent of an Angle. Use the D-T combination of scales. Turn the slider over so that the S, L, T scales are on top. Set the indices of the T scale in exact register with those of the D scale. To find the tangent of any angle (in the range from about 6° to 45°), locate the T scale, its tangent will be found in register on the D scale. Throughout the tangen significant digits begin immediately after the decimal point (for example, tan 19°20' ii To find the tangent of an angle|in the range 45° to 90°, find the tangent of 90° given angle, and take the reciprocal of this value as explained in Par. 199. Given the tangent of an angle, td find the angle: If the given tangent lies in the range 0. locate this number on D, and read the corresponding angle in register on the T scale: If the tangent exceeds |, find the reciprocal of the given number (Par. 19), locate this number D scale, read off the angle in Se) A this number on T, subtract this angle from 90° to the ‘required angle. | Alternative Methods. Use the C-T) combination. Place the slider in the ruler with the B-C scales on top. ad To find the tangent of an angle, locate the angle on the T scale, draw the slider over until angle comes into register with the feading edge on the back of the ruler, turn the ruler over without disturbing this setting, end read off the required tangent on the C scale in register with the right index of the D scale. j Given the tangent of an angle, to find ‘the angle: locete the given tangent on the C scale (between 0.1 and | as explained above), draw the slider over until this number comes into f register with the right index of D scale, turn the ruler over without disturbing this setting, pry’ read off the required angle on the|T scale in register with the reading edge on the back of the ruler. 23. Logarithm of a Number. Use, the D-L combination of scales. Turn the slider over in the body 4 so that the S, L, T sceles are on top. Set the indices of the L scale in exact register with those of © the D scale. 4 To find the logarithm of a number, locate the “significant digits on the D scale, the required logarithm will be found by use of the cursor in register on the L scale. The characteristic of the logarithm is to be found from the position of the decimal point in the same way one determines — it when using a logarithmic table. i Xe we fear | eh — . _ Given the logarithm of a number, to find the number: locate the mantissa of the logarithm upon the L scale, and read off the significant digits of the number in register on the D scale. The decimal point for the number is fixed by the characteristic of the given logarithm in the usual manner. Alternative Methods. Use the C-L combination of scales. Place the slider in the rule with the B-CI-C face up. To find the logarithm of a number, locate the number on the C scale, draw the slider over until this number comes into register with the right index of the D scale, turn the entire ruler over without _disturbing the setting and read off the required logarithm on the L scale in register with the reading ~ edge on the reverse side of the rule. Given the logarithm of a number, to find the number: locate the given mantissa on the L scale, draw the slider over until this number comes into register with the reading edge on the back side _ of the rule, turn the rule right side up without disturbing the setting, and read off the required number on the C scale in register with the right index of the D scale. REMEMBER 24. Accuracy will follow only if the body, slider and cursor are carefully set. Factors, divisors, dividends, reciprocals, sines, and so on, must be carefully read on the respective scales. The tuler itself will be found to be correct to within about one-tenth per cent. __ Speed in the use of this rule will follow only as the result of practice. Until the rules of operation are thoroughly learned, speed of operation should not even be sought—speed will be the natural consequence of a thorough understanding of the manipulations. Careful attention to the directions should be the learner's only care; speed will come when and only when the manipulator knows exactly what to do. : / Study these directions with care and attention to details. It may be (probably will be) necessary to read them over several times. By all means have the rule handy and actually carry out the directions step by step as you study the rules of manipulation. The first important step is to learn how to locate numbers accurately upon the several scales — (Par. 5). In reading off answers, the numbers often fall between the calibrations of the ruler. _ When this happens, one must estimate distances to get the last decimal place. ; In the beginning, work simple problems which you can check with ordinary arithmetic. Calculations on the rule will check your numerical results to within about three decimal places. Each operation can be mastered if a few such “check problems’ are worked out to illustrate each manipulation. The study of this slide rule will prove to be one of the most profitable investments of your time ou have ever made. Practice makes perfect. be. Satta! 8q. yd. = .8361 m' opp. ercury =1.133 ft. water] 151 opp. sq. mi. = 2.590 km? opp. 72 ere .4912 Ibs./sq.in.| $40 opp. 8q. mi. = 640 acres opp. 640 cu. in. = 18.39 em 15.5 opp. 254 eu. ft. = opp. 64 re Opp. 108 cu. ft. = opp. 111 “= 15.43 gr. 19.7 opp.