474 



NATURE 



[June io, 1920 



wires are .-ittached to two torsion heads, and the lower 

 ends B, D to a bar loaded with a considerable mass. 

 When the wires are free from torsion, they are in a 

 vertical plane. The distances AC = 2a,, BD = 2ao, are 

 nearly equal. If the torsion heads are turned through 

 ^ from their zeros, the bar will turn through B in 

 the same direction, until the bifilar couple balances 

 the couple due to the torsion of the wires. Then 

 sin 6' = C(0-6'), where C is, for practical purposes, inde- 

 pendent of <\> and B. By observing Q and (^, C is found. 

 Then, if r is the mean radius of the wires and M the 

 load supported by them, the rigidity, n, is ^i\<'n by 



;/=W2.MC. 



A damping^ device is provided so that steady readings 

 can be obtained in a room subject to vibration. Bends 

 in the wires near the upper ends have the same effect 

 as if the points A, C described small horizontal circles. 

 Errors due to this cause are eliminated by a rough 

 harmonic analysis. (2) An experimerVt on a piece of 

 common string. When a mass M is suspended by a 

 piece of common string from a fixed support, it be- 

 gins, when set free, to rotate about the axis of the 

 string. The string, therefore, exerts a couple, G, on 

 the body, and the relation of this couple to M is 

 studied in the experiment. If, starting from rest, the 

 body makes n revolutions in time t, the angular ac- 

 celeration a, assumed constant, is given by ^at' = 27711. 

 If K is the moment of inertia of the body, G = Ka. 

 If the length of the string is of the ordet of 2 metres, 

 the angular acceleration is approximately uniform for 

 at least the first 10 or 20 revolutions. The load is 

 supplied in the form of a number of equal inertia 

 bars which can be thieaded on a light rod carried by 

 the string. Then K is practically proportional to M. 

 It is found that the time for, say, 10 revolutions from 

 rest is nearlv constant. Hence G is nearly propor- 

 tional to M. (3) Experiments with a plane diffraction 

 grating, using converj^ent light. A lens forms a real 

 image B of a vertical slit S illuminated by sodium light. 

 A plane diffraction grating, with its rulings vertical, 

 is placed betvvet^'n the lens and B, so that the vertical 

 central plane of the beam, which cuts the grating in 

 O, makes an angle B with the normal to the grating, 

 and BO = ». If C is one of the "real" diffracted 

 imai^es of order p. and if CO or v makes an angle 

 tp with the normal, then 



71 sec" 6' = 'Z'sec-(/) . . . . (i) 

 If the grating interval is d, the wave-length is given by 



pX = d(/m<p-sme) .... (2) 

 In the experiment the relation (i) is tested, and 

 the wave-length is founc!! by (2). The images 

 are received on a glass scale moving along 

 an optical bench, the length of the scale being 

 horizontal and perpendicular to the bench. — Major 

 P. A. M^cMahon : Congruences with respect to com- 

 posite moduli. This paper deals with the primitive 

 roots of the binomial congruence the exponent of which 

 is anv divisor of the totient of a composite modulus. 

 Numbers being divided into categories according to 

 the number of their different prime divisors, tables of 

 primitive roots are given for the cases of the second 

 and third categories. — A. Kienast : Equivalence of 

 different mean values. This is a continuation of a 

 former paper by the author, and deals with the equi- 

 valence of conditions for the existence of the limit 

 of the mean sum of a continually increasiner number 

 of terms. — Prof. H. F. Baker : Construction of the 

 ninth intersection of two cubic curves passing through 

 eight given coplanar points. Let A. B, C, M, N and 

 P, Q. R be ttie given ooints ; take T external to their 

 plane; let TP, TQ, TR meet a quadric containing 

 NO. 2641, VOL. 105] 



A, B, C and the lines TM, TN, in further points 

 P', O', R' ; let the twisted cubic curve through T, A, P', 

 Q', R' which has BC for chord mee-t the quadric again 

 in O'; then TO passes through the required ninth 

 pomt. — W. E. H.* Berwick : Ouintic transformations 

 and singular invariants. This paper deals with tli«- 

 arithmetical solution of a certain sextic equation aris- 

 ing in the thoory of modular functions, the co- 

 efficients of which are functions of a certain algebraical 

 number. The arithmetical character of the number of 

 fields which arise \i, determined in detail. 



Manciiestek. 

 Literary and Pliilosophical Society, Mav 4.^ — Mr. 



William Thomson, vice-president, in the chair. — 

 Major T. Cherry: The origin of agriculture. The 

 annual flood-cycle of the Nile pi'ovided perfect condi- 

 tions for the growth of cereals. Since none other of 

 the great rivers on the banks of which civilisation 

 first appeared afforded such natural possibilities for 

 the growth of cereals, it was claimed that man must 

 have learned in Egypt irrigation and the cultivation 

 of cereals. The author, in discussing the origins of 

 wheat and barley, claimed that the originals of our 

 cultivated barley probably evolved in the Nile Valley, 

 and those of our wheat on one of the islands of the 

 yEgean Archipelago. 



Literary and Philosophical Society (Chemical Section), 

 April 30. — Mr. J. H. Lester, chairman, in the chair. — 

 Dr. J. A. R. Henderson: Alchemy and chemistry 

 among the Chinese. The early objects of the 

 alchemists were discussed, and their discoveries in 

 metallurgy, mineralogy, and botany detailed. The 

 latter included the manufacture of pigments, lacquers, 

 porcelain, paoer, and the early discovery of the ex- 

 plosive properties of gunpowder. The exploitation of 

 vast coal deoosits and of iron and other metallic ores, 

 and the production of oils and medicinal substances, 

 are taking iilace. 



Mav iJ. — Mr. J. H. Lester, chairman, in the chair. 

 — Prof. F. L. Pyman : The relation between chemical 

 constitution and physiological action. 



Dublin. 

 Royal Irish Academy, May 10. — The Most Rev. the 

 Right Hon. J. H. Bernard, president, in the chair. — 

 J. N. Halbert : Acarina of the Intertidal Zone. The 

 various forms, several of which are new to science, 

 were studied in their relation to the well-known 

 zones, or belts, of the orange lichen, Pelvelia, and 

 Fucus usuallv present, where there is sufficient foot- 

 hold for them", on the sea-shore. Excluding the 

 families Halacaridae and Hydrachnidae, the species are 

 distributed in the four terrestrial families as follows : 

 Gamasidae 28, Oribatidae 17, Tvroglvphidae 2, and 

 Trombidiidee 18.— Miss Jane Stephens: The fresh- 

 water sponges of Ireland. The fresh-water sponges 

 of Ireland number only five species. Their habitat, 

 mode of growth, and distribution are discussed. 

 Among the points of interest are the following : It 

 has been found that the sponges do not occur in 

 mountain streams, unless there is a lake, however 

 small, in the course of the stream, and that, on the 

 other hand, thev occur most luxuriantly in a stream 

 just below its exit from a lake. One species avoids 

 the limestone areas. The variations of the com- 

 moner species are traced at some length. The paper 

 is illustrated by numerous drawings of spicules and 

 bv maos showing the distribution of the species— T. A. 

 Stephenson : The genus Corallimorohus. Cor-allirrtor- 

 ohus is a genus of deen-sea Actiniaria, first described 

 bv Moselev in 1870. and I'riter bv Hertwig in 1882 and 

 1888. There are two soecim'-ns of C. rigidiis in the 

 collection of anemones made by the Fisheries Branch 



