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V^^',' €^4^ # '/^■Q[;A.i4^- i'(- ' ;■'/ '<^ 'vsemmsss^ /■ . •V • ON THE OFTHE M'- •to' '^ 3\' 3. me de rUniv^«iii ■ ^ ;:A r^i ^■'4r Uuivw8il4| .■..■-» \ '•/ '!•; ,;■ l>'>. ;•(' '■ /■ y.-lir^ :-'rir :V, '!;''/■ "'; C CARLES GAEPM AEL, M Am F.ELA.Sv - > ' ' . {tja% yzhWtw Of sr. '^fOttS'f? COLt., t!AMB,) ■•>.,■. ■jt ; Deputy Siipe.rinlf.ttdfM «/ <7»e Mel^oroloi^Ml Serviee of pimaiiif.. . n [5;.' .' .■» ■ ■ ■: ;tr,. ^; ^''W)Ffv^ & CO., PRI^iij^, COLBgME /STREET. j.ti ' ' .,'. ' .' ' " I ' I .'1 I ' ^MSf^^fSiS^ilimfiiSS^ ii Mi __ iii ii :'\ V ON THE REDUCTION OF THE BAMETER TO SEA LEYEL. ■•• L V $ £?*^ ■vt^ith: tj^l-bles. BY CHARLES CARPMAEL, M.A., F.R.A.S., (late fellow of ST. John's coll., camb.) Deputy Superintendent of the Meteorological Service of Canada. TORONTO: COPP, CLARK & CO., PRINTERS, COLBORNE STREET. 1878. f"'"" [From the Proceedings of the Canadian lAStitute.] ON THE REDUCTION OF THE BAROMETER TO SEA LEVEL. -«•► BY CHARLES CARPMAEL, M.A., P.R.A.S., (LATE FELLOW OP ST. JOHN'S COLL., CAMB.) Deputy Superintendent of the Meteorological Service of Canada. The application of an approximately correct reduction to baro- metric readings, taken at various levels, in order to reduce them U> what they would have been at one specified level, is absolutely necessary for their intercomparison. In the following paper several formulae which have been employed for this purpose are examined ; and tables are appended by means of which, with very little calcu- lation, a sufficiently correct rediiction may be obtained, and which are, moreover, peculiarly adapted to the computation of tables of i-eduction for ir dividual stations. Guyot's Tables* D, XVI. and XIX'., are commonly employed, on this continent, for the purpose of effecting the reduction. These give the height, in English feet, of a column of air corresponding to a tenth of an inch in the barometer at various temperatures, the barometric pressure at the base of the column being from 22 inches to 304 inches. A formula is given for use with Table XVI., which may be written where R represents the required reduction in inches, Z the differ- ence of height between the two stations, or the height above the sea (expressed in feet), iVthe number in the table, /3 the observed reading of the barometer reduced to 32° Fahr., and b the pressure on which the tabular number iV is based,! that is, 30 inches. • Meteorological and Physical Tables. Thirrl edition. Washington, 1859. By Arnold Giiyot, P.D., LL.D., Professor of Geology and Physical Geography, College of New Jersey. t Quyot defines what is here represented by 6, as " the normal height of barometer at the sea- level," and in an example which he gives, he employs 30 in. It is, however, only because the table is based on a barometric reading of 30 in., that this value of b is to be employed. * ON THE REDUCTION OF THE No formula is given for use with Table XIX.', but it is stated that the table may be employed " for reducing barometrical observa- tions to the level of the sea, and also to any other level by a similar process." An example is, however, given, applying tables in French measure, corresponding to XIX.', the method of which example may be represented by the formula Ji=. 2 Z A ^ b^'t 1 •10' (ii.) where N^ is the number in the table corresponding to the baro- metric reading* and temperature at the upper station, and N that ^ B T corresponding to those at the lower station ; an approximate reduced barometric reading and temperature being employed in taking out the latter quantity. Formula (i.) may also be employed with Table XIX.', h being any height and N the number hi the table corresponding to h. No advan- tage is, however, gained, by using this table instead of Table XVI. with formula (i.), unless b be taken nearly equal to /3, so that we may have, nearly Z ]i = 10 iV Laplace's formula for computing differences of elevation from baro- metrical observations, from which each of the above is deduced, may be written ^=^^log^, (iii.) where A^ is a constant, depending on the mean between the tem- peratures at the upper and lower stations. Strictly, it also depends upon the latitude of the station, and on the height above the sea ; but the variations due to these may be neglected, unless the height is very considerable. Now the number ^ iV^ , in the above mentioned tables, for baro- meter reading b, and temperature t, is the difference of elevation * Throughout this paper, when a barometric reading is spoken of, the reading reduced to temp, 32° Fahr. is to be understood. BAROMETER TO SEA LEVEL. 6 of two stations, the temperature being t, the barometer reading at lower station b, and at the upper station b - ^j. Hence, by (iii.), Also R being the reduction, (iii.) may be written t » (3 Combining these, we get log (1 + R Z . 10ft log b t 106 - 1 ' hence. .._ = 10 6 106-1 h t - V 106 1 I - Z 6 t = 1 + 6 t 1 1 + 10 6 1.2 by the binomial theorem. i^< Z 6^ + 1 10 6 t 10 6 1.2 Z 6^. Z b t + 1 10 6 •■■ (iv.) Formula (i.) is deduced from (iv.), by neglecting all terms beyond the first; and making 6 = 30 inches, if used with Table XVI.; but, if used with Table XIX.', b may be any reading within the range of the table, and iV the corresponding number from the table. Although (i.) is sufficiently accurate for small heights, it is evident, on comparing it with the full formula (iv.), that it becomes more and more inaccurate as the ueight increases. If, in (i.), the reduced height £, were substituted for the observed height /9, the error would be relatively less; for Laplace's formula may also be expanded in the form £ = 1 z 1 1 Z z 1 2 :i i", 106 1.2 'i", A - 1 106 + (V.) ON THE REDUCTION OF THE Tn this formula each term, after the first, is relatively smaller than the corresponding term in (iv.); and if -^ is large, the terms h t liaving sensible magnitude, are alternately positive and negative. Therefore the error, introduced by neglecting all terms beyond the first, is relatively loss in (v.) than in (iv.); but, since B is not known until It has been determined, this formula could only be employed by successive approximation, and is therefore inoonvenient. It may be seen by inspection that, in Table XIX.', N is very B t /5 nearly equal to -5 . N > That this should be so, may be proved thus : — AS already explained xt >. 1 10 5 ii log 105 105 - 1 log 10 j3 10/3 - 1 log /l - 1 \ 10 5 / log /l - 1 1 in aI 105 "*" 2 1 10^ 1 •^2 — nearly, 1 10 5 2 + , -2 10 jS (vi.) fi . *. „N = "^ • ^. nearly, as above stAted, JS t Jo p t BAROMETER TO SEA LEVEL. From (iv.) and (v.), together with (vi.), we may deduce (n.), thus In (iv.), let 6 = /9, wo obtain ^=-4.1+ ' ^N^ 10 1.2 N K fit ^ t ^ t " .i..i.^ 100/9 Similarly from (v.) making b = B, B t 10 1.2 ' 10 ■ ^. lOZf "^ E^t i 13 i B t) 10 1.2 10 ll0/3.^JV;'lO/f. iV ■'"l0/3"^10fll+• But from (vi.) B. N = /(3. .A^ nearly. •. (/3^< + £^<) ^ - 10 +l^-io' (i^ + I^) n«a^ly^ or, neglecting the second terra on the right, 2Z 1 i? = /5 iVT^,- 10 "^^^^y Here < is the mean between the temperatures at the upper and lower stations; whilst in (ii.) these two temperatures are respec- tively employed, in taking out the two numbers. The diflference thus introduced is very trifling ; as may easily be seen, if the value given below for A , be substituted in the expression for JV Formula (ii.), like (v.), is objectionable, in that it assumes a know- ledge of the reduced reading, which it is the object to ascertain. 6 ON THE REDUCTION OP THE The foregoing formulae being all either inconvenient, or not suffici- ■ently accurate except for small elevations, I have formed the accom- panying tables (A and B), to facilitate the calculation of the reduction. It will be noticed from the form of (iii.) that, at any place, the temperature being constant, the reduced reading, and therefore also the reduction, varies aa /?. It is, therefore, suflficient to calculate the reduction N , for one barometer reading (6) only; from which that 2 * for any other reading may be obtained by a simple proportion. It is immaterial whether the value adopted for b be one which could be attained, or not ; it may therefore be chosen with reference to con- venience alone. In Table A, b is taken equal to 100 inches, so that the reduction for any reading (/5) of the barometer, may be obtained by the formula /9 R = 100 2^, Table A was calculated by means of formula (iii.), the value of A^ being taken as* 60345.51 1 -f- t- 32 450 In this table is given the quantity iV , for values of Z equal to 100, 200, 300, &c. feet, for every second degree of temperature from -40° to 100° Fahr., and also, the difference for the next 100 feet at each height. It is sufficient to employ first differences only, in using the table. Table B is intended to diminish the la. our in applying formula (iii.), as will be explained in the sequel. Since calculating these tables, my attention has been called to a paper by Lieut. H. H. C. Dunwoody, U. S. Army, in the Report of the Chief Signal Officer, Washington, 1876. In this paper tables are given, based in part on observations taken by direction of the Chief Signal Officer, U. S. A., on Mount Washington, Mount Mitchell, and Pikes Peak. In the first table is given the decrease of temperature for each 100 feet of elevation at each hour in the day. In the second table is given the "weight of a column of air 100 feet high, at different barometric pressures and temperatures, expressed in decimals of an inch, calculated for north latitude 40°." The third table " shows a r\ J/ * See Guyot's Paper D, pp. 9 and 88. BAROMETER TO SEA LEVEL. Bmall empirical correction, determined from accurate comparison of reduced readings and actual observations, to be applied to Table II." A formula is also given, which may be written R = (N+N') Z, in which N is the number from Table II., and N' that from Table III. If we compare this formula with (iv.), it is evident that some cor- rection to N is necessary, since R does not vary as Z. The correction should, however, depend on the reading of the barometer (/3) as well as on Z and t; but the empirical correction N' is given without regard to /?. The constants and fonnula, on which Table II. is based, are not given; and the rate of variation of the numbers, with the pressure, seems to deviate more than it should, from Boyle's Law. Lieut. Dunwoody's Tables have not, so far as I am aware, been anywhere brought into use. The results given by his Tables II. and III. do not, however, differ much at moderate altitudes from those given by Table A, as will be seen from the following examples : EXAMPLES OF THE USE OP TABLE A. y; Example (1). — At a station 815 ft. above the sea, the reading of \ '' the barometer being 29.112 in., the temperature of the air 46° Fahr., Y to find the reduced reading. From Table A we find ^^N,^ = 3.0047, and the difference for 800 4o 100 ft. = 0.3819. Hence the reduction, 15 100 B = ( 3.0047 + ^ X 0.3819 ) x 0.29112 = 3.0620 x 0.29112 = 0.891, and the reduced reading is 30.003. Guyot's tables D, XVI. and XIX.' used with formula (i.), each give, for this reduction, 0.876 in. Lieut. Dunwoody's tables (ii.) and (iii.) give 0.890. Example (2). — At a station 1100 ft. above the sea, the reading of the barometer being 28 in., the temperature of the air 30° Fahr., to find the reduction to sea level. Here ,^i\^„„ = 3.9071, and the difference for 100 ft. is 0.3990, 1000 30 hence -R = (3.9071 h 0.3990) x 028 = 4.3061 x 0.2S = 1.206. ■PPM 10 ON THE REDUCTION OF THE Guyot's Tables D, XVI. and XIX.', if extended, used with for- mula (i.), would give in this case 1.179, and Lieut. Dunwoody's give 1.204. The value of Table A does not, however, consist so much in sup- plying a basis for working out isolated examples, as in furnishing data, in a convenient form, for the calculation of tables of reduction to sea level, for individual stations. To construct these all that is necessary is, first, to obtain the numbers N for every second Z t degree of temperature, the value assigned to Z being the height of the cistern of the barometer above the sea ; and then, to multiply these numbers by -^, and tabulate the values of the reduction so obtained for values of h, between convenient limits, and at larger or smaller intervals, according as the station is at a slight or consider- able elevation above the sea. The products for any given tempera- ture need not be obtained separately, but may be found, one from another, by continued addition, and the whole process may be very quickly performed with the aid of the Arithmometer of Thomas de Colmar, for use with which the table is specially adapted. The time occupied in forming a table in this way, is less than one half of what is required if the formula of Laplace (iii. of this paper) be employed. For stations more than 1100 ft. above the sea, Table B (from which Table A was deduced) may be employed. In this table tbe values „ 100,000 of A are given ; so that if iV is the number in the table for temperature t, formula iii. becomes , B log — = 100,000 t ' z °'^"«^=ioo;ooo^< + ^^'^- For isolated examples this form is sufficiently convenient; but, in constinieting a table for any station, it is better to make /? = 100. The foimula then becomes g log(l00+^i^J=-^^^+2, 100,000 t BAROMETER TO SEA LEVEL. 1| and the table may be calculated from the value of N in the same Z t way as when Table A is employed. A table for reducing the barometer to sea level is furnished from the Central Office, Toronto, to each station in connection with the Meteorological Service of the Dominion. Formerly these wore computed directly from formula iii. (using a slightly different constant from that given above.) The accom- panying tables were recently calculated to diminish the labour of computation. r In Canada, no reduction for height is applied to the observed temperature of the air; as, although some correction might be of advantage, it is by no means certain that a correction, obtained from observations on a mountain, would be suited to a station on an elevated table-land. The correction, if it were applied, would, how- ever, be very small at nearly all our stations. I hope to discuss, more fully, on some future occasion the ouestion of the necessity for a correction to the observed temperature of the air in reducing barometric readings. 12 ON THE REDUCTION OF THE TABLE A. Giving the value of JV for various temperatures and elevations, and the difference Z i for an additional 100 feet at each height. 2 100 Feet. 200 Feet. 300 Feet. 400 Feet. 600 Feet. 1 Diff. Diff. Diff. Diff. Diff. B U for N for N for N for i^ for a H Z t 100 ft. Z t 100 ft. Z t 100 ft. Z t 100 ft. Z t 100 ft. ^ O —40 0.4553 .4573 0.9126 .4595 1.3721 .4615 1.8336 .4636 2.2972 .4658 o —40 —38 0.4529 .4549 0.9078 .4570 1.3648 .4590 1.8238 .4612 2.2850 .4«)32 —38 —36 0.4505 .4525 0.9030 .4546 1.3576 .4566 1.8142 .4587 2.2729 .4007 —36 —34 0.4482 .4501 0,8983 .4522 1.3505 .4542 1.8047 .4562 2.2609 .4583 —34 —32 0.4458 .4478 0.8936 .4498 1.3434 .4519 1.7953 .4538 2.2491 .4558 -32 —30 0.4435 .4455 0.8890 .4475 1.3365 .4494 1.7859 .4515 2.2374 .4534 30 —28 0.4412 .4432 0.8844 .4452 1.3296 .4471 1.7707 .4491 2.2258 .4510 —28 —26 0.4300 .4409 0.8799 .4428 1.3227.4448 1.7675 .4468 2.2143 .4487 —26 —24 0.4368 .4386 0.8754 .4406 1.3160.4425 1.7585 .4444 2.2029 .4464 —24 —22 0.4345 .4365 0.8710 .4383 1.3093 .4402 1.7495 .4422 2.1917 .4440 —22 —20 0.4324 .4342 0.8666 .4361 1.3027 .4380 1.7407 .4398 2.1805 .4418 —20 —18 0.4302 .4320 0.8622 .4339 1.2961 .4358 1.7319 .4376 2.1695 .4395 —18 —16 0.4280 .4299 0.8579 .4317 1.2896.4336 1.7232 .4354 2.1586 .4373 —16 —14 0.4259 .4277 0.8536 .4290 1.2832 .4314 1.7146 .4332 2.1478 .4351 —14 —12 0.4238 .4256 0.8494 .4274 1.2768 .4293 1.7061 .4310 2.1371 .4329 —12 —10 0.4217 .4235 0.8452 .4253 1.2705 .4271 1.6976 .4289 2.1265 .4307 —10 — 8 0.4197 .4214 0.8411 .4232 1.2643 .4250 1.6893 .4267 2.1160 .4286 — 8 — 6 0.4176 .4194 0.8370 .4211 1.2581 .4229 1.6810 .4247 2.1057 .4264 — 6 — 4 0.4156 .4)73 0.8329 .4191 1.2520 !4208 1.6728 .4226 2.0954 .4243 — 4 — 2 0.4136 .4153 0.8289 .4171 1.2460 .4187 1.6647 .4205 2.0852 .4222 — 2 0.4116 .4133 0.8249 .4151 1.2400 .4167 1.6567 .4184 2.0751 .4202 2 0.4097.4113 0.8210;.4130 1.2340 .4147 1.6487 .4164 2.0651 .4182 2 4 0.4077 .4094 0.8171.4110 1.228i:.4128| 1.6409 .4144 2.0553.4160 4 6 0.4058 .4074 0.8132 .4091 1.2223 .4107 1.6330 .4125 2.0455.4141 6 8 0.4039 .4055 0.8094 .4071 1.2165 .4088 1.6253 .4105 2.0358 .4121 8 10 0.4020 .4036 0.8056 .4052 1.2108 .4069 1.6177 .4085 2.0262 .4101 10 12 0.4001 .4017 0.8018 .4033 1.2051 .4050 1.6101 .4065 2.0166.4082 12 14 0.3982 .399!> 0.7981'. 4014 1.1995 .4031 1.6026 .4046 2.0072 .4063 14 16 0.3964 .3980 0.7944 .3996 1.1940 .4011 1.5951 .4028 1.9979.4043 16 18 0.3946 .3961 0.7907 .3978 1.1885 .3992 1.5877 .4009 1.9886 .4025 18 20 0.3928 .3943 0.7871 .3959 1. 1830 .3974 1.5804 .3990 1.9794 .4006 20 22 0.3910 .3925 0.7835 .3941 1.1776 .3956 1.5732 .3972 1.9704.3987 22 24 0.3892 .3908 0.7800.3922 1.1722 .3938 1.5660 .3954 1.9614.3968 24 26 0.3875 .3889 0.7764.3905 1.1669 .3920 1.5589.3935 1.9524.3951 26 28 0.3857 .3872 0.7729.3888 1 1.1617 .3902 1.5519..3917 1.9436 .3932 1 28 BAROMETER TO SEA LEVEL. 18 TABLE A.— Continued. 600 Feet. 700 Feet. 800 Feet. 900 Feet, 1000 Feet. Diff. Diff. Diff. Diff. Diff 2 a N for N for JV for N for A' lor S ^ Z t 100 ft. Z t 100 ft. z t 100 ft. Z t 100 ft. Z t 100 ft. H o -40 2.7630 .4678 3.2308 .4700 3.7008 .4721 4.1729 .4743 4.6472 .4764 o -40 —38 2.7482 .4653 3.2135 .4675 3.6810 .4695 4.1505 .4717 4.6222 .4738 -38 —36 2.7336 .4629 3.1965 .4649 3.6614 .4670 4.1284 .4690 4.5974 .4713 —36 —34 2.7192 .4603 3.1795 .4624 3.6419 .4645 4.1064 .4666 4.5730 .4686 —34 —32 2.7049 .4579 3.1628 .4599 3.6227 .4620 4.0847 .4640 4.5487 .4661 -32 —30 2.6908 .4555 3.1463 .4574 3.6037 .4595 4.0632 .4616 4.5248 .4636 —30 —28 2.6768 .4531 3.1299 .4550 3.5849 .4571 4.0420 .4591 4.5011 .4611 —28 —26 2.6630 .4507 3.1137 .4526 3.5663 .4546 4.0209 .4567 4.4776 .4586 —26 —24 2.6493 .4483 3.0976 .4503 3.5479 .4522 4.0001 .4543 4.4544 .4562 —24 —22 2.6357 .4460 3.0817 .4480 3.5297 .4498 3.9795 .4519 4.4314 .4538 -22 —20 2.6223 .4437 3.0660 .4456 3.5116 .4475 3.9591 .4495 4.4086 .4514 —20 —18 2.6090 .4414 3.0504 .4433 3.4937 .4453 3.9390 .4471 4.3861 .4490 —18 —16 2.5959 .4391 3.0350 .4411 3.4761 .4429 3.9190 .4448 4.3638 .4467 —16 —14 2.5829 .4369 3.0198 .4388 3.4586 .4406 3.8992 .4425 4.3417 .4444 —14 —12 2.5700 .4347 3.0047 .4365 3.4412 .4384 3.8796 .4403 4.3199 .4421 —12 —10 2.5572 .4325 2.9897 .4344 3.4241 .4362 3.8603 .4380 4.2983 .4398 —10 — 8 2.5446 .4303 2.9749 .4.322 3.4071 .4340 3.8411 .4358 4.2769 .4376 — 8 — 6 2.5321 .4282 2.9603 .4300 3.3903 .4318 3.8221 .4336 4.2557 .4354 — 6 — 4 2.5197 .4261 2.9458 .4278 3.3736 .4297 3.8033 .4314 4.2347 .4332 — 4 — 2 2.5074 .4240 2.9314 .4257 3.3571 .4275 3.7846 .4293 4.2139 .4310 — 2 2.4953 .4219 2.9172 .4236 3.3408 .4254 3.7662 .4271 4.1933 .4289 2 2.4833 .4198 2.9031 .4215 3.3246 4233 3.7479i.4250 4.1729 .4268 2 4 2.4713 .4178 2.8891 .4195 3.3086 .4212 3.7298 .4230 4.1528 .4246 4 6 2.4596 .4157 2.8753 .4175 3.2928 .4191 3.71191.4209 4.1328 .4225 6 8 2.4479 .4137 2.8616 .4153 3.2769 .4173 3.6942 .4188 4.1130 .4205 8 10 2.4363 .4118 2.8481 .4134 3.2615 .4151 3.6766 .4168 4.09.34 .4184 10 12 2.4248 .4098 2.8346 .4115 3.2461 .4131 3.6592!.4147 4.0739 .4165 12 14 2.4135 .4078 2.8213 .4095 3.2308 .4111 .3. 6419'. 4128 4.0547 .4144 14 16 2.4022 .4059 2.8081 .4076 3.2157 .4092 3.62491.4107 4.0356 .4125 16 18 2.3911 .4040 2.7951 .4056 3.2007 .4072 3.6079 .4089 4.0168 .4104 18 20 2.3800 .4021 2.7821 .4038 3.1859 .4053 3.5912 .4069 3.9981 .4085 20 22 2.3691 .4002 2.7693 .4019 3.1712 .4034 3.5746.4049 3.9795 4066 22 24 2.3582 .3984 2.7566 .4000 3.1566 .4015 3.5581 U031 3.9612 .4046 24 26 2.3475 .3965 2.7440 .3981 3.1421 .3997 .3.5418.4012 3.9430 .4027 26 28 2.3368 .3948 2.7316 .3962 3.1278 .3978 3.5256.3994 1 3.9250 .4008 28 14 ON THE REDUCTION OF THE TABLE A.— Continued. 1 100 Feet. 200 Feet. 300 Feet. 400 Feet. 600 Feet. t 1 Diff. Diff. Diff. Diff. Diff. N for W for iV for iV for iV for S H Z i 100 ft. z t 100 ft. z t 100 ft. z % 100 ft. z t 100 ft. S o 30 0.3840 .3855 0.7695 .3869 1.1564 .3885 1.5449 .3899 1.9348 .3915 30 32 0.3823 .3838 0.7661 .3852 1.1513 .3867 1.5380 .3882 1.9262 .3896 32 34 0.3806 .3820 0.7626 .3836 1.1462 .3849 1.5311 .3864 1.9175 .3879 34 36 0.3789 .3804 0.7593 .3818 1.1411 .3832 1.5243 .3847 1.9090 .3862 36 38 0.3773 .3786 0.7559 .3801 1.1360 .3816 1.5176 .3830 1.9006 .3844 38 40 0.3756 .3770 0.7526 .3785 1.1311 .3798 1.5109 .3813 1.8922 .3827 40 42 0.3740 .3753 0.7493 .3768 1.1261 .3782 1.5043 .3796 1.8839 .3810 42 44 0.3723 .3738 0.7461 .3751 1.1212 .3765 1.4977 .3780 1.8757 .3793 44 46 0.3707 .3722 0.7429 .3734 1.1163 .3749 1.4912 .3763 1.8675 .3777 46 48 0.3691 .3706 0.7397 .3718 1.1115 .3733 1.4848 .3746 1.8594 .3760 48 50 0.3676 .3689 0.7365 .3703 1.1068 .3716 1.4784 .3730 1.8514 .3744 50 52 0.3G60 .:>673 0.7333 .3687 1.1020 .3700 1.4720 .3714 1.8434 .3728 52 54 0.3644 .3658 0.7302 .3671 1.0973 .3685 1.4658 .3698 1.8356 .3711 54 56 0.3629 .3642 0.7271 .3656 1.0927 .3668 1.4595 .3682 1.8277 .3696 56 58 0.3614 .3627 0.7241 .3640 1.0881 .3653 1.4534 .3666 1.8200 .3679 58 60 0.3599 .3611 0.7210 .3625 1.0835 .3037 1.4472 .3651 1.8123 .3664 60 62 0.3584 .3596 0.7180 .3609 1.0789 .3623 1.4412 .3635 1.8047 .3648 62 64 0.3569 .3581 0.7150 .3594 1.0744 .3607 1.4351 .3620 1.7971 .3633 64 66 0.3554 .3566 0.7120 .3580 1.0700 .3592 1.4292 .3604 1.7896 .3618 66 68 0.3539 .3552 0.7091 .3564 1.0655 .3577 1.4232 .o590 1.7822 .3602 68 70 0.3525 .3537 0.7062 .3550 1.0612 .3562 1.4174 .3574 1.7748 .3588 70 72 0.3510 .3523 0.7033 .3535 1.0568 .3547 1.4115 .3560 1.7675 .3573 72 74 0.3496 .3508 0.7004 .3521 1.0525 .3533 1.4058 .3545 1.7603 .3557 74 76 0.3482 .3494 0.6976 .3506 1.0482 .3518 1.4000 .3531 1.7531 .3543 76 78 0.3468 .3480 0.6948 .3492 1.0440 .3504 1.3944 .3516 1.7460 .3529 78 80 0.3454 .3466 0.6920 .3477 1.0397 .3490 1.3887 .3502 1.7389 .3514 80 82 0.3440 .3452 0.6892 .3464 1.0356 .3475 1.3831 .3488 1.7319 .3499 82 84 0.3426 .3438 0.6864 .3450 1.0314 .3462 1.3776 .3473 1.7249 .3486 84 86 0.3413 .3424 0.6>37 .3436 1.0273 .3448 1.3721 .3459 1.7180 .3471 86 88 0.3399 .3411 0.6810 .3422 1.0232 .3434 1.3666 .3446 1.7112 .3457 88 90 0.3386 .3397 0.6783 .3409 1.0192 .3420 1.3612 .3432 1.7044 .3443 90 92 0.3372 .3384 0.6756 .3395 1.0151 .3407 1.3558 .3418 1.6976 .3430 92 94 0.3359 .3371 0.6730 .3382 1.0112 .3383 1.3505 .3404 1.6909 .3416 94 96 0.3346 .3358 0.6704 .3368 1.0072 .3380 1.3452 .3391 1.6843 .3403 96 98 0.3333 .3344 0.6677 .3356 1.0033 .3366 1.3399 .3378 1.6777 .3389 98 100 0.3320 .3332 0.6652 .3342 0.9994 .3353 1.3347 .3365 1.6712 .3376 100 BAROMETER TO SEA LEVEL. 16 TABLE A.— Continued. t 600 Feet. 700 Feet. 800 Feet. 900 Feet. 1000 Feet. 1 Diff. Diflf. Diff. Diff. Diff. a N for N for N for N for N for i & Z t 100 ft. Z t 100 ft Z t 100 ft. Z t 100 ft. Z t 100 ft. H o 30 2.3263 .3929 2.7192 .3945 3.1137 .3959 3.5096 .3975 3.9071 .3990 30 32 2.3158 .3912 2.7070 .3926 3.0996 .3941 3.4937 .3957 3.8894 .3972 32 34 2.3054 .3894 2.6948 .3909 3.0857 .3923 3.4780 .3939 3.8719 .3953 34 36 2.2952 .3876 2.6828 .3891 3.0719 .3905 3.4624 .3921 3.8545 .3935 36 38 2.2850 .3859 2.6709 .3873 3.0582 .3888 3.4470 .3903 3.8373 .3917 38 40 2.2749 .3842 2.6591 .3855 3.0446 .3871 3.4317 .3885 3.8202 .3899 40 42 2.2649 .3824 2.6473 .3839 3.0312.38531 3.4165 .3868 3.8033 .3882 42 44 2.2550 .3807 2.6357 .3822 3.0179 .3836 3.4015 .3850 3.7865 .3864 44 46 2.2452 .3790 2.6242 .3805 3.0047 .3819 3.3866 .3833 3.7699 .3847 46 48 2.2354 .3774 2.6128 .3788 2.9916 .3802 3.3718 .3816 3.7534 .3830 48 50 2.2258 .3757 2.6015 .3771 2 9786 .3785 3.3571 .3799 3.7370 .3813 50 52 2.2162 .3741 2.5903 .3755 2.9658 .3768 3.3426 .3783 3.7209 .3796 52 54 2.2067 .3725 2.5792 .3738 2.9530 .3752 3.3282 .3766 3.7048 .3779 54 56 2.1973 .3709 2.5682 .3722 2.9404 .3735 3.3139 .3750 3.6889 .3763 56 58 2.1879 .3693 2.5572 .3706 2.9278 .3720 3.2998 .3733 3.6731 .3747 58 60 2.1787 .3677 2.5464 .3690 2.9154 .3704 3.2858 .3717 3.6575 .3730 60 62 2.1695 .3661 2.5356 .3675 2.9031 .3688 3.2719 .3700 3.6419 .3715 62 64 2.1604 .3646 2.5250 .3659 2.8909 .3672 3.2581 .3685 3.6266 .3698 64 66 2.1514 .3630 2.5144 .3644 2.8788 .3656 3.2444 .3669 3.6113 3682 66 68 2.1424 .3616 2.5040 .3627 2.8667 .3641 3.2308 .3654 3.5962 .3666 68 70 2.1336 .3600 2.4936 .3613 2.8549 .3625 3.2174 .3638 3.5812 .3651 70 72 2.1248 .3585 2.4833 .3597 2.8430 .3610 3.2040 .3623 3.5663 .3636 72 74 2.1160 .3570 2.4730 .3583 2.8313 .3595 3.1908 .3608 3.5516 .3620 74 76 2.1074 .3555 2.4629 .3568 2.8197 .3580 3.1777 .3592 3.5369 .3605 76 7& 2.0989 .3540 2.4529 .3552 2.8081 .3566 3.1647 .3577 3.5224 .3590 78 80 2.0903 .3526 2.4429 .3538 2.7967 .3551 3.1518 .3562 3.5080 .3575 80 82 2.0818 .3512 2.4330 .3524 2.7854 .3535 3.1389 .3548 3.4937 .3561 82 84 2.0735 .3497 2.4232 .3509 2.7741 .3522 3.1263 .3533 3.4796 .3545 84 86 2.0651 .3484 2.4135 .3495 2.7630 .3507 3.1137 .3518 3.4655 .3531 86 88 2.0569 .3469 2.4038 .3481 2.7519 .3493 3.1012 .3504 3.4516 .3514 88 90 2.0487 .3455 2.3942 .3467 2.7409 .3479 3.0888 .3490 3.4378 .3502 90 92 2.0406 .3441 2.3847 .3453 2.7300 .3465 3.0765 .3476 3.4241 .3488 92 94 2.0325 .3428 2 3753 .3439 2.7192 .3451 3.0643 .3462 3.4105 .3474 94 96 2.0246 .3414 2.3660 .3425 2.7085 1.3437 3.0522 .3448 3.3970 .3460 96 98 2.0166 .3401 2.3567 .3411 2.6978 .3424 4.0402 .3434 3.3836 .3446 68 100 2.0088 .3387 2.3475 .3398 2.6873 .3409 3.0282 .3421 3.3703 .3432 100 16 REDUCTION OF THE BAROMETER TO SEA LEVEL. TABLE B, 100,000 Giving the value of — -j — • for vaiioua values of t, the value of A^ being 60345 .51 \ 1 + -— - \ \ 450 J 1 100,000 1 100,000 100,000 o —40 1.972767 8 1.750483 o 56 1.573219 38 1.962384 10 1.742303 58 1.566609 —36 1.952110 12 1.734200 60 1.560054 -34 1.941942 14 1.726171 62 1.553554 32 1.931880 16 1.718216 64 1.547108 —30 1.921922 18 1.710335 66 1.540715 —28 1.912066 20 1.702525 68 1.534374 —26 1.902311 22 1.694786 70 1.528086 —24 1.892654 24 1.687117 72 1.521849 —22 1.883096 26 1.679518 74 1.515662 —20 1.873633 28 1.671986 76 1.509526 —18 1.864265 30 1.664522 78 1.503439 —16 1.854990 32 1.657124 80 1.497401 —14 1.845807 34 1.649792 82 1.491412 —12 1.836714 36 1.642524 84 1.485470 —10 1.827710 38 1.635320 86 1.479575 — 8 1.818795 40 1.628179 88 1.473727 — 6 1.809966 42 1.621100 90 1.467925 — 4 1.801222 44 1.614082 92 1.462168 — 2 1.792562 46 1.607125 94 1.456457 1.783985 48 1.600227 96 1.450790 2 1.775490 50 1.593389 98 1.445166 4 1.767075 52 1.586608 100 1.439587 6 1.758740 54 1.579885 '<■ ■'7'! '/§! 1 ^t '. -=^< t>: ,j;,^;:A;|,,>i^.:;; ^. S'Virj , 'J/ "<.i f*.^ ^ V ,/.j ^.*^ /-;i''* < ' 'V" M^i^'