ac

The velocity acquired at the end of any given time may be found thus. Suppofe a body begins to move with a celerity constantly encreasing in such a manner as would carry it through 16 feet in one fecond, at the end of this space it will have quired fuch a degree of velocity as would carry it 32 feet in the next fecond, though it fhould then receive no new impulfe from the cause by which its motion had been accelerated. But as the fame accelerating caufe continues conftantly to act, it will move 16 feet farther the next fecond, confequently it will have run 64 feet, and acquire fuch velocity as would, in the fame time, carry it over double the space. And fo on.

EXAMPLE I.

How far will a body fall in 6 feconds?

62=36

36×16=576 feet.

EXAMPLE II.

In what time will a body defcend through 11664 feet?
16)11.664(729(27 feconds.

Required the laft acquired velocity, when a body has fallen

8 feconds of time.

32 the additional velocity per fecond.

8 the time.

256 the laft acquired velocity is 256 feet per fecond.

EXAMPLE

PROBLEM IX.

To meafure heights and diflances by the geometrical fquare.

When the plane is horizontal, the inftrument is to be fupported and placed horizontally at any point A, and it is to be turned till the remote point F, whose distance is to be meafured, is feen through the fixed fights; then turn the dex, till, through the fights upon it, you fee any acceffible object B; then place the inftrument at the point B, directing the fixed fights to the firft ftation A, and the moveable ones to the point F; and if the index cut the reclined fide of the fquare, as in the point E, then, from fimilar triangles, ES: SB: as BA: AG; but if the index cut the right fide of the fquare K, it will be BR: RK:: BA: AF. In either of thefe cafes, the distance required may be found by the rule of three *.

Perpendicular heights, when acceffible, may be obtained by the quadrant only. For example, If you wanted the height of a house, tree, &c. approach towards or retire from the object, till it fubtends an angle of 45°; then fhall the height of the object be equal to its horizontal diftance. Euclid, I. 6.

A fimilar obfervation may be made of the other instruments used for heights and distances; but this, and many more, will daily occur in practice.

The fide DE is called the right fide, E the reclined fide.

TABLES.

CONTAINING,

I. A TABLE OF THE LOGARITHMS OF NUMBERS FROM I TO 10000.

II. A TABLE OF LOGARITHMIC SINES, TANGENTS, SECANTS, AND VERSED SINES, TO EVERY DEGREE and MINUTE OF THE QUADRANT.

III. A TABLE OF LOGARITHMIC SINES, TANGENTS, AND SECANTS, TO EVERY POINT, HALF POINT, AND QUARTER POINT OF THE COMPASS.

A TABLE of the LOGARITHMS of NUMBERS from 1 to 10000,

Log. N°. Log.

Log N°. Log. (N°. Log.

1C.00000211.32222 411.61278 611.78533 811.90848 20.30103 22 1.34242 421.62325 621.79239 821.91381 30.47712 23 1.36173 431.63347 631.7993 83 1.91908 40.60206 24 1.38021 441.64345 64 1.80618 84 1.92428 50.69897 251.39794 45 1.65321 65 1.81291 851.92942 60.77815 26 1.41497 461.66276 661.81954 861.93450 70.8451C 271.43136 47 1.67220 671.82607 871.93952 80.90309 28 1.44786 48 1.68124 681.83251 881.94448 90.95424 29 1.46240 49 1.69029 69 1.83885 891.94939 101.00000 301.47712 50 1.69897 701.84510 901.95424 111.04139 311.49136 511.70757 71 1.85126 911.95904) 12 1.07918 32 1.50515 521.71600 72 1.85733 921.96379 131.11394 33 1.51851 53 1.72428 731.86332 93 1.96848 141.14613 34 1.53148 541.73239 74 1.86923 94-97313 15 1.17609 35 1.54407 55 1.74036 75 1.87506 9597772 16 1.20412 361.55630 561.74819 761.88081 901.98227 171.23045 371.5682c 571.75587 771.88649 91-98677 581.76343 781.89209 981.99123] 59 1.77085 79 1.89763 991-99563 601.7781 81.903090042.00000

18 1.25527 38 1.57978
19 1.27875 391.5910
20/1.30105 40 1.6020

100 0000000043 00087 00130 00173 00217 00260 00303 00346 00389 101 00432 00475 00518 00561 00604 00647 00689 00732 00775 00817 102 00860 00903 00945 00988 01030 01072 01115 01157 01199 01242 103 01284 01326 01368 01410 01452 01494 01536 01578 01620 C1662 104 01703 01745 01787 01828 01870 01912 01953 01995 02036 02078 105 02119 02160 02202 02243 02284 02325 02366 02407 02449 02490 106 02531 02572 02612 02653 02094 02735 02776 02816 02857 02898 107 02938 02979 03019 03060 03100 03141 03181 03222 03262 03302 108 03342 03383 03423 03463 03503 03543 03583 03623 03663 03703 109 03743 03782 03822 03862 03902 03941 03981 04021 04060 04100 110 04139 04179 04218 04258 04297 04336 04376 04415 04454 04493 III 4532 04571 04610 04650 04689 04727 04766 04805 04844 04883 112 04922 04961 04999 05038 05077 05115 05154 05192 05231 05269| 113 05308 05346 05385 05423 05461 05500 05538 05576 05614 05652 114 05690 05729 05767 05805 05843 05881 05918 05956 05994 06032 115 0607 06108 06145 06183 06221 06258 06296 06333 06371 06408 116 06446 06483 06521 06558 06595 06633 06670 06707 06744 06781 117 06819 06850 0689306930 06967 07004 07041 07078 07115 07151 118 07180 07225 07262 07298 07335 07372 07408 07445 07482 07518 119 07555 07591 07628 07664 07700 07737 07773 07809 07846 07882 120 07918 07954 07990 08027 08063 08099 08135 08171 08207 08243 121 08279 08314 08350 08386 08422 08458 08493 08529 08565 08600 122 08636 08672 08707 08743 08778 08814 08849 08884 08920 08955 123 08991 09026 09061 09096 09132 09167 09202 09237 09272 09307 124 09342 09377 09412 09447 09482 09517 09552 09587 09621 59656 125 09691 09726 09760 09795 09830 09864 09899 09934 0996810003 126 10037 10072 10106 10140 10175 10209 10243 10278 10312 10346 127 10380 10415 10449 10483 10517 10551 10585 10619 10653 10687 128 10721 10755 10789 10823 10856 10890 10924 10958 10992 11025 129 11059 11093 11126 1116 11193 11227 11260 11294 11327 11361 130 11394 11428 11461 11494 11528 11561 11594 11628 11661 11694 131 11727 11760 11793 11826 1186c 11893 11926 11959 11992 12024 132 12057 12090 12123 12156 12189| 12222 12254 12287 1232012352 133 12385 12418 12450 1248 12516 12548 12581 12613 12646 12678 134 12710 12743 12775 12808 12840 12872 12905 12937 12969 13001 135 13033 13066 13098 13130 13162 13194 13226 13258 13290 13322 136 13354 13386 13418 13450 13481 13513 13545 13577 13609| 13640| 137 13672 13704 13735 13767 13799 13830 13862 13893 13925 13956 138 13988 14019 14051 14082 14114 14145 14176 14208 14239 14270 139 14301 14333 14364 14395 14426 14457 14489 14520 14551 14582 14C 14613 14644 14675 14706 14737 14768 14799 14829 14850 14891 141 14922 14053 14983 15014 15045 15076 15100 15137 15168 15198 142 15229 15259 15290 15320 15351 15381 15412 15442 15473 15503 143 15534 15564 5594 15625 15655 15685 15715 15746 15776 15806 144 15836 15866 15897 15927 15957 15987 16017 16047 16077 16107 145 16137 16167 16197 1622; 16256 16286 16316 16346 16376 16406 146 16435 16465 16495 16524 16554 16584 16613 16643 16673 16702) 147 16732 16761 16791 16820 1685 16879 16909 16938 16967 16997 148 17026 17056 17085 17114 17143 17173 17202 17231 17200 17289 149 17319 17348 17377 17406 17435 17464 17493 17522 17551 17580 150 17609 17638 17667 17696 17725 17754 17782 17811 17840 17869 151 17898 17926 17955 17984 18013 18041 18070 1899 18127 18156 152 18184 18213 18241 18270 18298 18327 18355 18384 18412 18441 153 18469 18498 1852 18554 18583 18611 18639 18667 18696 18724 154 18752 18780 18808 18837 18865| 18893 18921 18949 18977 19005 155 19033 19061 19089 19117 19145 19173 19201 19229 19257 19285 156 19312 19340 19368 19396 19424 19451 19479 19507 19535 19562 157 19590 19618 9645 19673 19700 19728 19756 19783 19811 19838 1519866 19893 19921 19948 19976 20003 20030 20058 20085 20112 159 20140 20167 20194 20222 20249 20276 20303 20330 20358 20385 NO. O 6

2

3 4 5

7

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9

I

2

3

4

5

6

1

8

9

NO. O 160 20412 20439 20466 20493 205 20 20547 20575 20602 20629 20656 161 20683 20710 20736 20763 20790 20817 20844 20871 20898 20925 162 20951 20978 21005 21032 21059 21085 21112 21139 21165 21192 163 21219 21245 21272 21299 21325 21352 21378 21405 21431 21458 164 21484 21511 21537 21564 21590 21617 21643 21669 21696 21722 165 21748 21775 21801 21827 21854 21880 21906 21932 21958 21985 166 22011 22037 22063 22089 22115 22141 22167, 22194 22220 22246 167 22272 22298 22324 22350 22376 22401 22427 22453 22479 22505 168 22531 22557 22583 22608 22634 22660 22686 22712 22737 22763 169 22789 22814 22840 22866 22891 22917 22943 22968 22994 23019 170 23045 23070 23096 23121 23147 23172 23198 23223 23249 23274 171 23300 23325 23350 23376 23401 23426 23452 23477 23502 23528 172 23553 23578 23603 23629 23654 23679 23704 23729 23754 23779 173 23805 23830 23855 23880 23905 23930 23955 23980 24005 24030 174 24055 24080 24105 24130 24155 24180 24204, 24229 24254 24279 175 24304 24329 24353 2437824403 24428 24452 24477 24502 24527 176 24551 24576 24601 24625 24650 24674 24699 24724 24748 24773 177 24797 24822 24846 24871 24895 24920 24944 24969 24993 25018 178 25042 25066 25091 25115 25139 25164 25188 25212 25237 25201 179 25285 25310 25334 25358 25382 25406 25431 25455 25479 25503 180 25527 25551 25575 25600 25624 25648 25672 25696 25720 25744 181 25768 25792 25816 25840 25864 25888 25912 25935 25959 25983 182 26007 26031 26055 26079 26102 26126 26150 26174 20198 262211 183 26245 26269 26293 26316 26340 26364 26387 26411 26435 26458 184 26482 26505 20529 26553 26576 26600 26623 2664726670 26694 185 26717 26741 26764 26788 26811 26834 26858 26881||26905 26928 186 26951 26975 26998 27021 27045 27068 27091 27114 27138 27161 187 27184 27207 27231 27254 27277 27300 27323 27346 27370 27393 188 27416 27439 27462 27485 27508 27531 27551 27577 27600 27623 189 27646 27669 27692 27715 27738 27761 27784 27807 27830 27852 19 27875 27898 27921 27944 27967 27989 28012 28035 20058 28081 191 28103 28126 28149 28171 28194 28217 2824 28262 28285 28307 192 28330 28353 28375 28398 28421 28443 28466 28488 28511 28533 193 28556 28578 286c1 28623 28646 28668 28691 28713 28735 28758 194 28780 28803 28825 28847 28870 28892 2891428937 28959 28981 195 29003 29026 29048 29070 29092 29115 29137 29159||29181 29203 190 29226 29248 29270 29292 29314 29336 29358 29380 2940329425 197 29447 29460 29491 29513 29535 29557 29579 29601 29623 29645 198 29667 29688 2971 29732 29754 29776 29798 2982c 29842 29863 199 29885 29907 29929 29951 29973 29994 30016 30038 30060 30081 200 30103 30125 30140 30168 30190 30211 30233 30255 30276 30298|| 201 30320 30341 30363 30384 30406 30428 30449 3047 30492| 30514) 202 30535 30557 30578 30000 30621 30642 30664|| 30685|| 30707| 30728 203 30750 30771 30792 30814 30835 30856 30878 30899 30920 30942 204 30963 30984 31606 31027 31048 31069 31091 31112 31133 31154) 205 31175 31197 31218 31239 31260 31281 31302 31323 31345 31366 206 31387 31408 31429 31450 31471 31492 31513 31534 31555 31576 207 31597 31618 31639 31660 31681 31702 31723 31744 31705 31785 208 31806 31827 31848 31869 31890 31911 31931 31952 31973 31994 209 32015 32035 32056 32077 32098 32118 32139 32160 32181 32201 210 32222 32243 32263 32284 32305 32325 32346 32366 32387 32408 211 32428 32449 32469 32490 32510 32531 32552 32572 32543 32613 212 32634 32654 32675 32695 32715 32736 32756 32777 32797 32818 213 32838 32858 32879 32899 32919 32940 32960 32980 33001 33021 214 33041 33062 33082 33102 33122 33143 33163| 3316, 33203 33224 215 33244 33264 33284 33304 33325 33345 33365 33385 33405 33425 216 33445 33465 33486 33506 33526 33546 33566 33586 33606 33626 217 33646 33666 33686 337c6 33726 33746 33766 33786 33806 33826|| 218 33846 33866 33885 33905 33925 33945 33965 33985 34005 34025 219 34044 34064 34084 34104 34124 34143 34163, 34183 34203 34223 No. Q

I

2

3

5

6

7.

8

9