B.S. Lark

Retired Professor

Department of Chemistry, Guru Nanak Dev University, Amritsar, Punjab, India.


A simple graph paper vernier scale has been described to improve the readability of the scale of various laboratory equipment like burette, graduated pipette, cylinder, thermometer etc.

To enhance the readability of the scale of various graduated simple laboratory like burette, graduated pipette, cylinder, dilatometer thermometer etc. the author introduced a paper vernier scale. This paper vernier is very simple to make and is used just like a parallax card. With the help of this the level of the liquid in any of the above equipment having a graduated stem can be read quite precisely even when it lies anywhere between the graduation marks. In this way for example, the level in a burette calibrated up to 0.1 ml can be read up to 0.01 ml. Presently a modification is being suggested which renders the making of the paper vernier still simpler. Originally a vernier scale was suggested to be made by drawing the scale on a plane piece of paper, where 9 major scale divisions (MSDs) of the graduated part of the equipment are divided into 10 vernier scale divisions (VSDs) to give a least count of 0.1 of the size of the MSD (I.E. 0.01 ml in the case of an ordinary burette).

In the present modification, instead of making the scale on a piece of plane paper, use of a piece of graph paper has been suggested. The emergence of various combinations leading to various least counts and their usefulness has been discussed.


A rectangular piece (4 cm x 6 cm) of evenly cut graph paper is taken and its one smooth edge is aligningly placed against the scale of the graduated stem of the equipment. Number of vernier (graph paper) scale divisions matching against the main (equipment) scale divisions are read. Some different simple combinations and least counts of the corresponding vernier scales are summarized in Table 1. It may be remarked here that only those combinations wherein the matched VSDs and MSDs differ by either one or two divisions have been included in the table. When the difference is one, the least count of the vernier scale so obtained, is simply 1/n times the size of the MSD, if the difference is 2, then the least count becomes 2/n times and so on. Concomitantly the usefulness of the scale falls, as in one complete vernier scale, two or more units would lapse. The comments for the usefulness of the various combinations are also given in the table.

Table 1: Least Count of Various Combinations 

MSD VSD Least Count= (VSD- MSD)/ VSD Remarks
2 3 1/3 not useful
3 4 ¼ not useful
4 5 1/5 not very useful, but easy
5 6 1/6 some useful
6 7 1/7 some useful
7 8 1/8 quite useful
8 9 1/9 quite useful
9 10 1/10 most useful
10 11 1/11 quite useful
3 5 2/5 not so useful, but easy
5 7 2/7 not so useful, but easy
7 9 2/9 not so useful, but easy
9 11 2/11 not so useful, but easy


A vernier scale made on a piece of cm graph paper is illustrated in A Simple Graph Paper Vernier Scale Graph papers of other dimensions available in the market or self-prepared may also be used.

Slits S1 and S2 are made on the graph paper vernier scale so as to make the vernier scale slip on the burette or any other such device underuse. Slit S3 is meant to make visible the matching of zero of vernier scale with the level of the liquid in the burette and the matching of MSDs and VSDs.


  1. Lark, B. S (1996). A Paper Vernier Scale for Various Laboratory Equipments. J Chem. Educ 1996, 73 (2), p 177.








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