Chapter III: Preface (3)

+------------+------------+----------+
|Alcohol in | Specific |Difference|
|100 measures| gravity | of the |
| of spirit. |at 60° Fahr.| sp. gr. |
+------------+------------+----------+
| 0 | 9991 | |
| 1 | 9976 | 15 |
| 2 | 9961 | 15 |
| 3 | 9947 | 14 |
| 4 | 9933 | 14 |
| 5 | 9919 | 14 |
| 6 | 9906 | 13 |
| 7 | 9893 | 13 |
| 8 | 9881 | 12 |
| 9 | 9869 | 12 |
| 10 | 9857 | 12 |
| 11 | 9845 | 12 |
| 12 | 9834 | 11 |
| 13 | 9823 | 11 |
| 14 | 9812 | 11 |
| 15 | 9802 | 10 |
| 16 | 9791 | 11 |
| 17 | 9781 | 10 |
| 18 | 9771 | 10 |
| 19 | 9761 | 10 |
| 20 | 9751 | 10 |
| 21 | 9741 | 10 |
| 22 | 9731 | 10 |
| 23 | 9720 | 11 |
| 24 | 9710 | 10 |
| 25 | 9700 | 10 |
| 26 | 9689 | 11 |
| 27 | 9679 | 10 |
| 28 | 9668 | 11 |
| 29 | 9657 | 11 |
| 30 | 9646 | 11 |
| 31 | 9634 | 12 |
| 32 | 9622 | 12 |
| 33 | 9609 | 13 |
| 34 | 9596 | 13 |
| 35 | 9583 | 13 |
| 36 | 9570 | 13 |
| 37 | 9556 | 14 |
| 38 | 9541 | 15 |
| 39 | 9526 | 15 |
| 40 | 9510 | 16 |
| 41 | 9494 | 16 |
| 42 | 9478 | 16 |
| 43 | 9461 | 17 |
| 44 | 9444 | 17 |
| 45 | 9427 | 17 |
| 46 | 9409 | 18 |
| 47 | 9391 | 18 |
| 48 | 9373 | 18 |
| 49 | 9354 | 19 |
| 50 | 9335 | 19 |
| 51 | 9315 | 20 |
| 52 | 9295 | 20 |
| 53 | 9275 | 20 |
| 54 | 9254 | 21 |
| 55 | 9234 | 20 |
| 56 | 9213 | 21 |
| 57 | 9192 | 21 |
| 58 | 9170 | 22 |
| 59 | 9148 | 22 |
| 60 | 9126 | 22 |
| 61 | 9104 | 22 |
| 62 | 9082 | 22 |
| 63 | 9059 | 23 |
| 64 | 9036 | 23 |
| 65 | 9013 | 23 |
| 66 | 8989 | 24 |
| 67 | 8965 | 24 |
| 68 | 8941 | 24 |
| 69 | 8917 | 24 |
| 70 | 8892 | 25 |
| 71 | 8867 | 25 |
| 72 | 8842 | 25 |
| 73 | 8817 | 25 |
| 74 | 8791 | 26 |
| 75 | 8765 | 26 |
| 76 | 8739 | 26 |
| 77 | 8712 | 27 |
| 78 | 8685 | 27 |
| 79 | 8658 | 27 |
| 80 | 8631 | 27 |
| 81 | 8603 | 28 |
| 82 | 8575 | 28 |
| 83 | 8547 | 28 |
| 84 | 8518 | 29 |
| 85 | 8488 | 30 |
| 86 | 8458 | 30 |
| 87 | 8428 | 30 |
| 88 | 8397 | 31 |
| 89 | 8365 | 32 |
| 90 | 8332 | 33 |
| 91 | 8299 | 33 |
| 92 | 8265 | 34 |
| 93 | 8230 | 35 |
| 94 | 8194 | 36 |
| 95 | 8157 | 37 |
| 96 | 8118 | 39 |
| 97 | 8077 | 41 |
| 98 | 8034 | 43 |
| 99 | 7988 | 46 |
| 100 | 7939 | 49 |
+------------+------------+----------+

_Remarks on the preceding Table of Alcohol._

The third column of this table exhibits the differences of the specific gravities, which give the denominator of the fraction for such densities as are not found sufficiently near in the table; and the difference of their numerators is the next greatest to the density found in the table. For example: if the specific gravity of the liquor found for 60° Fahr. = 9605 (the per centage will be between 33 and 34), the difference from 9609 (which is the next greatest number in the table) = 4, and the fraction is 4/13; therefore the true per centage is 33-4/13. From the construction of this table the per centage of alcohol by weight may also be found. For instance: we multiply the number representing the _volumes_ of alcohol (given in the table for any determinate specific gravity of the mixture) by the specific gravity of the pure alcohol, that is, by 7939, and the product is the number of pounds of alcohol in so many pounds as the specific gravity multiplied by 100 gives. Thus, in the mixture of 9510 specific gravity, there are 40 measures of alcohol; hence there are also in 95,100 pounds of this spirit 7939 + 40 = 31·756 pounds of alcohol; and in 100 pounds of the spirits of 0·9510 specific gravity, 33·39 pounds of alcohol are contained.

As the preceding table gives the true alcoholic content when the portion of spirit under trial has the normal temperature of 60° Fahr., the following table gives the per centage of alcohol for the specific gravities corresponding to the accompanying temperatures.

For example: if we have a spirituous liquor at 80° Fahr., whose specific gravity is 0·9342, the alcohol present is 45 per cent. of the volume, or that specific gravity at that temperature is equal to the specific gravity 0·9427 at the normal temperature of 60° Fahr. This table may also be employed for every degree of the thermometer and every per centage, so as to save computation for the intervals. It is evident from inspection that a difference of 5° Fahr. in the temperature changes the specific gravity of the liquor by a difference nearly equal to 1 volume per cent. of alcohol; thus at 35° and 85° Fahr. the very same specific gravity of the liquor shows nearly 10 volumes per cent. of alcohol more or less; the same, for example, at 60 and 40 per cent.

+-------+-----------------------------------------------------------+
|Alcohol| Temperature. |
| per +----+----+----+----+----+----+----+----+----+----+----+----+
| cent. | 30°| 35°| 40°| 45°| 50°| 55°| 60°| 65°| 70°| 75°| 80°| 85°|
| | F.| F.| F.| F.| F.| F.| F.| F.| F.| F.| F.| F.|
+-------+----+----+----+----+----+----+----+----+----+----+----+----+
| 0 |9994|9997|9997|9998|9997|9994|9991|9987|9991|9976|9970|9962|
| 5 |9924|9926|9926|9926|9925|9922|9919|9915|9909|9903|9897|9889|
| 10 |9868|9869|9868|9867|9865|9861|9857|9852|9845|9839|9831|9823|
| 15 |9823|9822|9820|9817|9813|9807|9802|9796|9788|9779|9771|9761|
| 20 |9786|9782|9777|9772|9766|9759|9751|9743|9733|9722|9711|9700|
| 25 |9753|9746|9738|9729|9720|9709|9700|9690|9678|9665|9652|9638|
| 30 |9717|9707|9695|9684|9672|9659|9646|9632|9618|9603|9588|9572|
| 35 |9671|9658|9644|9629|9614|9599|9583|9566|9549|9532|9514|9495|
| 40 |9615|9598|9581|9563|9546|9528|9510|9491|9472|9452|9433|9412|
| 45 |9544|9525|9506|9486|9467|9447|9427|9406|9385|9364|9342|9320|
| 50 |9460|9440|9420|9399|9378|9356|9335|9313|9290|9267|9244|9221|
| 55 |9368|9347|9325|9302|9279|9256|9234|9211|9187|9163|9139|9114|
| 60 |9267|9245|9222|9198|9174|9150|9126|9102|9076|9051|9026|9000|
| 65 |9162|9138|9113|9088|9063|9038|9013|8988|8962|8936|8909|8882|
| 70 |9046|9021|8996|8970|8944|8917|8892|8866|8839|8812|8784|8756|
| 75 |8925|8899|8873|8847|8820|8792|8765|8738|8710|8681|8652|8622|
| 80 |8798|8771|8744|8716|8688|8659|8631|8602|8573|8544|8514|8483|
| 85 |8663|8635|8606|8577|8547|8517|8488|8458|8427|8396|8365|8333|
| 90 |8517|8486|8455|8425|8395|8363|8322|8300|8268|8236|8204|8171|
+-------+----+----+----+----+----+----+----+----+----+----+----+----+

The importance of extreme accuracy in determining the density of alcoholic mixtures in the United Kingdom, on account of the great revenue derived from them to the State, and their consequent high price in commerce, induced the Lords of the Treasury a few years ago to request the Royal Society to examine the construction and mode of applying the instrument now in use for ascertaining and charging the duty on spirits. This instrument, which is known and described in the law as Sikes’s hydrometer, possesses, in many respects, decided advantages over those formerly in use. The committee of the Royal Society state, that a definite mixture of alcohol and water is as invariable in its value as absolute alcohol can be; and can be more readily, and with equal accuracy, identified by that only quality or condition to which recourse can be had in practice, namely, specific gravity. The committee further proposed, that the standard spirit be that which, consisting of alcohol and water alone, shall have a specific gravity of 0·92 at the temperature of 62° Fahr., water being unity at the same temperature; or, in other words, that it shall at 62° weigh 92/100 or 23/25 of an equal bulk of water at the same temperature.

This standard is rather weaker than the old proof, which was 12/13, or 0·923; or in the proportion of nearly 1·1 gallon of the present proof spirit per cent. The proposed standard will contain nearly one half by weight of absolute alcohol. The hydrometer ought to be so graduated as to give the indication of strength; not upon an arbitrary scale, but in terms of specific gravity at the temperature of 62°.

The committee recommend the construction of an equation table, which shall indicate the same strength of spirit at every temperature. Thus in standard spirit at 62° the hydrometer would indicate 920, which in this table would give proof spirit. If that same spirit were cooled to 40°, the hydrometer would indicate some higher number; but which, being combined in the table with the temperature as indicated by the thermometer, should still give proof or standard spirit as the result.

It is considered advisable, in this and the other tables, not to express the quality of the spirit by any number over or under proof, but to indicate at once the number of gallons of standard spirit contained in, or equivalent to, 100 gallons of the spirit under examination. Thus, instead of saying 23 over proof, it is proposed to insert 123; and in place of 35·4 under proof, to insert its difference to 100, or 64·6.

It has been considered expedient to recommend a second table to be constructed, so as to show the bulk of spirit of any strength at any temperature, relative to a standard bulk of 100 gallons at 62°. In this table a spirit which had diminished in volume, at any given temperature, 0·7 per cent., for example, would be expressed by 99·3; and a spirit which had increased at any given temperature 0·7 per cent., by 100·7.

When a sample of spirit, therefore, has been examined by the hydrometer and thermometer, these tables will give first the proportion of standard spirit at the observed temperature, and next the change of bulk of such spirit from what it would be at the standard temperature. Thus, at the temperature of 51°, and with an indication (sp. gr.) of 8240, 100 gallons of the spirit under examination would be shown by the first table to be equal to 164·8 gallons of standard spirit of that temperature; and by the second table it would appear that 99·3 gallons of the same spirit would become 100 at 62°, or in reality contain the 164·8 gallons of spirit in that state only in which it is to be taxed.

But as it is considered that neither of these tables can alone be used for charging the duty (for neither can express the actual quantity of spirit of a specific gravity of 0·92 at 62° in 100 gallons of stronger or weaker spirit at temperatures above or below 62°), it is considered essential to have a third table, combining the two former, and expressing this relation directly, so that upon mere inspection it shall indicate the proportion of standard spirit in 100 gallons of that under examination in its then present state. In this table the quantities should be set down in the actual number of gallons of standard spirit at 62°, equivalent to 100 of the spirit under examination; and the column of quantities may be expressed by the term _value_, as it in reality expresses the proportion of the only valuable substance present. As this will be the only table absolutely necessary to be used with the instrument for the purposes of the excise, it may, perhaps, be thought unnecessary to print the former two.

The following specimen table has been given by the committee:--

+-------------------------------++----------------------------+
| Temperature 45°. || Temperature 75°. |
+--------------+---------+------++-----------+---------+------+
|Indication.[3]|Strength.|Value.||Indication.|Strength.|Value.|
+--------------+---------+------++-----------+---------+------+
| 9074 | 114·5 | || 8941 | 114·5 | |
| 7 | 114·3 | || 4 | 114·3 | |
| 9 | 114·2 | || 5 | 114·2 | |
| 81 | 114·0 | || 8 | 114·0 | |
| 3 | 113·9 | || 9 | 113·9 | |
| 5 | 113·7 | || 52 | 113·7 | |
| 6 | 113·6 | || 3 | 113·6 | |
| 9 | 113·4 | || 6 | 113·4 | |
| 90 | 113·3 | || 7 | 113·3 | |
| 3 | 113·1 | || 9 | 113·1 | |
+--------------+---------+------++-----------+---------+------+

[3] By specific gravity.

The mixture of alcohol and water, taken as spirit in Mr. Gilpin’s tables, is that of which the specific gravity is 0·825 at 60° Fahr., water being unity at the same temperature. The specific gravity of water at 60° being 1000, at 62° it is 99,981. Hence, in order to compare the specific gravities given by Mr. Gilpin with those which would result when the specific gravity of water at 62° is taken at unity, all the former numbers must be divided by 99,981.

Table of the Specific Gravities of different Mixtures, by Weight, of Alcohol and Water, at different Temperatures; constructed by Mr. Gilpin, for the use of the British Revenue on Spirits.

+------+-------+-------+-------+-------+-------+-------+-------+
|Tem- | Pure | 100 | 100 | 100 | 100 | 100 | 100 |
|pera- | Alco- |Alcohol|Alcohol|Alcohol|Alcohol|Alcohol|Alcohol|
|ture, | hol. | 5 | 10 | 15 | 20 | 25 | 30 |
|Fahr. | | Water.| Water.| Water.| Water.| Water.| Water.|
+------+-------+-------+-------+-------+-------+-------+-------+
|_Deg._| | | | | | | |
| 30 |0·83896|0·84995|0·85957|0·86825|0·87585|0·88282|0·88921|
| 35 | ·83672| ·84769| ·85729| ·86587| ·87357| ·88059| ·88701|
| 40 | ·83445| ·84539| ·85507| ·86361| ·87184| ·87838| ·88481|
| 45 | ·83214| ·84310| ·85277| ·86131| ·86905| ·87613| ·88255|
| 50 | ·82977| ·84076| ·85042| ·85902| ·86676| ·87384| ·88030|
| 55 | ·82736| ·83834| ·84802| ·85664| ·86441| ·87150| ·87796|
| 60 | ·82500| ·83599| ·84568| ·85430| ·86208| ·86918| ·87569|
| 65 | ·82262| ·83362| ·84334| ·85193| ·85976| ·86686| ·87337|
| 70 | ·82023| ·83124| ·84092| ·84951| ·85736| ·86451| ·87105|
| 75 | ·81780| ·82878| ·83851| ·84710| ·85496| ·86212| ·86864|
| 80 | ·81530| ·82631| ·83603| ·84467| ·85248| ·85966| ·86622|
| 85 | ·81291| ·82396| ·83371| ·84243| ·85036| ·85757| ·86411|
| 90 | ·81044| ·82150| ·83126| ·84001| ·84797| ·85518| ·86172|
| 95 | ·80794| ·81900| ·82877| ·83753| ·84550| ·85272| ·85928|
| 100 | ·80548| ·81657| ·82630| ·83513| ·84038| ·85031| ·85688|
+------+-------+-------+-------+-------+-------+-------+-------+

+------+-------+-------+-------+-------+--------+-------+-------+
|Tem- | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
|pera- |Alcohol|Alcohol|Alcohol|Alcohol|Alcohol |Alcohol|Alcohol|
|ture, | 35 | 40 | 45 | 50 | 55 | 60 | 65 |
|Fahr. | Water.| Water.| Water.| Water.| Water. | Water.| Water.|
+------+-------+-------+-------+-------+--------+-------+-------+
|_Deg._| | | | | | | |
| 30 |0·89511|0·90054|0·90558|0·91023|0·91449 |0·91847|0·92217|
| 35 | ·89294| ·89839| ·90345| ·90811| ·91241 | ·91640| ·92009|
| 40 | ·89073| ·89617| ·90127| ·90596| ·91026 | ·91428| ·91799|
| 45 | ·88849| ·89396| ·89909| ·90380| ·90812 | ·91211| ·91584|
| 50 | ·88626| ·89174| ·89684| ·90160| ·90596 | ·90997| ·91370|
| 55 | ·88393| ·88945| ·89458| ·89933| ·90367 | ·90768| ·91144|
| 60 | ·88169| ·88720| ·89232| ·89707| ·90144 | ·90549| ·90927|
| 65 | ·87938| ·88490| ·89006| ·89479| ·89920 | ·90328| ·90707|
| 70 | ·87705| ·88254| ·88773| ·89252| ·89695 | ·90104| ·90484|
| 75 | ·87466| ·88018| ·88538| ·89018| ·89464 | ·89872| ·90252|
| 80 | ·87228| ·87776| ·88301| ·88781| ·89225 | ·89639| ·90021|
| 85 | ·87021| ·87590| ·88120| ·88609| ·89043 | ·89460| ·89843|
| 90 | ·86787| ·87360| ·87889| ·88376| ·88817 | ·89230| ·89617|
| 95 | ·86542| ·87114| ·87654| ·88146| ·88588 | ·89003| ·89390|
| 100 | ·86302| ·86879| ·87421| ·87915| ·883671| ·88769| ·89158|
+------+-------+-------+-------+-------+--------+-------+-------+

+------+-------+-------+-------+-------+-------+-------+-------+
|Tem- | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
|pera- |Alcohol|Alcohol|Alcohol|Alcohol|Alcohol|Alcohol|Alcohol|
|ture, | 70 | 75 | 80 | 85 | 90 | 95 | 100 |
|Fahr. | Water.| Water.| Water.| Water.| Water.| Water.| Water.|
+------+-------+-------+-------+-------+-------+-------+-------+
|_Deg._| | | | | | | |
| 30 |0·92563|0·92889|0·93191|0·93474|0·93741|0·93991|0·94222|
| 35 | ·92355| ·92680| ·92986| ·93274| ·93541| ·93790| ·94025|
| 40 | ·92151| ·92476| ·92783| ·93072| ·93341| ·93592| ·93827|
| 45 | ·91937| ·92264| ·92570| ·92859| ·93131| ·93382| ·93621|
| 50 | ·91723| ·92051| ·92358| ·92647| ·92919| ·93177| ·93419|
| 55 | ·91502| ·91837| ·92145| ·92436| ·92707| ·92963| ·93208|
| 60 | ·91287| ·91622| ·91933| ·92225| ·92499| ·92758| ·93002|
| 65 | ·91066| ·91400| ·91715| ·92010| ·92283| ·92546| ·92794|
| 70 | ·90847| ·91181| ·91493| ·91793| ·92069| ·92333| ·92580|
| 75 | ·90617| ·90952| ·91270| ·91569| ·91849| ·92111| ·92364|
| 80 | ·90385| ·90723| ·91046| ·91340| ·91622| ·91891| ·92142|
| 85 | ·90209| ·90558| ·90882| ·91186| ·91465| ·91729| ·91969|
| 90 | ·89988| ·90342| ·90688| ·90967| ·91248| ·91511| ·91751|
| 95 | ·89763| ·90119| ·90443| ·90747| ·91029| ·91290| ·91531|
| 100 | ·89536| ·89889| ·90215| ·90522| ·90805| ·91066| ·91310|
+------+-------+-------+-------+-------+-------+-------+-------+

+------+-------+-------+-------+-------+-------+-------+-------+
|Tem- | 95 | 90 | 85 | 80 | 75 | 70 | 65 |
|pera- |Alcohol|Alcohol|Alcohol|Alcohol|Alcohol|Alcohol|Alcohol|
|ture, | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
|Fahr. | Water.| Water.| Water.| Water.| Water.| Water.| Water.|
+------+-------+-------+-------+-------+-------+-------+-------+
|_Deg._| | | | | | | |
| 30 |0·94447|0·94675|0·94920|0·95173|0·95429|0·95681|0·95944|
| 35 | ·94249| ·94484| ·94734| ·94988| ·95246| ·95502| ·95772|
| 40 | ·94058| ·94295| ·94547| ·94802| ·95060| ·95328| ·95602|
| 45 | ·93860| ·94096| ·94348| ·94605| ·94871| ·95143| ·95423|
| 50 | ·93658| ·93897| ·94149| ·94414| ·94683| ·94958| ·95243|
| 55 | ·93452| ·93696| ·93948| ·94213| ·94486| ·94767| ·95057|
| 60 | ·93247| ·93493| ·93749| ·94018| ·94296| ·94579| ·94876|
| 65 | ·93040| ·93285| ·93546| ·93822| ·94099| ·94388| ·94689|
| 70 | ·92828| ·93076| ·93337| ·93616| ·93898| ·94193| ·94500|
| 75 | ·92613| ·92865| ·93132| ·93413| ·93695| ·93989| ·94301|
| 80 | ·92393| ·92646| ·92917| ·93201| ·93488| ·93785| ·94102|
+------+-------+-------+-------+-------+-------+-------+-------+

+------+-------+-------+-------+-------+-------+-------+-------+
|Tem- | 60 | 55 | 50 | 45 | 40 | 35 | 30 |
|pera- |Alcohol|Alcohol|Alcohol|Alcohol|Alcohol|Alcohol|Alcohol|
|ture, | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
|Fahr. | Water.| Water.| Water.| Water.| Water.| Water.| Water.|
+------+-------+-------+-------+-------+-------+-------+-------+
|_Deg._| | | | | | | |
| 30 |0·96209|0·96470|0·96719|0·96967|0·97200|0·97418|0·97635|
| 35 | ·96048| ·96315| ·96579| ·96840| ·97086| ·97319| ·97556|
| 40 | ·95879| ·96159| ·96434| ·96706| ·96967| ·97220| ·97472|
| 45 | ·95703| ·95993| ·96280| ·96563| ·96840| ·97110| ·97384|
| 50 | ·95534| ·95831| ·96126| ·96420| ·96708| ·96995| ·97284|
| 55 | ·95357| ·95662| ·95966| ·96272| ·96575| ·96877| ·97181|
| 60 | ·95181| ·95493| ·95804| ·96122| ·96437| ·96752| ·97074|
| 65 | ·95000| ·95318| ·95635| ·95962| ·96288| ·96620| ·96959|
| 70 | ·94813| ·95139| ·95469| ·95802| ·96143| ·96484| ·96836|
| 75 | ·94623| ·94957| ·95292| ·95638| ·95987| ·96344| ·96708|
| 80 | ·94431| ·94768| ·95111| ·95467| ·95826| ·96192| ·96568|
+------+-------+-------+-------+-------+-------+-------+-------+

+------+-------+-------+-------+-------+-------+
|Tem- | 25 | 20 | 15 | 10 | 5 |
|pera- |Alcohol|Alcohol|Alcohol|Alcohol|Alcohol|
|ture, | 100 | 100 | 100 | 100 | 100 |
|Fahr. | Water.| Water.| Water.| Water.| Water.|
+------+-------+-------+-------+-------+-------+
|_Deg._| | | | | |
| 30 |0·97860|0·98108|0·98412|0·98804|0·99334|
| 35 | ·97801| ·98076| ·98397| ·98804| ·99344|
| 40 | ·97737| ·98033| ·98373| ·98795| ·99345|
| 45 | ·97666| ·97980| ·98338| ·98774| ·99338|
| 50 | ·97589| ·97920| ·98293| ·98745| ·99316|
| 55 | ·97500| ·97847| ·98239| ·98702| ·99284|
| 60 | ·97410| ·97771| ·98176| ·98654| ·99244|
| 65 | ·97309| ·97688| ·98106| ·98594| ·99194|
| 70 | ·97203| ·97596| ·98028| ·98527| ·99134|
| 75 | ·97086| ·97495| ·97943| ·98454| ·99066|
| 80 | ·96963| ·97385| ·97845| ·98367| ·98991|
+------+-------+-------+-------+-------+-------+

Experiments were made, by direction of the committee, to verify Gilpin’s tables, which showed that the error introduced in ascertaining the strength of spirits by tables founded on Gilpin’s numbers must be quite insensible in the practice of the revenue. The discrepancies thus detected, on a mixture of a given strength, did not amount in any one instance to unity in the fourth place of decimals. From a careful inspection of such documents the committee are of opinion, that Gilpin’s tables possess a degree of accuracy far surpassing what could be expected, and sufficiently perfect for all practical or scientific purposes.

The following table is given by Mr. Lubbock, for converting the _apparent_ specific gravity, or _indication_, into true specific gravity:--

+-----+-----------------------------------------+-----+
|Indi-| - Temperature + |Indi-|
| ca- +------+------+------+------+------+------+ ca- |
|tion.| 30° | 32° | 37° | 42° | 47° | 52° |tion.|
+-----+------+------+------+------+------+------+-----+
| ·82 |·00083|·00078|·00065|·00052|·00039|·00025| ·82 |
| ·83 |·00084|·00079|·00066|·00052|·00039|·00026| ·83 |
| ·84 |·00085|·00080|·00066|·00053|·00039|·00026| ·84 |
| ·85 |·00086|·00081|·00067|·00054|·00040|·00026| ·85 |
| ·86 |·00087|·00082|·00068|·00054|·00040|·00027| ·86 |
| ·87 |·00088|·00083|·00069|·00055|·00041|·00027| ·87 |
| ·88 |·00089|·00084|·00070|·00055|·00041|·00027| ·88 |
| ·89 |·00090|·00085|·00070|·00055|·00042|·00028| ·89 |
| ·90 |·00091|·00085|·00071|·00056|·00042|·00028| ·90 |
| ·91 |·00092|·00086|·00072|·00057|·00043|·00028| ·91 |
| ·92 |·00093|·00087|·00073|·00058|·00043|·00029| ·92 |
| ·93 |·00094|·00088|·00073|·00059|·00044|·00029| ·93 |
| ·94 |·00095|·00089|·00074|·00059|·00044|·00029| ·94 |
| ·95 |·00096|·00090|·00075|·00060|·00045|·00029| ·95 |
| ·96 |·00097|·00091|·00076|·00060|·00045|·00030| ·96 |
| ·97 |·00098|·00092|·00077|·00061|·00046|·00030| ·97 |
| ·98 |·00099|·00093|·00077|·00062|·00046|·00030| ·98 |
| ·99 |·00100|·00094|·00078|·00062|·00047|·00031| ·99 |
|1·00 |·00101|·00095|·00079|·00063|·00047|·00031|1·00 |
+-----+------+------+------+------+------+------+-----+

+-----+-----------------------------------------+-----+
|Indi-| - Temperature + |Indi-|
| ca- +------+------+------+------+------+------+ ca- |
|tion.| 57° | 62° | 67° | 72° | 77° | 80° |tion.|
+-----+------+------+------+------+------+------+-----+
| ·82 |·00012| |·00011|·00024|·00035|·00042| ·82 |
| ·83 |·00012| |·00012|·00024|·00036|·00042| ·83 |
| ·84 |·00013| |·00012|·00024|·00036|·00043| ·84 |
| ·85 |·00013| |·00012|·00025|·00037|·00043| ·85 |
| ·86 |·00013| |·00012|·00025|·00037|·00044| ·86 |
| ·87 |·00013| |·00012|·00025|·00037|·00044| ·87 |
| ·88 |·00013| |·00012|·00026|·00038|·00045| ·88 |
| ·89 |·00013| |·00012|·00026|·00038|·00045| ·89 |
| ·90 |·00014| |·00013|·00026|·00039|·00046| ·90 |
| ·91 |·00014| |·00013|·00026|·00039|·00046| ·91 |
| ·92 |·00014| |·00013|·00027|·00040|·00047| ·92 |
| ·93 |·00014| |·00013|·00027|·00040|·00047| ·93 |
| ·94 |·00014| |·00013|·00027|·00040|·00048| ·94 |
| ·95 |·00014| |·00013|·00028|·00041|·00048| ·95 |
| ·96 |·00014| |·00013|·00028|·00041|·00049| ·96 |
| ·97 |·00015| |·00014|·00028|·00042|·00049| ·97 |
| ·98 |·00015| |·00014|·00028|·00042|·00050| ·98 |
| ·99 |·00015| |·00014|·00029|·00043|·00050| ·99 |
|1·00 |·00015| | | | | |1·00 |
+-----+------+------+------+------+------+------+-----+

The hydrometer constructed, under the directions of the Commissioners of Excise, by Mr. Bate, has a scale of 4 inches in length divided into 100 parts, and 9 weights. It has thus a range of 900 divisions, and expresses specific gravities at the temperature of 62° Fahr. In order to render this instrument so accurate a measurer of the specific gravity, at the standard temperature, as to involve no error of an appreciable amount, Mr. Bate has constructed the weights (which in this instrument are immersed in the fluid of different specific gravities) so that each successive weight should have an increase of bulk over the preceding weight equal to that part of the stem occupied by the scale, and an increase of weight sufficient to take the whole of the scale, and no more, down to the liquid. This arrangement requires great accuracy of workmanship, and enhances the price of the instrument. But it allows of increased strength in the ball, where it is very much required, and it gives, upon inspection only, the indication (apparent specific gravity) by which the general table is to be examined and the result ascertained. _Fig._ 5. represents this instrument and two of its nine ballast weights. It comprehends all specific gravities between 820 and 1000. It indicates true specific gravity with almost perfect accuracy at the temperature of 62° Fahr.; but it does not exclude other instruments from being used in conjunction with tables. The latter are, in fact, independent of the instrument, and may be used with gravimeters, or any instrument affording indications by specific gravity at a given temperature.

The commercial value of spirituous liquors being much lower in France than in England, a less sensible instrument becomes sufficient for the wants of that country. Baumé’s and Cartier’s hydrometers, with short arbitrary scales, are very much employed, but they have been lately superseded by an ingenious and ready instrument contrived by M. Gay Lussac, and called by him an _alcoomètre_. He takes for the term of comparison pure alcohol by volume, at the temperature of 15° Cent., and represents the strength of it by 100 _centimes_, or by unity. Consequently, the strength of a spirituous liquid is the number of centimes in volume of pure alcohol which that liquid contains at the temperature of 15° Cent. The instrument is formed like a common hydrometer, and is graduated for the temperature of 15° Cent. Its scale is divided into 100 parts or degrees, each of which denotes a centime of alcohol; the division 0 at the bottom of the stem corresponds to pure water, and the division 100 at its top, to pure alcohol. When immersed in a spirituous liquor at 15° Cent. (59° Fahr.) it announces its strength directly. For example: if in spirits supposed at the temperature of 15° Cent. it sinks to the division 50, it indicates that the strength of this liquor is 50 per cent., or that it contains 50 centimes of pure alcohol. In our new British proof spirit, it would sink to nearly 57, indicating 57 by volume of pure alcohol, allowing for condensation, or 50 by weight. A table of correction is given for temperature, which he calls “Table of real strength of spirituous liquors.” The first vertical column of this table contains the temperatures, from 0° to 30° Cent., and the first horizontal line the indications of the alcoomètre. In the same table we have most ingeniously inserted a correction for the volume of the spirits when the temperature differs from 15° Cent. If we take 1000 litres or gallons, measured at the temperature of 2°, of a spirituous liquor whose apparent strength is 44^{c}; its real strength at 15° will from the preceding mode of correction be 49^{c}. On heating this liquid to 15°, in order to find its real specific gravity or strength, its bulk will become greater; and, instead of 1000 litres or gallons, which it measured at 2°, we shall have 1009 at 15° C. This number is inscribed in smaller characters in the same square cell with the real force, precisely under 49^{c}. All the numbers in small characters, printed under each _real strength_, indicate the volume which 1000 litres of a spirituous liquor would have, when measured at the temperature at which its apparent strength is taken. In the above example, the quantity in litres or gallons of pure alcohol contained in 1000 litres or gallons of the spirits, measured at the temperature of 2°, will be, therefore,--1009 lit. × 0·49 = 494 lit. 41.

This quantity of pure alcohol, thus estimated, is called _richness of spirit in alcohol_, or simply _richness_.

Let us take an example similar to the preceding, but at a higher temperature than 15° Cent. Suppose we have 1000 litres measured, at the temperature of 25°, of spirits whose apparent strength is 53^{c}, what is the real quantity of pure alcohol which this spirit contains at the temperature of 15°? We shall find in the table, first of all, that the real strength of the spirits is 49^{c}·3. As to its bulk or volume, it is very clear that the 1000 litres in cooling from 25° to 15°, will occupy a smaller space. This volume will be 993 litres; it is inscribed directly below 49^{c}·3, the real strength. We shall therefore have of pure alcohol, contained in the 1000 litres of spirits, measured at the temperature of 25°, or their _richness_, 993 lit. × 0·493 = 489 lit. 55.

Alcometrical Table of real Strength, by M. Gay Lussac.

+-------+------+------+------+------+------+------+------+------+
|Temper-|31^{c}|32^{c}|33^{c}|34^{c}|35^{c}|36^{c}|37^{c}|38^{c}|
| ature | | | | | | | | |
| C. | | | | | | | | |
+-------+------+------+------+------+------+------+------+------+
| _Deg._| | | | | | | | |
| 10 | 33·0 | 34 | 35 | 36 | 37 | 38 | 39 | 40 |
| | 1002 | 1002 | 1003 | 1003 | 1003 | 1003 | 1003 | 1003 |
| +------+------+------+------+------+------+------+------+
| 11 | 32·6 | 33·6 | 34·6 | 35·6 | 36·6 | 37·6 | 38·6 | 39·6 |
| | 1002 | 1002 | 1002 | 1002 | 1002 | 1002 | 1002 | 1002 |
| +------+------+------+------+------+------+------+------+
| 12 | 32·2 | 33·2 | 34·2 | 35·2 | 36·2 | 37·2 | 38·2 | 39·2 |
| | 1001 | 1001 | 1002 | 1002 | 1002 | 1002 | 1002 | 1002 |
| +------+------+------+------+------+------+------+------+
| 13 | 31·8 | 32·8 | 33·8 | 34·8 | 35·8 | 36·8 | 37·8 | 38·8 |
| | 1001 | 1001 | 1001 | 1001 | 1001 | 1001 | 1001 | 1001 |
| +------+------+------+------+------+------+------+------+
| 14 | 31·4 | 32·4 | 33·4 | 34·4 | 35·4 | 36·4 | 37·4 | 38·4 |
| | 1001 | 1001 | 1001 | 1001 | 1001 | 1001 | 1001 | 1001 |
| +------+------+------+------+------+------+------+------+
| 15 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 |
| | 1000 | 1000 | 1000 | 1000 | 1000 | 1000 | 1000 | 1000 |
| +------+------+------+------+------+------+------+------+
| 16 | 30·6 | 31·6 | 32·5 | 33·5 | 34·5 | 35·5 | 36·5 | 37·5 |
| | 1000 | 1000 | 999 | 999 | 999 | 999 | 999 | 999 |
| +------+------+------+------+------+------+------+------+
| 17 | 30·2 | 31·2 | 32·1 | 33·1 | 34·1 | 35·1 | 36·1 | 37·1 |
| | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 |
| +------+------+------+------+------+------+------+------+
| 18 | 29·8 | 30·8 | 31·7 | 32·7 | 33·7 | 34·7 | 35·7 | 36·7 |
| | 999 | 999 | 998 | 998 | 998 | 998 | 998 | 998 |
| +------+------+------+------+------+------+------+------+
| 19 | 29·4 | 30·4 | 31·3 | 32·3 | 33·3 | 34·3 | 35·3 | 36·3 |
| | 998 | 998 | 998 | 998 | 998 | 998 | 998 | 998 |
| +------+------+------+------+------+------+------+------+
| 20 | 29 | 30 | 30·9 | 31·9 | 32·9 | 33·9 | 34·9 | 35·9 |
| | 998 | 998 | 997 | 997 | 997 | 997 | 997 | 997 |
| +------+------+------+------+------+------+------+------+
| 21 | 28·6 | 29·6 | 30·5 | 31·5 | 32·5 | 33·5 | 34·5 | 35·5 |
| | 997 | 997 | 997 | 997 | 997 | 997 | 997 | 996 |
| +------+------+------+------+------+------+------+------+
| 22 | 28·2 | 29·2 | 30·1 | 31·1 | 32·1 | 33·1 | 34·1 | 35·1 |
| | 997 | 997 | 996 | 996 | 996 | 996 | 996 | 996 |
| +------+------+------+------+------+------+------+------+
| 23 | 27·8 | 28·8 | 29·7 | 30·7 | 31·7 | 32·7 | 33·7 | 34·7 |
| | 996 | 996 | 996 | 996 | 996 | 996 | 996 | 995 |
| +------+------+------+------+------+------+------+------+
| 24 | 27·4 | 28·4 | 29·3 | 30·3 | 31·3 | 32·3 | 33·3 | 34·3 |
| | 996 | 996 | 995 | 995 | 995 | 995 | 995 | 995 |
| +------+------+------+------+------+------+------+------+
| 25 | 27 | 28 | 28·9 | 29·9 | 30·9 | 31·9 | 32·9 | 33·9 |
| | 995 | 995 | 995 | 995 | 995 | 994 | 994 | 994 |
+-------+------+------+------+------+------+------+------+------+

+-------+------+------+------+------+------+------+------+------+
|Temper-|39^{c}|40^{c}|41^{c}|42^{c}|43^{c}|44^{c}|45^{c}|46^{c}|
| ature | | | | | | | | |
| C. | | | | | | | | |
+-------+------+------+------+------+------+------+------+------+
| _Deg._| | | | | | | | |
| 10 | 41 | 42 | 43 | 44 | 45 | 46 | 46·9 | 47·9 |
| | 1003 | 1003 | 1003 | 1004 | 1004 | 1004 | 1004 | 1004 |
| +------+------+------+------+------+------+------+------+
| 11 | 40·6 | 41·6 | 42·6 | 43·6 | 44·6 | 45·6 | 46·6 | 47·6 |
| | 1003 | 1003 | 1003 | 1003 | 1003 | 1003 | 1003 | 1003 |
| +------+------+------+------+------+------+------+------+
| 12 | 40·2 | 41·2 | 42·2 | 43·2 | 44·2 | 45·2 | 46·2 | 47·2 |
| | 1002 | 1002 | 1002 | 1002 | 1002 | 1002 | 1002 | 1002 |
| +------+------+------+------+------+------+------+------+
| 13 | 39·8 | 40·8 | 41·8 | 42·8 | 43·8 | 44·8 | 45·8 | 46·8 |
| | 1001 | 1001 | 1001 | 1001 | 1001 | 1002 | 1002 | 1002 |
| +------+------+------+------+------+------+------+------+
| 14 | 39·4 | 40·4 | 41·4 | 42·4 | 43·4 | 44·4 | 45·4 | 46·4 |
| | 1001 | 1001 | 1001 | 1001 | 1001 | 1001 | 1001 | 1001 |
| +------+------+------+------+------+------+------+------+
| 15 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 |
| | 1000 | 1000 | 1000 | 1000 | 1000 | 1000 | 1000 | 1000 |
| +------+------+------+------+------+------+------+------+
| 16 | 38·5 | 39·5 | 40·6 | 41·6 | 42·6 | 43·6 | 44·6 | 45·6 |
| | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 |
| +------+------+------+------+------+------+------+------+
| 17 | 38·1 | 39·1 | 40·2 | 41·2 | 42·2 | 43·2 | 44·9 | 45·2 |
| | 999 | 999 | 999 | 999 | 999 | 998 | 998 | 998 |
| +------+------+------+------+------+------+------+------+
| 18 | 37·7 | 38·7 | 39·8 | 40·8 | 41·8 | 42·8 | 43·8 | 44·9 |
| | 998 | 998 | 998 | 998 | 998 | 998 | 998 | 998 |
| +------+------+------+------+------+------+------+------+
| 19 | 37·3 | 38·3 | 39·4 | 40·4 | 41·4 | 42·5 | 43·5 | 44·5 |
| | 997 | 997 | 997 | 997 | 997 | 997 | 997 | 997 |
| +------+------+------+------+------+------+------+------+
| 20 | 36·9 | 37·9 | 39 | 40 | 41 | 42·1 | 43·1 | 44·1 |
| | 997 | 997 | 997 | 997 | 997 | 997 | 996 | 996 |
| +------+------+------+------+------+------+------+------+
| 21 | 36·5 | 37·5 | 38·6 | 39·6 | 40·6 | 41·7 | 42·7 | 43·7 |
| | 996 | 996 | 996 | 996 | 996 | 996 | 996 | 996 |
| +------+------+------+------+------+------+------+------+
| 22 | 36·1 | 37·1 | 38·2 | 39·2 | 40·2 | 41·3 | 42·3 | 43·3 |
| | 996 | 996 | 996 | 995 | 995 | 995 | 995 | 995 |
| +------+------+------+------+------+------+------+------+
| 23 | 35·7 | 36·7 | 37·8 | 38·8 | 39·8 | 40·9 | 41·9 | 42·9 |
| | 995 | 995 | 995 | 995 | 995 | 994 | 994 | 994 |
| +------+------+------+------+------+------+------+------+
| 24 | 35·3 | 36·3 | 37·4 | 38·4 | 39·4 | 40·5 | 41·5 | 42·5 |
| | 995 | 994 | 994 | 994 | 994 | 994 | 994 | 994 |
| +------+------+------+------+------+------+------+------+
| 25 | 34·9 | 35·9 | 37 | 38 | 39 | 40·1 | 42·1 | 42·2 |
| | 994 | 994 | 994 | 994 | 993 | 993 | 993 | 993 |
+-------+------+------+------+------+------+------+------+------+

+-------+------+------+------+------+------+------+------+------+
|Temper-|47^{c}|48^{c}|49^{c}|50^{c}|51^{c}|52^{c}|53^{c}|54^{c}|
| ature | | | | | | | | |
| C. | | | | | | | | |
+-------+------+------+------+------+------+------+------+------+
| _Deg._| | | | | | | | |
| 10 | 48·9 | 49·9 | 50·9 | 51·8 | 52·8 | 53·8 | 54·8 | 55·8 |
| | 1004 | 1004 | 1004 | 1004 | 1004 | 1004 | 1004 | 1004 |
| +------+------+------+------+------+------+------+------+
| 11 | 48·6 | 49·5 | 50·5 | 51·5 | 52·5 | 53·5 | 54·4 | 55·4 |
| | 1003 | 1003 | 1003 | 1003 | 1003 | 1003 | 1003 | 1003 |
| +------+------+------+------+------+------+------+------+
| 12 | 48·2 | 49·2 | 50·2 | 51·1 | 52·1 | 53·1 | 54·1 | 55 |
| | 1002 | 1002 | 1002 | 1002 | 1002 | 1002 | 1002 | 1002 |
| +------+------+------+------+------+------+------+------+
| 13 | 47·8 | 48·8 | 49·8 | 50·8 | 51·8 | 52·7 | 53·7 | 54·7 |
| | 1002 | 1002 | 1002 | 1002 | 1002 | 1002 | 1002 | 1002 |
| +------+------+------+------+------+------+------+------+
| 14 | 47·4 | 48·4 | 49·4 | 50·4 | 51·4 | 52·3 | 53·3 | 54·3 |
| | 1001 | 1001 | 1001 | 1000 | 1001 | 1001 | 1001 | 1001 |
| +------+------+------+------+------+------+------+------+
| 15 | 47 | 48 | 49 | 50 | 51 | 52 | 53 | 54 |
| | 1000 | 1000 | 1000 | 1000 | 1000 | 1000 | 1000 | 1000 |
| +------+------+------+------+------+------+------+------+
| 16 | 46·6 | 47·6 | 48·6 | 49·6 | 50·6 | 51·6 | 52·6 | 53·6 |
| | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 |
| +------+------+------+------+------+------+------+------+
| 17 | 46·2 | 47·2 | 48·2 | 49·2 | 50·3 | 51·3 | 52·3 | 53·3 |
| | 998 | 998 | 998 | 998 | 998 | 998 | 998 | 998 |
| +------+------+------+------+------+------+------+------+
| 18 | 45·9 | 46·9 | 47·9 | 48·9 | 49·9 | 50·9 | 51·9 | 52·9 |
| | 998 | 998 | 998 | 998 | 998 | 998 | 998 | 998 |
| +------+------+------+------+------+------+------+------+
| 19 | 45·5 | 46·5 | 47·5 | 48·5 | 49·5 | 50·6 | 51·6 | 52·6 |
| | 997 | 997 | 997 | 997 | 997 | 997 | 997 | 997 |
| +------+------+------+------+------+------+------+------+
| 20 | 45·1 | 46·1 | 47·2 | 48·2 | 49·2 | 50·2 | 51·2 | 52·2 |
| | 996 | 996 | 996 | 996 | 996 | 996 | 996 | 996 |
| +------+------+------+------+------+------+------+------+
| 21 | 44·8 | 45·8 | 46·8 | 47·8 | 48·8 | 49·8 | 50·8 | 51·8 |
| | 996 | 996 | 995 | 995 | 995 | 995 | 995 | 995 |
| +------+------+------+------+------+------+------+------+
| 22 | 44·3 | 45·3 | 46·4 | 47·4 | 48·4 | 49·4 | 50·4 | 51·4 |
| | 995 | 995 | 995 | 995 | 995 | 995 | 995 | 994 |
| +------+------+------+------+------+------+------+------+
| 23 | 43·9 | 44·9 | 46 | 47 | 48 | 49·1 | 50·1 | 51·1 |
| | 994 | 994 | 994 | 994 | 994 | 994 | 994 | 994 |
| +------+------+------+------+------+------+------+------+
| 24 | 43·6 | 44·6 | 45·6 | 46·6 | 47·6 | 48·7 | 49·7 | 50·7 |
| | 994 | 994 | 993 | 993 | 993 | 993 | 993 | 693 |
| +------+------+------+------+------+------+------+------+
| 25 | 43·2 | 44·2 | 45·2 | 46·3 | 47·3 | 48·3 | 49·3 | 50·3 |
| | 993 | 993 | 993 | 993 | 993 | 993 | 993 | 992 |
+-------+------+------+------+------+------+------+------+------+

+-------+------+------+------+------+------+------+------+------+
|Temper-|55^{c}|56^{c}|57^{c}|58^{c}|59^{c}|60^{c}|61^{c}|62^{c}|
| ature | | | | | | | | |
| C. | | | | | | | | |
+-------+------+------+------+------+------+------+------+------+
| _Deg._| | | | | | | | |
| 10 | 56·8 | 57·8 | 58·8 | 59·7 | 60·7 | 61·7 | 62·7 | 63·7 |
| | 1004 | 1004 | 1004 | 1004 | 1004 | 1004 | 1004 | 1004 |
| +------+------+------+------+------+------+------+------+
| 11 | 56·4 | 57·4 | 58·4 | 59·4 | 60·4 | 61·4 | 62·4 | 63·4 |
| | 1003 | 1003 | 1003 | 1003 | 1003 | 1003 | 1003 | 1003 |
| +------+------+------+------+------+------+------+------+
| 12 | 56 | 57 | 58 | 59 | 60 | 61 | 62 | 63 |
| | 1002 | 1002 | 1002 | 1002 | 1002 | 1002 | 1002 | 1002 |
| +------+------+------+------+------+------+------+------+
| 13 | 55·7 | 56·7 | 57·7 | 58·7 | 59·7 | 60·7 | 61·7 | 62·7 |
| | 1002 | 1002 | 1002 | 1002 | 1002 | 1002 | 1002 | 1002 |
| +------+------+------+------+------+------+------+------+
| 14 | 55·3 | 56·3 | 57·3 | 58·3 | 59·3 | 60·3 | 61·3 | 62·3 |
| | 1001 | 1001 | 1001 | 1001 | 1001 | 1001 | 1001 | 1001 |
| +------+------+------+------+------+------+------+------+
| 15 | 55 | 56 | 57 | 58 | 59 | 60 | 61 | 62 |
| | 1000 | 1000 | 1000 | 1000 | 1000 | 1000 | 1000 | 1000 |
| +------+------+------+------+------+------+------+------+
| 16 | 54·6 | 55·6 | 56·6 | 57·6 | 58·6 | 59·6 | 60·6 | 61·7 |
| | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 |
| +------+------+------+------+------+------+------+------+
| 17 | 54·3 | 55·3 | 56·3 | 57·3 | 58·3 | 59·3 | 60·3 | 61·3 |
| | 998 | 998 | 998 | 998 | 998 | 998 | 998 | 998 |
| +------+------+------+------+------+------+------+------+
| 18 | 53·9 | 54·9 | 55·9 | 56·9 | 57·9 | 58·9 | 59·9 | 61 |
| | 998 | 998 | 998 | 997 | 997 | 997 | 997 | 997 |
| +------+------+------+------+------+------+------+------+
| 19 | 53·6 | 54·6 | 55·6 | 56·6 | 57·6 | 58·6 | 59·6 | 60·6 |
| | 997 | 997 | 997 | 997 | 997 | 997 | 997 | 997 |
| +------+------+------+------+------+------+------+------+
| 20 | 53·2 | 54·2 | 55·2 | 56·2 | 57·2 | 58·2 | 59·2 | 60·3 |
| | 996 | 996 | 996 | 996 | 996 | 996 | 996 | 996 |
| +------+------+------+------+------+------+------+------+
| 21 | 52·9 | 53·9 | 54·9 | 55·9 | 56·9 | 57·9 | 58·9 | 59·9 |
| | 995 | 995 | 995 | 995 | 995 | 995 | 995 | 995 |
| +------+------+------+------+------+------+------+------+
| 22 | 52·5 | 53·5 | 54·5 | 55·5 | 56·5 | 57·5 | 58·5 | 59·5 |
| | 994 | 994 | 994 | 994 | 994 | 994 | 994 | 994 |
| +------+------+------+------+------+------+------+------+
| 23 | 52·1 | 53·1 | 54·1 | 55·1 | 56·1 | 57·1 | 58·1 | 59·2 |
| | 994 | 994 | 994 | 993 | 993 | 993 | 993 | 993 |
| +------+------+------+------+------+------+------+------+
| 24 | 51·8 | 52·8 | 53·8 | 54·8 | 55·8 | 56·8 | 57·8 | 58·9 |
| | 993 | 993 | 993 | 993 | 993 | 992 | 992 | 992 |
| +------+------+------+------+------+------+------+------+
| 25 | 51·4 | 52·4 | 53·4 | 54·4 | 55·5 | 56·5 | 57·5 | 58·5 |
| | 992 | 992 | 992 | 992 | 992 | 992 | 992 | 992 |
+-------+------+------+------+------+------+------+------+------+

+-------+------+------+------+------+------+------+------+------+
|Temper-|63^{c}|64^{c}|65^{c}|66^{c}|67^{c}|68^{c}|69^{c}|70^{c}|
| ature | | | | | | | | |
| C. | | | | | | | | |
+-------+------+------+------+------+------+------+------+------+
| _Deg._| | | | | | | | |
| 10 | 64·7 | 65·7 | 66·7 | 67·6 | 68·6 | 69·6 | 70·6 | 71·6 |
| | 1004 | 1004 | 1004 | 1004 | 1004 | 1004 | 1004 | 1004 |
| +------+------+------+------+------+------+------+------+
| 11 | 64·4 | 65·4 | 66·4 | 67·3 | 68·3 | 69·3 | 70·3 | 71·3 |
| | 1003 | 1003 | 1003 | 1003 | 1003 | 1004 | 1004 | 1004 |
| +------+------+------+------+------+------+------+------+
| 12 | 64 | 65 | 66 | 67 | 68 | 69 | 70 | 71 |
| | 1002 | 1002 | 1002 | 1002 | 1003 | 1003 | 1003 | 1003 |
| +------+------+------+------+------+------+------+------+
| 13 | 63·7 | 64·7 | 65·7 | 66·7 | 67·7 | 68·7 | 69·6 | 70·6 |
| | 1002 | 1002 | 1002 | 1002 | 1002 | 1002 | 1002 | 1002 |
| +------+------+------+------+------+------+------+------+
| 14 | 63·3 | 64·3 | 65·3 | 66·3 | 67·3 | 68·3 | 69·3 | 70·3 |
| | 1001 | 1001 | 1001 | 1001 | 1001 | 1001 | 1001 | 1001 |
| +------+------+------+------+------+------+------+------+
| 15 | 63 | 64 | 65 | 66 | 67 | 68 | 69 | 70 |
| | 1000 | 1000 | 1000 | 1000 | 1000 | 1000 | 1000 | 1000 |
| +------+------+------+------+------+------+------+------+
| 16 | 62·7 | 63·7 | 64·7 | 65·7 | 66·7 | 67·7 | 68·7 | 69·7 |
| | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 |
| +------+------+------+------+------+------+------+------+
| 17 | 62·3 | 63·3 | 64·3 | 65·3 | 66·3 | 67·3 | 68·3 | 69·3 |
| | 998 | 998 | 998 | 998 | 998 | 998 | 998 | 998 |
| +------+------+------+------+------+------+------+------+
| 18 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 |
| | 997 | 997 | 997 | 997 | 997 | 997 | 997 | 997 |
| +------+------+------+------+------+------+------+------+
| 19 | 61·6 | 62·7 | 63·7 | 64·7 | 65·7 | 66·7 | 67·7 | 68·7 |
| | 997 | 997 | 997 | 997 | 997 | 997 | 996 | 996 |
| +------+------+------+------+------+------+------+------+
| 20 | 61·3 | 62·3 | 63·3 | 64·3 | 65·4 | 66·4 | 67·4 | 68·4 |
| | 996 | 996 | 996 | 996 | 996 | 996 | 996 | 996 |
| +------+------+------+------+------+------+------+------+
| 21 | 61 | 62 | 63 | 64 | 65 | 66 | 67 | 68·1 |
| | 995 | 995 | 995 | 995 | 995 | 995 | 995 | 995 |
| +------+------+------+------+------+------+------+------+
| 22 | 60·6 | 61·6 | 62·7 | 63·7 | 64·7 | 65·7 | 66·7 | 67·7 |
| | 994 | 994 | 994 | 994 | 994 | 994 | 994 | 994 |
| +------+------+------+------+------+------+------+------+
| 23 | 60·2 | 61·3 | 62·3 | 63·3 | 64·3 | 65·4 | 66·4 | 67·4 |
| | 993 | 993 | 993 | 993 | 993 | 993 | 993 | 993 |
| +------+------+------+------+------+------+------+------+
| 24 | 59·9 | 61 | 62 | 63 | 64 | 65 | 66 | 67·1 |
| | 992 | 992 | 992 | 992 | 992 | 992 | 992 | 992 |
| +------+------+------+------+------+------+------+------+
| 25 | 59·5 | 60·6 | 61·6 | 62·6 | 63·7 | 64·7 | 65·7 | 66·7 |
| | 992 | 991 | 991 | 991 | 991 | 991 | 991 | 991 |
+-------+------+------+------+------+------+------+------+------+

+-------+------+------+------+------+------+------+------+------+
|Temper-|71^{c}|72^{c}|73^{c}|74^{c}|75^{c}|76^{c}|77^{c}|78^{c}|
| ature | | | | | | | | |
| C. | | | | | | | | |
+-------+------+------+------+------+------+------+------+------+
| _Deg._| | | | | | | | |
| 10 | 72·6 | 73·5 | 74·5 | 75·5 | 76·5 | 77·5 | 78·5 | 79·5 |
| | 1004 | 1004 | 1005 | 1005 | 1005 | 1005 | 1005 | 1005 |
| +------+------+------+------+------+------+------+------+
| 11 | 72·3 | 73·2 | 74·2 | 75·2 | 76·2 | 77·2 | 78·2 | 79·2 |
| | 1004 | 1004 | 1004 | 1004 | 1004 | 1004 | 1004 | 1004 |
| +------+------+------+------+------+------+------+------+
| 12 | 72 | 72·9 | 73·9 | 74·9 | 75·9 | 76·9 | 77·9 | 78·9 |
| | 1003 | 1003 | 1003 | 1003 | 1003 | 1003 | 1003 | 1003 |
| +------+------+------+------+------+------+------+------+
| 13 | 71·6 | 72·6 | 73·6 | 74·6 | 75·6 | 76·6 | 77·6 | 78·6 |
| | 1002 | 1002 | 1002 | 1002 | 1092 | 1002 | 1002 | 1002 |
| +------+------+------+------+------+------+------+------+
| 14 | 71·3 | 72·3 | 73·3 | 74·3 | 75·3 | 76·3 | 77·3 | 78·3 |
| | 1001 | 1001 | 1001 | 1001 | 1001 | 1001 | 1001 | 1001 |
| +------+------+------+------+------+------+------+------+
| 15 | 71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 |
| | 1000 | 1000 | 1000 | 1000 | 1000 | 1000 | 1000 | 1000 |
| +------+------+------+------+------+------+------+------+
| 16 | 70·7 | 71·7 | 72·7 | 73·7 | 74·7 | 75·7 | 76·7 | 77·7 |
| | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 |
| +------+------+------+------+------+------+------+------+
| 17 | 70·3 | 71·3 | 72·3 | 73·3 | 74·3 | 75·4 | 76·4 | 77·4 |
| | 998 | 998 | 998 | 998 | 998 | 998 | 998 | 998 |
| +------+------+------+------+------+------+------+------+
| 18 | 70 | 71 | 72 | 73 | 74 | 75·1 | 76·1 | 77·1 |
| | 997 | 997 | 997 | 997 | 997 | 997 | 997 | 997 |
| +------+------+------+------+------+------+------+------+
| 19 | 69·7 | 70·7 | 71·7 | 72·7 | 73·7 | 74·7 | 75·8 | 76·8 |
| | 996 | 996 | 996 | 996 | 996 | 996 | 996 | 996 |
| +------+------+------+------+------+------+------+------+
| 20 | 69·4 | 70·4 | 71·4 | 72·4 | 73·4 | 74·4 | 75·5 | 76·5 |
| | 996 | 996 | 995 | 995 | 995 | 995 | 995 | 995 |
| +------+------+------+------+------+------+------+------+
| 21 | 69·1 | 70·1 | 71·1 | 72·1 | 73·1 | 74·1 | 75·2 | 76·2 |
| | 995 | 995 | 995 | 994 | 994 | 994 | 994 | 994 |
| +------+------+------+------+------+------+------+------+
| 22 | 68·8 | 69·8 | 70·8 | 71·8 | 72·8 | 73·8 | 74·8 | 75·9 |
| | 994 | 994 | 994 | 994 | 993 | 993 | 993 | 993 |
| +------+------+------+------+------+------+------+------+
| 23 | 68·4 | 69·4 | 70·5 | 71·5 | 72·5 | 73·5 | 74·5 | 75·5 |
| | 993 | 993 | 993 | 993 | 992 | 992 | 992 | 992 |
| +------+------+------+------+------+------+------+------+
| 24 | 68·1 | 69·1 | 70·1 | 71·2 | 72·2 | 73·2 | 74·2 | 75·2 |
| | 992 | 992 | 992 | 992 | 992 | 992 | 992 | 991 |
| +------+------+------+------+------+------+------+------+
| 25 | 67·8 | 68·8 | 69·8 | 70·8 | 71·8 | 72·8 | 73·9 | 74·9 |
| | 991 | 991 | 991 | 991 | 991 | 991 | 991 | 991 |
+-------+------+------+------+------+------+------+------+------+