run the risk of spoiling so remarkable a specimen which it might turn out to be difficult or impossible to replace. I therefore had another ring made of iron from the same parcel, and believed to have been cut from the same bar as the first. As, however, there was some doubt about this latter point, I thought it better in the first instance to anneal the new ring, and test it with a few turns of wire wound upon it. Its behaviour was found not to differ materially from that of Ring I. A very small elongation-too small to be measurablewas, however, observed with a magnetising force of only 3 C.G.S. units, contraction beginning when the force was increased beyond this value. The ring was then made red hot, and plunged into cold water, with the object of hardening it, after which operation it was replaced in its boxwood jacket and wound with 473 convolutions of wire.

This ring, called Ring II, was now found to give the same results as the old unannealed rings and straight wires. As appears in Table II and fig. 2, it attained its maximum elongation of about 33 ten-millionths in a field of 80, its original length was recovered in a field of about 440, and a retraction of 11 ten-millionths occurred in a field of 560.

It appears, therefore, that as regards magnetic changes of dimensions, an iron rod or ring is affected by annealing in very nearly the same manner as by tensile stress,* a result which would hardly have been anticipated.†

Notes regarding Details.

The apparatus and methods of experiment were the same as those fully described in 'Phil. Trans.,' vol. 179, A, pp. 218-224, the instrument being arranged so as to have a magnifying power of 43,745.

The height of each little square in fig. 2 corresponds to a length of about one-millionth of an inch (0·00000088 in. for Ring I and 0.00000103 in. for Ring II).

The wires and rings were demagnetised by reversals before every single observation. For a description and diagram of the demagnetising apparatus, see loc. cit., p. 207.

*Roy. Soc. Proc.,' vol. 47 (1890), p. 469.

The less so since the length of an iron rod seeins to be diminished by annealing. A piece of iron wire 100 mm. long, cut from the same hank as that used in the experiments, was heated in a Bunsen flame, and slowly cooled. It was found to have contracted 0.07 mm., i.e., 0·07 per cent. It was then heated in the blowpipe flame, and dropped into cold water. This produced an elongation of about 0.02 mm., leaving the wire 005 mm. shorter than it was originally. These measurements were made with a rough apparatus extemporised for the purpose, and I do not attach much importance to the quantitative results, though there can be little doubt that they are qualitatively correct.

The dimensions of the iron rings and their boxwood jackets were as follows:

The rings were formed from rectangular bars with welded joints, and were turned in the lathe to the above dimensions.

The magnetic fields were calculated from the formula H = 2ni/r where n is the number of convolutions, i the C.G.S. current, and the mean radius.

The current was derived from a battery of twenty-seven storage cells used for lighting the house.

IX. "On Correlation of certain External Parts of Palomon serratus." By H. THOMPSON. Communicated by Professor WELDON, F.R.S. Received January 25, 1894.

In 1890 Professor Weldon published (Roy. Soc. Proc., vol. 47, p. 445) the results of measurements of certain organs of the common shrimp, with a view to establish by accurate data the degree of variation existing in those organs. In a later paper (Roy. Soc. Proc.,' vol. 51, p. 2) he determined, by Mr. Galton's method there described, the degree of correlation existing between four organs of the same animal, and in a recent paper (Roy. Soc. Proc.,' vol. 54, p. 318) similar determinations have been worked out by him for certain organs of Carcinus monas.

Some time ago it was suggested to me by Professor Weldon that I should determine the values of correlated variations in a number of parts of the hard exoskeleton of the common prawn (Palæmon serratus). Accordingly, 1000 adult female prawns, chosen at random, were procured from Plymouth and measured. Twenty-two measurements were made of each prawn, except in the case of two or three measurements which were made on part only of the sample. The parts measured were the following :

I. Length of body from tip of rostrum to end of telson (excluding terminal spines).

II. From hindermost point of orbit to hinder edge of carapace in a straight line.

III. From tip of rostrum to median point of hinder edge of cara

pace.

IV. From tip of rostrum to tip of first dorsal spine.

V. From tip of rostrum to tip of last (hindermost) dorsal

spine.

VI. From tip of first to tip of last dorsal spine.

VII. From tip of last dorsal spine to tip of the last but one. VIII. From tip of last dorsal spine to median point of hinder edge of carapace (post-spinous portion of carapace). IXa. The right squame from tip of tooth to posterior edge of the external articular tubercle.

IX. The left squame measured in like manner.

X. The anterior and posterior median points of the 1st abdomi

nal tergum.

XI. Posterior portion of the 1st abdominal tergum measured in like manner.

XII. The 2nd abdominal tergum measured in like manner.

XVII. The telson from the median point of the anterior edge to the tip of the median posterior projecting tooth (ie., excluding the terminal spines).

XVIIIa. Exopodite of the 6th abdominal right appendage from the tip of the dorsal or fixed tooth to the posterior edge of the dorsal articular tubercle.

XVIII. Exopodite of the 6th abdominal left appendage measured in like manner.

XIXa. From base of lateral spine projecting from the posterior end of the telson to the base of the posterior spine on the dorsal surface of the telson on the right side. XIXb. Similar measurement for the left side.

Measurements I to III were made with compasses, and may be regarded as accurate to within about 0.5 mm., except No. I, the body length, which is somewhat less accurate. The remaining measurements were made under a microscope, and are accurate to within 0.05 mm.

For the purpose of comparison the measurements are all expressed in terms of the body length, which is taken as = 1000.

Diagram of exoskeleton of Palæmon serratus with appendages removed. The numerals refer to the numbers of the measurements.

Out of the 1000 prawns seven had a deformed rostrum, and six had a deformed telson. In several of the numerical results set out below these thirteen animals have been excluded because their deformities affected the body length to such an extent as to give a wholly fictitious value to the reduced measurements of the other organs.

The existence of a long rostrum in the prawn has proved a serious hindrance, since its length in proportion to that of the body is very variable, and hence those parts in which the rostrum is an element present a degree of correlation which is very slight, and render impossible any real comparison with the corresponding parts in the shrimp, for instance, which has scarcely any rostrum at all.

Selection was made of the female prawn as being larger than the male, and therefore more convenient for the purposes of measurement. The largest measured 111 mm. in total body length, the smallest 61.5 mm.

All the measurements having been reduced, as above stated, to fractions of the total body length, they were next arranged in order of magnitude for each organ separately, and in almost every case the values were found to range themselves with a fair degree of symmetry around the median value, and to correspond with more or less accuracy to calculated probability curves. In one case, however (measurement No. VII), the curve presented features of asymmetry which have been investigated by Professor Karl Pearson (Roy. Soc. Proc., vol. 54, p. 329).

The next step was to determine the degree of correlation between various pairs of the organs measured. The method used was that originally suggested by Mr. Galton, and sufficiently explained by Professor Weldon in his paper above referred to, so that it is unnecessary to repeat it here.

The following table gives the value of "Galton's function" for 56 pairs of organs :—

Values of Galton's Function (r) for Pairs of Organs in the Common

Prawn.

(The Roman numerals refer to the list of organs measured given

An examination of these values shows that, as might be expected, the highest degree of correlation exists between the paired organs, viz., between the right and left squames, 0.94; between the right and left exopodites of the 6th pair of swimmerets, which, with the telson, form the propelling organ of the prawn, 0.86; between the distances of the spines on the telson from its posterior end, 0·76.

Next, we observe that a strong correlation obtains between the terga of adjacent abdominal segments; their values range between 0.58 and 0.71; while those of segments that do not lie next each other range between 0:47 and 0.61. A considerable fall occurs in the degree of correlation between the telson and the segments of the abdomen-it varies from 0.26 to 0.29, except in the case of the 6th abdominal segment, which lies next to the telson, when the value rises to 0-51. It is interesting to note that Professor Weldon found the corresponding value for the telson and 6th abdominal tergum in the