LOCOMOTORY DIRECTIVE MOVEMENTS 543 



Taking into account the facts we have already learned as to stimuli, we 

 are led in the present instance to seek for the liminal intensity of concentration 

 of malic acid which will give an obvious attractive result. In PFEFFER'S experi- 

 ments that concentration was found to be o-ooi per cent. ; still weaker solutions 

 had only a casual effect. As might be expected, the liminal value altered with 

 the age of the organism, just as in the case of other factors, e. g. temperature 

 ( VOGLER, 1891). In fact, extraordinarily minute quantities of various substances 

 may operate as chemical stimuli. In one of PFEFFER'S experiments the tube 

 contained not more than 0-0000000284 mg. of malic acid, and of that naturally 

 only the minutest fraction could come in contact with a single sperm. Such 

 an amount is, however, by no means so insignificant when the weight of the 

 sperm is taken into account ; still if the weight of the sperm be estimated at 

 about 0-00000025 m g- it is only ten times as great as that of the malic acid which 

 was used. Quite as minute quantities of other chemicals are able to induce 

 reactions, for DARWIN (1876, p. 246) found that 0-00000328 mg. of ammonium 

 phosphate excited a response in Drosera, and ENGELMANN (1883) showed that 

 a trillion th part of a milligram of oxygen could act as a stimulus to Bacteria. 



It has already been pointed out that fern antherozoids distribute them- 

 selves uniformly in a homogeneous solution of malic acid, but it would be quite 

 incorrect to suppose that the sperms were not stimulated by such a solution ; it 

 renders them, as a matter of fact, less sensitive to a unilateral action of the acid 

 and the liminal intensity of the stimulus is higher for sperms swimming in such 

 solution than for those swimming in pure water. Moreover, the increase in 

 the liminal intensity is quite proportional to the concentration of the solution in 

 which they lie. In water o-ooi per cent, of malic acid is required to induce 

 a stimulus. 



In 0-0005 % malic acid, 0-0015 % is required to effect a stimulus 

 ooor o % o.o3 o % 



>> - 01 % -3 % ?> > 



>> 0> 5 % J -5% 



It will be seen that the liquid in the capillary tube must always be 30 times as 

 concentrated as the culture liquid, and hence the absolute difference in concentra- 

 tion necessary to induce a response is much greater when the culture solution 

 is concentrated than when it is weak. We have already become acquainted 

 with the law which governs the relation of sensation to stimulation, a law which 

 was first established with reference to certain human sensitivities and is known 

 as WEBER'S law or the law of psychophysics. So far as regards our own special 

 sensitiveness to weight, for instance, a weight of I mg. must be increased J, 

 a weight of 10 mg. must be increased ^ before we can appreciate a difference 

 between them. This law, it would appear, is of very general, but by no means 

 universal, application. It is limited to certain concentrations, for instance, 

 in the case of fern antherozoids, and does not apply to very high or very low 

 concentrations. A capillary tube containing a 0-0003 per cent, solution of malic 

 acid can attract sperms swimming in a o-ooooi percent, solution, and yet, as we 

 have seen, this solution, after diffusing into water, is unable to act as a stimulus 

 on the sperm ; on the other hand, PFEFFER was unable to attract sperms float- 

 ing in a 0-04 per cent, solution by concentrations either 30, 40, or 50 times as great. 

 In the last mentioned experiment PFEFFER found that the sperms were quite in- 

 different to a 3-4 J per cent, solution. No end was to be gained by raising the 

 concentration higher than that, for 5 per cent, solutions were found to act quite 

 obviously in a repellent manner. Of this phenomena we shall speak later on. 



According to PFEFFER'S experiments, fern antherozoids react only to malic 

 acid and its salts as also to maleic acid (which does not occur in nature), but not 

 to its stereoisomer fumaric acid. The reaction is so specific that antherozoids 



