The values for the spiral spring—i.e. extension for a given load—having been determined by previous observations in a special apparatus, the curve obtained is at once a measure and a permanent record of these cardinal factors, breaking strain and elasticity. As with all other such instruments, the recording apparatus introduces certain errors, which, however, by careful investigation and modification in accordance with the results, have been reduced to a minimum. Nevertheless, the director, Dr. Martens, has recently adopted a simpler instrument, altogether similar in principle, but based upon a direct reading of the two movements, in which of course these errors do not appear. For the student, however, the recording instrument is the more instructive, and we have given it preference for description here, more especially as no difference in essential parts is involved. Those who wish to pursue the matter into the most interesting details of the investigations made upon the subject, are referred to the papers published by the Institute for 1885.[15] [Footnote 15: Mittheilungen a. d. Königl. Techn. Versuchsanst, Berlin.] In testing the strength of papers by this or similar machines, it is important to observe the hygrometric state of the atmosphere at the time the trials are made, as this has been found to exert a considerable influence on the results, a paper being weaker the moister the atmosphere. The results of the tests are expressed in the following terms:—The elongation is given directly in percentage of the original length. This is uniformly taken at 180 mm., a length arrived at after laborious investigation, as minimising the errors of experiment; in other words, as giving mean value with the minimum of variation. For the breaking strain an ingenious expression has been arrived at, viz. the length of the paper which suspended vertically, with one end hanging freely, the other fixed, would determine fracture at the fixed end. As the breaking strain would vary with the thickness, the numbers obtained in {197} units of force or weight for strips of constant breadth, would need correction in order to admit of strict comparison with one another. By substituting an expression in terms of the paper itself—since a paper of greater thickness, and requiring therefore a proportionately greater force to fracture it, weighs more per unit of area, and in the same proportion—all the numbers for breaking strains are strictly comparative one with the other. In the same way also the question of width may be disregarded.