John A. R. Newlands (1837-1898)

On Relations among the Equivalents

Chemical News Vol. 7, Feb. 7, 1863, pp. 70-72.

To the Editor of the CHEMICAL NEWS.

SIR,--Many chemists, and M. Dumas in particular, have, on several occasions, pointed out some very interesting relations between the equivalents of bodies belonging to the same natural family or group; and my present purpose is simply to endeavour to proceed a little further in the same direction. I must, however, premise that many of the observations here collected together are well known already, and are only embodied in my communication for the purpose of rendering it more complete.

Before proceeding any further, I may also remark, that in the difficult task of grouping the elementary bodies, I have been guided more by chemical characteristics than by physical appearances, and have, therefore, taken no notice of the ordinary distinction between metals and non-metallics. The numbers which I have attached to the various groups are merely for the purpose of reference, and have no further significance whatever. For the sake of perspicuity, I have employed the old equivalent numbers, these atomic weights being, with one or two exceptions, taken from the 8th edition of "Fownes' Manual."

The following are among the most striking relations observed on comparing the equivalents of analogous elements. (In order to avoid the frequent repetition of the word "equivalent," I have generally used the names of the different elements as representing their equivalent numbers--thus, when I say that zinc is the mean of magnesium and cadmium, I intend to imply that the equivalent of zinc is the mean of those of magnesium and cadmium, and so on, throughout the paper):--

Group I. Metals of the alkalies:-- Lithium, 7; sodium, 23; potassium, 39; rubidium, 85, caesium, 123; thallium, 204.

The relation among the equivalents of this group (see CHEMICAL NEWS, January 10, 1863) may, perhaps, be most simply stated as follows:--

1 of lithium + 1 of potassium = 2 of sodium.
1 " + 2 " = 1 of rubidium.
1 " + 3 " = 1 of caesium.
1 " + 4 " = 163, the equivalent of a metal not yet discovered.
1 " + 5 " = 1 of thallium.

Group II. Metals of the alkaline earths:-- Magnesium, 12; calcium, 20; strontium, 43.8; barium, 68.5.

In this group, strontium is the mean of calcium and barium.

Group III. Metals of the earths:-- Beryllium, 6.9; aluminium, 13.7; zirconium, 33.6; cerium, 47; lanthanium, 47; didymium, 48; thorium, 59.6.

Aluminium equals two of beryllium, or one-third of the sum of beryllium and zirconium. (Aluminium also is one-half of manganese, which, with iron and chromium, forms sesquioxides, isomorphous, with alumina.)

1 of zirconium + 1 of aluminium = 1 of cerium.
1 " + 2 " = 1 of thorium.

Lanthanium and didymium are identical with cerium, or nearly so.

Group IV. Metals whose protoxides are isomorphous with magnesia:-- Magnesium, 12; chromium, 26.7; manganese, 27.6; iron, 28; cobalt, 29.5; nickel, 29.5; copper, 31.7; zinc, 32.6; cadmium, 56.

Between magnesium and cadmium, the extremities of this group, zinc is the mean. Cobalt and nickel are identical. Between cobalt and zinc, copper is the mean. Iron is one-half of cadmium. Between iron and chromium, manganese is the mean.

Group V.-- Fluorine, 19; chlorine, 35.5; bromine, 80; iodine, 127.

In this group, bromine is the mean between chlorine and iodine.

Group VI.-- Oxygen, 8; sulphur, 16; selenium, 39.5; tellurium, 64.2.

In this group selenium is the mean between sulphur and tellurium.

Group VII.-- Nitrogen, 14; phosphorus, 31; arsenic, 75; osmium, 99.6; antimony, 120.3; bismuth, 213.

In this group arsenic is the mean between phosphorus and antimony.

Osmium approaches the mean of arsenic and antimony, and is also almost exactly half the difference between nitrogen and bismuth, the two extremities of this group; thus, (213-14)/2 = 99.5.

Bismuth equals 1 of antimony + 3 of phosphorus; thus, 120.3 + 93 = 213.3.

Group VIII.-- Carbon, 6; silicon, 14.20; titanium, 25; tin, 58.

In this group the difference between tin and titanium is nearly three times as great as that between titanium and silicon.

Group IX.-- Molybdenum, 46; vanadium, 68.6; tungsten, 92; tantalium, 184.

In this group vanadium is the mean between molybdenum and tungsten.

Tungsten equals 2 of molybdenum, and tantalium equals 4 of molybdenum.

Group X.-- Rhodium, 52.2; ruthenium, 52.2; palladium, 53.3; platinum, 98.7; iridium, 99.

In this group the first three are identical, or nearly so, and are rather more than half of the other two. (I may mention, by the way, that platinum is rather more than the half of gold; thus 98.7 x 2 = 197.4, gold being 197.)

Group XI.-- Mercury, 100; lead, 103.7; silver, 108.

Lead is here the mean of the other two.

If we deduct the member of a group having the lowest equivalent from that immediately above it, we frequently observe that the numbers thus obtained bear a simple relation to each other, as in the following examples:--

Member of group having One immediately above Difference.
lowest equivalent. the preceding.  
Magnesium 12 Calcium 20 8
Oxygen 8 Sulphur 16 8
Carbon 6 Silicon 14.2 8.2
Lithium 7 Sodium 23 16
Fluorine 19 Chlorine 35.5 16.5
Nitrogen 14 Phosphorus 31 17

A similar relation, though not quite so obvious as the above, may be shown by deducting the lowest member of a triad from the highest. The numbers thus obtained in the different triads correspond to a great extent. (By a triad I understand a group of analogous elements, the equivalent of one of which is the mean of the other two.) Of this relation I append a few examples:--

Lowest term of triad. Highest term of triad. Difference.
Lithium 7 Potassium 39 32
Magnesium 12 Cadmium 56 44
Molybdenum 46 Tungsten 92 46
Sulphur 16 Tellurium 64.2 48.2
Calcium 20 Barium 68.5 48.5
Phosphorus 31 Antimony 120.3 89.3
Chlorine 35.5 Iodine 127 91.5

In the relation previously pointed out, the difference between the lowest member of a group, and the next above it, was either 8, or 8 x 2 = 16; and in the first of these triads the difference is 8 x 4 = 32; in the next four it approaches 8 + 6 = 48 (sic; obviously 8 x 6 is intended.); and in the last two triads it is nearly twice as great.

The difference between the highest member of the platinum group, viz., iridium 99, and the lowest, rhodium 52.2, is 46.8, a number which approximates very closely to those obtained in some of the above triads; and it, therefore, appears possible that the platinum metals are the extremities of a triad, the central term or mean of which is at present unknown.

I am, &c.

J. A. R. N.

P.S. With the view of economising space I have omitted most of the calculations, which, however, are very simple, and can be verified in a moment by the reader. The equivalents thus obtained by calculation will be found to approximate those procured by experiment, as closely as can be expected in such cases.

I also freely admit that some of the relations above pointed out are more apparent than real; others, I trust, will prove of a more durable and satisfactory description.

Relations between Equivalents.

Chemical News Vol. 10, July 30, 1864, pp. 59-60.

To the Editor of the CHEMICAL NEWS.

SIR,-- In your impression of the 2nd inst. a correspondent, under the name of "Studiosus," has called attention to the existence of a law to the effect "that the atomic weights of the elementary bodies are, with few exceptions, either exactly or very nearly multiples of eight."

Now, in a letter "On Relations among the Equivalents," which was signed with my initials, and inserted in the CHEMICAL NEWS of February 7, 1863, I called attention to the numerical differences between the equivalents of certain allied elements, and showed that such differences were generally multiples of eight, as in the following examples:--

Member of a Group having One immediately above Difference.  
Lowest Equivalent. the Preceding. H=1 O=1
Magnesium 24 Calcium 40 16 1
Oxygen 16 Sulphur 32 16 1
Lithium 7 Sodium 23 16 1
Carbon 12 Silicon 28 16 1
Fluorine 19 Chlorine 35.5 16.5 1.031
Nitrogen 14 Phosphorus 31 17 1.062
Lowest Term of Triad. Highest Term of Triad.    
Lithium 7 Potassium 39 32 2
Magnesium 24 Cadmium 112 88 5.5
Molybdenum 96 Tungsten 184 88 5.5
Phosphorus 31 Antimony 122 91 5.687
Chlorine 35.5 Iodine 127 91.5 5.718
Potassium 39 Caesium 133 94 5.875
Sulphur 32 Tellurium 129 97 6.062
Calcium 40 Barium 137 97 6.062

In the last of the above columns the difference is given referred to 16, the equivalent of oxygen, as unity, and it will be seen that, generally speaking, the equivalent of oxygen is the unit of these differences, just as the equivalent of hydrogen, in "Prout's law," is the unit of the atomic weights. Exceptions there are, however, in both cases which render it necessary to take one half or one quarter of the equivalent of oxygen in the one case, and of hydrogen in the other, in order to represent all the numbers obtained as multiples by a whole number of the given standard.

Now, if the law of "Studiosus" had any real existence, the above facts would resolve themselves into particular cases of its application. For if "the atomic weights are multiples of eight," any differences between them must also be divisible by eight. We have here the symbols and the atomic weights of sixty-one elements, placed in their numerical order, and in the third column is the difference between each atomic weight and the one immediately preceding it:--

H 1     Ca 40 1   Ce 92 2.5   V 137 0
Li 7 6   Ti 50 10   La 92 0   Ta 138 1
G 9 2   Cr 52.5 2.5   Di 96 4   W 184 46
B 11 2   Mn 55 2.5   Mo 96 0   Nb 195 11
C 12 1   Fe 56 1   Ro 104 8   Au 196 1
N 14 2   Co 58.5 2.5   Ru 104 0   Pt 197 1
O 16 2   Ni 58.5 0   Pd 106.5 2.5   Ir 197 0
Fl 19 3   Cu 63.5 5   Ag 108 1.5   Os 199 2
Na 23 4   Y 64 0.5   Cd 112 4   Hg 200 1
Mg 24 1   Zn 65 1   Sn 118 6   Tl 203 3
Al 27.5 3.5   As 75 10   U 120 2   Pb 207 4
Si 28 0.5   Se 79.5 4.5   Sb 122 2   Bi 210 3
P 31 3   Br 80 0.5   I 127 5   Th 238 28
S 32 1   Rb 85 5   Te 129 2        
Cl 35.5 3.5   Sr 87.5 2.5   Cs 133 4        
K 39 3.5   Zr 89.5 2   Ba 137 4        

Now, it will be observed that in all the above differences the number eight occurs but once, and we never meet with a multiple of eight, whereas if the law of "Studiosus" were true the equivalents of the elements, in whatever order they might be placed, should, when not identically the same, differ either by eight or by some multiple of eight in every case.

While upon the subject of "relations among the equivalents," I may observe that the most important of these may be seen at a glance in the following table:--

      Lowest term. Mean. Highest term.  
I.   Li 7 +17 = Mg 24 Zn 65 Cd 112  
II.   B 11       Au 196
III.   C 12 +16 = Si 28   Sn 118  
IV.   N 14 +17 = P 31 As 75 Sb122 +88 = Bi 210
V.   O 16 +16 = S 32 Se 79.5 Te 129 +70 = Os 199
VI.   F 19 +16.5 = Cl 35.5 Br 80 I 127  
VII. Li 7 +16 = Na 23 +16 = K 39 Rb 85 Cs 133 +70 = Tl 203
VIII. Li 7 +17 = Mg 24 +16 = Ca 40 Sr 87.5 Ba 137 +70 = Pb 207
IX.     Mo 96 V 137 W 184  
X.     Pd 106.5   Pt 197  

This table is my no means as perfect as it might be; in fact, I have some by me of a more complete character, but as the position to be occupied by the various elements is open to considerable controversy, the above only is given as containing little more than those elementary groups the existence of which is almost universally acknowledged.

I now subjoin a few explanatory remarks on the different groups contained in the above table, the number attached to each group being merely for the purpose of reference.

Group II.-- Boron is here classed with gold, both these elements being triatomic, although the latter is sometimes monatomic.

Group III.-- Silicon and tin stand to each other as the extremities of a triad. Titanium is usually classed along with them, and occupies a position intermediate between silicon and the central term or mean of the triad, which is at present wanting; thus,

(Si 28 + Sn 118)/2 = 73, mean of triad, and
(Si 28 + Mean of triad 73)/2 = 50.5, the eq. of Ti being 50.

Group IV.-- The equivalent of antimony is nearly the mean of those of phosphorus and bismuth; thus,

(31+210)/2 = 120.5, the eq. of Sb being 122.

Group VII.-- The relations which M. Dumas has pointed out between the members of this group are well known; a slight alteration must be made, owing to the atomic weight of caesium having been raised. The relations, then, will be thus:--

Li + K = 2 Na, or in figures, 7 + 39 = 46
Li + 2 K = Rb, " " 7 + 78 = 85
2 Li + 3 K = Cs, " " 14 + 117 = 131
Li + 5 K = Tl, " " 7 + 195 = 202
3 Li + 5 K = 2 Ag, " " 21 + 195 = 216

The equivalent of silver is thus connected with those of the alkali metals. It may also, which amounts to the same thing, be viewed as made up of the equivalents of sodium and rubidium, thus, 23 + 85 = 108. It is likewise nearly the mean between rubidium and caesium, thus, (85+133)/2 = 109.

Group VIII.-- If lithium may be considered as connected with this group as well as with the foregoing (and by some chemists its oxide is viewed as a connecting link between the alkalies and the alkaline earths), we may perform the same calculations in this group that M. Dumas has done in the preceding, thus,- -

Li + Ca = 2 Mg, or in figures, 7 + 40 = 47
Li + 2 Ca = Sr " " 7 + 80 = 87
2 Li + 3 Ca = Ba " " 14 + 120 = 134
Li + 5 Ca = Pb " " 7 + 200 = 207

Again, there are two triads in the group of alkali metals, one which has been long known--viz., lithium, sodium, and potassium, and the other, which was pointed out by Mr. C. W. Quin, in the CHEMICAL NEWS of November 9, 1861--viz., potassium, rubidium, and caesium. Potassium is thus the highest term of one triad and the lowest term of another.

In like manner, if we include lithium, we shall have among the metals of the alkaline earths two triads, the first comprising lithium, magnesium, and calcium, and the second calcium, strontium, and barium, calcium standing at the top of one triad and at the bottom of the other.

The element lead occupies a position in relation to the metals of the alkaline earths similar to that filled by thallium in the group of alkali metals. Osmium appears to play a similar part in the sulphur group, and bismuth in the phosphorus group. The analogous term in the chlorine group is not yet known. Thallium, in its physical properties, bears some resemblance to lead, and it frequently happens that similar terms taken from different groups, such as oxygen and nitrogen, or sulphur and phosphorus, bear more physical resemblance to each other than they do to the members of the groups to which, for chemical reasons we are compelled to assign them.

It will be observed that the difference between the equivalents of tellurium and osmium, caesium, and thallium, and barium and lead, respectively, is the same in each case--viz., 70.

Group X.-- Palladium and platinum appear to be the extremities of a triad, the mean of which is unknown.

So frequently are relations to be met with among the equivalents of allied elements, that we may almost predict that the next equivalent determined, that of indium, for instance, will be found to bear a simple relation to those of the group to which it will be assigned.

In conclusion, I may mention that the equivalents I have adopted in this letter were taken from the highly-interesting and important paper by Professor Williamson, lately published in the Journal of the Chemical Society.

I am, &c.

John A. R. Newlands, F.C.S.
Laboratory, 19, Great St. Helens, E. C., July 12.

On Relations Among the Equivalents

Chemical News Vol. 10, August 20, 1864, pp. 94-95.

To the Editor of the CHEMICAL NEWS.

SIR,-- In addition to the facts stated in my late communication, may I be permitted to observe that if the elements are arranged in the order of their equivalents, calling hydrogen 1, lithium 2, glucinum 3, boron 4, and so on (a separate number being attached to each element having a distinct equivalent of its own, and where two elements happen to have the same equivalent, both being designated by the same number), it will be observed that elements having consecutive numbers frequently either belong to the same group or occupy similar positions in different groups, as in the following examples:--

      No.   No.   No.   No.   No.
Group a. N 6 P 13 As 26 Sb 40 Bi 54
" b. O 7 S 14 Se 27 Te 42 Os 50
" c. Fl 8 Cl 15 Br 28 I 41 -- --
" d. Na 9 K 16 Rb 29 Cs 43 Tl 52
" e. Mg 10 Ca 17 Sr 30 Ba 44 Pb 53

Here the difference between the number of the lowest member of a group and that immediately above it is 7; in other words, the eighth element starting from a given one is a kind of repetition of the first, like the eighth note of an octave in music. The differences between the numbers of the other members of a group are frequently twice as great; thus in the nitrogen group, between N and P there are 7 elements; between P and As, 13; between As and Sb, 14; and between Sb and Bi, 14.

In conclusion, I may remark that just as we have several examples of the apparent existence of triads, the extremities of which are known, whilst their centres are wanting (such as the metals of the platinum group, which may be conceived to be the extremities of three distinct triads, and perhaps also silver and gold may be related to each other in this manner), so we may look upon certain of the elements, e.g., Mn, Fe, Co, Ni, and Cu, as the centres of triads, the extremes of which are at present unknown, or, perhaps, in some cases only unrecognised.

I am, &c.

John A. R. Newlands, F.C.S.
Laboratory, 19, Great St. Helens, E. C., August 8.

On the Law of Octaves.

Chemical News Vol. 12, Aug. 18, 1865, p. 83.

To the Editor of the CHEMICAL NEWS.

SIR,-- With your permission, I would again call attention to a fact pointed out in a communication of mine, inserted in the CHEMICAL NEWS for August 20, 1864.

If the elements are arranged in the order of their equivalents, with a few slight transpositions, as in the accompanying table, it will be observed that elements belonging to the same group usually appear on the same horizontal line.

No. No. No. No. No. No. No. No.
H 1 F 8 Cl 15 Co & Ni 22 Br 29 Pd 36 I 42 Pt & Ir 50
Li 2 Na 9 K 16 Cu 23 Rb 30 Ag 37 Cs 44 Tl 51
G 3 Mg 10 Ca 17 Zn 25 Sr 31 Bd [sic-Cd] 38 Ba & V 45 Pb 54
Bo 4 Al 11 Cr 19 Y 24 Ce & La 33 U 40 Ta 46 Th 56
C 5 Si 12 Ti 18 In 26 Zr 32 Sn 39 W 47 Hg 52
N 6 P 13 Mn 20 As 27 Di & Mo 34 Sb 41 Nb 48 Bi 55
O 7 S 14 Fe 21 Se 28 Ro & Ru 35 Te 43 Au 49 Os 51

(NOTE.-- Where two elements happen to have the same equivalent, both are designated by the same number.)

It will also be seen that the numbers of analogous elements generally differ either by 7 or by some multiple of seven; in other words, members of the same group stand to each other in the same relation as the extremities of one or more octaves in music. Thus, in the nitrogen group, between nitrogen and phosphorus there are 7 elements; between phosphorus and arsenic, 14; between arsenic and antimony, 14; and lastly, between antimony and bismuth, 14 also.

This peculiar relationship I propose to provisionally term the "Law of Octaves".

I am, &c.

John A. R. Newlands, F.C.S.
Laboratory, 19, Great St. Helen's, E.C., August 8, 1865.

Report on the Law of Octaves

The following account of Newlands' paper on the law of octaves was published in Chemical News Vol. 13, March 9, 1866, p. 113.



Thursday, March 1.


Mr. JOHN A. R. NEWLANDS read a paper entitled "The Law of Octaves, and the Causes of Numerical Relations among the Atomic Weights." The author claims the discovery of a law according to which the elements analogous in their properties exhibit peculiar relationships, similar to those subsisting in music between a note and its octave. Starting from the atomic weights on Cannizzarro's system, the author arranges the known elements in order of succession, beginning with the lowest atomic weight (hydrogen) and ending with thorium (=231.5); placing, however, nickel and cobalt, platinum and iridium, cerium and lanthanum, &c., in positions of absolute equality or in the same line. The fifty-six elements so arranged are said to form the compass of eight octaves, and the author finds that chlorine, bromine, iodine, and fluorine are thus brought into the same line, or occupy corresponding places in his scale. Nitrogen and phosphorus, oxygen and sulphur, &c., are also considered as forming true octaves. The author's supposition will be exemplified in Table II., shown to the meeting, and here subjoined:--

Table II.--Elements arranged in Octaves.
No. No. No. No. No. No. No. No.
H 1 F 8 Cl 15 Co & Ni 22 Br 29 Pd 36 I 42 Pt & Ir 50
Li 2 Na 9 K 16 Cu 23 Rb 30 Ag 37 Cs 44 Os 51
G 3 Mg10 Ca 17 Zn 24 Sr 31 Cd 38 Ba & V 45 Hg 52
Bo 4 Al 11 Cr 19 Y 25 Ce & La 33 U 40 Ta 46 Tl 53
C 5 Si 12 Ti 18 In 26 Zr 32 Sn 39 W 47 Pb 54
N 6 P 13 Mn 20 As 27 Di & Mo 34 Sb 41 Nb 48 Bi 55
O 7 S 14 Fe 21 Se 28 Ro & Ru 35 Te 43 Au 49 Th 56

Dr. GLADSTONE made objection on the score of its having been assumed that no elements remain to be discovered. The last few years had brought forth thallium, indium, caesium, and rubidium, and now the finding of one more would throw out the whole system. The speaker believed there was as close an analogy subsisting between the metals named in the last vertical column as in any of the elements standing on the same horizontal line.

Professor G. F. FOSTER humorously inquired of Mr. Newlands whether he had ever examined the elements according to the order of their initial letters? For he believed that any arrangement would present occasional coincidences, but he condemned one which placed so far apart manganese and chromium, or iron from nickel and cobalt.

Mr. NEWLANDS said that he had tried several other schemes before arriving at that now proposed. One founded upon the specific gravity of the elements had altogether failed, and no relation could be worked out of the atomic weights under any other system than that of Cannizzarro.