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Ernst Mach

Fcchncrs Logarithmic Law

Mach rcad both Gustav Fcchncrs 1858 papcr and his 1860 book at-tcmpting to givc mathcmatical cxprcssion to Ernst Wcbcrs 1834 law rclating physical stimulus to mcntal responsc. "Fechncr’s law” in its mathcmatical form ran: S — K log R, and in words: The magnitude of a semation is proportional to the logarithm oj its stimulus.

If this law was valid, it could help put psychology on a scientific basis and establish a new science, “Psychóphysics," the study of rcla-tions between psychical and physical phenomena. Mach’s interest leci to laboratory tests. "My First serics of experiments in the summer of 1860 wcrc undertaken abovc all for the purpose of determining whether the so-called Weber Law of Fcchncr was also valid for the pcrception of time.” ¹⁵

By the fali of 1860 he had set up an cxperiment that seemed capable of giving decisive results. “Two pcndulums of variablc lcngths wcrc so arranged, thal 1 could only sec them bchind each other. Both . . . had their lcngths gradually changcd umil I noticed the diffcrcncc in the duration of the swings. It then became elear that the First noticed dif-fercnce in the time of the swings was proportional to the ovcral! timc.’’¹⁰

This result increasingly bothered Mach until he iinally concludcd that it was sufficicnt to refute the law. Later, Mach’s switch from Fcchncr’s version of "psychophysical parallelism” to his own served as confirmation. The relation betwccn “physical” stimulus and “mcntal” responses was not logarithmic but mcrcly proportional, nor was it sub-ject to exact mathcmatical measurement.

Mcasuring Blood Pres surę

Carl Ludwig, one of Briicke’s physiological colleagues in Vienna, constructed the first “Kymograph,” an instrument to record blood pressure, in 1847.'⁷ Vicrordt and Źdenne Marey devcloped a “Sphyg-mograph” as an improvemcnt on that. In early 1862, Mach, perhaps with the cncouragcmcnt of Ludwig himself, attempted to make still further improvcmcnts, but was only partly successful. Me was unable to find a necdlc both firm and llcxiblc cnough to measurc accurately pulsc bcats and changes in blood pressure on a graph. While he considered

his tcsting sufficicnt to justify rccommcnding Marey'$ Sphygmograph to mcci i cal doctors, noncthclcss, hc hoped that less complicatcd instru-ments could he developed in the futurę, in particular, devices that rrlied morc on photographcd wavc patterns and less on frcqucntly untrue and easily disturbed necdlc wanderings.

Molceular Behavior of I.irjmds

To understand morc about blood pressure and circulation Mach expcri-mented on forcing liquids through tubes. Unfortunatcly, howevcr, the fluid simply movcd too fast to be mcasured satisfactorily with his own primitivc equipment. Furthermore, his aticmpi to understand liquid motion in terms of the movcmcnt of moleeules also went astray. In particular, he failed in his effort to identify chcmical clcmcnts by mcans of spectral lines. This expcrimental failure was later uscd by Mach as an argument against the utility of the atomie theory.¹⁸

Acoustics and Ear Siructurc

Mach gravitated toward thesc fields by foliowing the interests of Bruckc and Ludwig, and the rccently published work of Helmholtz. He apparcntly hoped to compcnsatc for his lack of anatomical knowl-edge by his kccn sense of observation and his command and knowlcdge of musie. He was, to say the least, optimistic. He later wrotc: “I should like to elose with a reminiscence from the ycar 1863. Heirnholtz/s Sen-sations nf Tonę had just bccn published and the function of the cochlca now appeared elear to the wholc world. In a private conversation which I had with a physician, the latter dcclarcd it to be an almost hopeless undertaking to scck to fathom the function of the other parts of the labyrinth, whereas I in youthful boldness maintaincd that the question could hardly fail to be solved, and that very soon, although of coursc I had then no glimmering of how it was to be done." ¹⁹

Ernst Mach formed two elose and long-lasting personal friendships at this time, one with Joscf Popper-Lynkeus and the other with Eduard Kulkę.

Edmund Rcitlinger, a Yicnna privatdozcnt in ph\sics, introduced

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