Interpolation with Natural Sines: If one cannot find a sine exactly corresponding with an 

 angle in the table, or an angle corresponding with a sine found in solving a problem, the sine or 

 angle can be closely approximated by the method of Interpolation: Find the sine in the table nearest 

 the sine whose angle is to be determined. Get the difference of the sines of the angles greater and 

 less than the sine whose angle is to be determined. That will give the increase of sine for that 

 region of the arc for 15 minutes. Divide this increase by 15 and it will give with approximate accu- 

 racy the increase for 1 minute. Now get the difference between the sine whose angle* is to be 

 determined and the sine just below it in value. Divide this difference by the amount found neces- 

 sary for an increase in angle of 1 minute and the quotient will give the number of minutes the 

 sine is greater than the next lower sine whose angle is known. Add this number of minutes to the 

 angle of the next lower sine and the sum will represent the desired angle. Or if the sine whose 

 angle is to be found is nearer in size to the sine just greater, proceed exactly as before, getting the 

 difference in the sines, but subtract the number of minutes of difference and the result will give the 

 angle sought. For example, take the case in Section 108 where the sine of the angle of 28 54' is 

 given as 0.48327. If one consults the table the nearest sines found are 0.48099, the sine of 28 45', 

 and 0.48481, the sine of 29. Evidently then the angle sought must lie between 28 45', and 29. 

 If the difference between 0.48481 and 0.48099 is obtained, 0.48481 - 0.48099 = 0.00382, and if this 

 increase for 15' be divided by 15 it will give the increase for 1 minute; 0.00382 -=- 15 = 0.000254. 

 Now the difference between the sine whose angle is to be found and the next lower sine is 0.48327 

 -0.48099 = 0.00382. If this difference be divided by the amount found necessary for 1 minute it 

 will give the total minutes above 28 45', 0.00228 -^ 0.000254 = 9. That is, the angle sought is 9 

 minutes greater than 28 45' = 28 54'. 



Table of Metric and English Measures : 



Meter (unit of length) = 100 centimeters; 1000 Kilogram = 1000 grams; 2.2046 (2 1/5 Ibs.). 



millimeters; 1,000,000 microns Ox); 39.3700 Yard, 3 feet, 36 inches; 0.9144 meter; 91.4399cm. 



inches; 3.2808 feet. Foot = 1/3 yard; 12 inches; 0.3048 meter; 



Centimeter (cm.) = 10 millimeters; 10,000 mi- 30.48 cm. 



crons; 0.01 meter; 0.3937 (2/5) inch. Inch = 1/36 yard; 1/12 foot; 2.54 cm.; 25.4mm. 



Millimeter, (mm.) = 1,000 microns GU); 0.1 cm.; Mile = 1760 yards; 5280 feet; 1.61 kilometers. 



0.001 meter; 0.03937 (1/25 inch). 



Micron (unit of length in micrometry) (/*) (246) Quart = 1/4 gallon; 2 pints; 32 fluid ounces; 



= 0.001, one thousandth of a millimeter; - 947 "'ter (947 cc.). (U. S. liquid). 



0.000001, one millionth of a meter; 0.00003937 Fluid unc . e = 8 nuidrachms; 1/32 of a quart; 



(1/25000) inch. 1/16 pint; 29.574 cubic centimeters (30 cc. 



Kilometer = lOOo'meters; 0.621 or 5/8 mile. approximately). 



Ounce avoirdupois = 437 1/2 grams; 28.349 



Liter (unit of capacity) = 1000 cubic centimeters grams. 



(or milliliters) ; 1 quart approximately. Ounce apothecaries or Troy = 480 grains; 31.103 



Gram (unit of weight) = 1 cc. of water; 15.432 grams. 



grains. Pound (avoirdupois) = 16 ounces, 453.6 grams. 



To Change from Centigrade to Fahrenheit and the Reverse : 



From centigrade to Fahrenheit: Multiply the degrees centigrade by 9/5 and add 32. Exam- 

 ple: 20 C. = 20 x 9/5 + 32 or 68 F. 



From Fahrenheit to centigrade: Subtract 32 and multiply by 5/9. Example: 77 F. = 77 32 

 X 5/9 or 25 C. 



To change from centigrade to absolute temperature and the reverse: Add 273 to the degrees in 

 centigrade and the sum will be the absolute temperature. Example. Ice melts at C. or + 

 273 == 273 absolute, and water boils at 100 C. or 100 + 273 = 373 absolute. If the abso- 

 lute temperature is given subtract 273 and the result will be the temperature on the centigrade 

 scale. Example: Ice melts at 273 absolute, 273 - 273 = 0, that is, ice melts at C. See Fig. 

 36, where absolute temperature is given. 



American Manufacturers and Dealers in Microscopes and Microscopical Supplies: 



The Bausch & Lomb Optical Company, Roch- Arthur H. Thomas Company, Philadelphia Pa. 



ester, New York. Ernst Leitz, Optician, New York City, N. Y. 



The Spencer Lens Company, Buffalo, New York. Eimer & Amend, New York City, N. Y. 



The Gundlach Manhattan Optical Company, The G. Cramer Dry Plate Company, St. Louis, 



Rochester, New York. Mo. (Photographic plates and color screens). 



Joseph Zentmayer, Philadelphia, Pa. The Eastman Kodak Co., Rochester, N. Y. 

 'Edward Pennock, 3609 Woodland Ave., Phila : (Dry plates, color screens, velox developing 



delphia, Pa. paper). 



The Corning Glass Works, Corning, New York. Ansco Company, Binghamton; N. Y. (Cyco 



(Daylight glass and Pyrex glass). developing papers, etc.). 



C. H. Stocking Company, Chicago, 111. Lumiere Jougla Co., New York. (Autochrome 

 Williams Brown & Earle, Philadelphia, Pa. plates). 



When ready to buy a microscope or supplies get the latest catalogues of the manu- 

 facturers; then the newest models can be seen and the current prices determined. 



