March 28, 1901] 



NATURE 



5»5 



The difference between the results is too great to be accounted 

 for by differences in care in scraping or errors of the weighings. 

 It is either due to the fact that more dust had been carried off 

 one table by the rain than off the other, or it shows that near 

 the house the distribution was uneven. Still, the mean of the 

 two gives an idea of the order of the density on the inner 

 terrace, which was about o'oo"i35 gram per square inch, or, 

 taking 25 mm. = i inch, 2*2 grams per square metre, or about 

 5?5 tons per square mile, though, of course, to argue as to the 

 average fall over so large an area as a square mile is a big 

 extrapolation. 



Note upon a New Form of Spermatophore in an 

 Earthworm. 

 It is well known that the Oligochseta (like many other 

 animals such as molluscs, insects, &c.) form spermatophores. 

 Up to the present time two types of these spermatophores have 

 been recognised in the Oligochccta. In the Lumbricidse, Crio-- 

 drilus, kc, they are compact cases, generally open at one end, 

 and found invariably attached to the outside of the body in the 

 neighbourhood of the reproductive orifices ; they are sometimes 

 even slightly imbedded in the skin. The other type of sperma- 

 tophore characterises Tubifex and several allied genera, as well 

 as the Eudrilid earthworm, Polytoreutus. These are long thin 

 motile bodies. They are found only in the spermathecse of those 

 Annelids which they characterise. I have lately studied the 

 structure of a third variety of spermatophore which I found m 

 the spermathecal sac of another Eudrilid genus, Stuhltnannia." 

 This worm is long and slender, not measuring more than 2 mm. 

 in diameter. The spermathecal sac in which the spermatophores 

 are found is about 7 or 8 mm. long. I never found more than 

 two of ithe spermatophores in a sac ; they measure some 3 mm. 

 in length. The shape is peculiar. There is a "head" very 

 similar to that of the spermatophore of Tubifex, a long " beak," 

 open at the extremity, is followed by a circumferential swelling, 

 which is again succeeded by a narrow neck ; this in its turn 

 gradually widens until at the middle the spermatophore is large 

 and plump. The interior was a mass of separate spermatozoa 

 entirely uncompacted together. The site of the formation of 

 the spermatophores has been much disputed. It seems to be 

 clear, from the investigations of Mr. Lankester, that in Tubifex 

 they are at least moulded in the spermatheca, since the collar 

 of the head of the spermatophore not only corresponded in form 

 with certain foldings of the spermathecal wall, but was actually 

 observed lying in situ. As to the origin of the material, Mr. 

 Lankester and Prof Vejdovsky were disposed to trace it, 

 partly at least, to the "cement gland" of the male efferent 

 apparatus. I find in Stuhltnannia that the moulding of the 

 head of the spermatophore must be accomplished in the sperma- 

 thecal sac, since I also observed a spermatophore lying in 

 situ with its convexities fitting into corresponding concavities of 

 the walls of that sac. Further, the large size of the spermato- 

 phore necessitates the hypothesis that the whole of it is moulded 

 in the sac, since it could not possibly be contained — even with 

 the greatest stretching — in the spermiducal gland. As to the 

 origin of the material of the case, I hold it to be proved that 

 part comes from the spermiducal gland and that the rest is, in 

 all probability, a result of the breaking down of the abundant 

 cells which line the spermathecal sac. I may add that no 

 spermatozoa protrude through the case. This spermatophore 

 of Stuhltnannia is evidently somewhat intermediate in its 

 characters between the two types already known. 



Frank E. Beddard. 



Graphic Solutions of the Cubics and the Quartics. 



The note by Prof. G. B. Mathews, F.R.S., published in 

 Nature of November 16, 1899, has encouraged me to write 

 the following, which may be also of some interest. I have con- 

 sidered not only the quartics, but also the cubics. For the 

 quartics, the methods in this letter will be simpler than those of 

 Prof. Mathews. We require to have a sheet of squared paper 

 on which the curve ^ = x' for the cubic and the curve _j' = a'^ + ^* 

 for the quartic have been printed. 



I. For the cubic, take the c\xr\e y = x^ and a straight line the 



equation of which is — + _ = i. Then the abscissze of the inter- 

 a I 



sections of the curve and the straight line are the real roots of 

 x'^ + -1=0. Now the general cubic is at once reducible to 



NO. 1639, Vol. 6^'\ 



the form z^+pz-\-q=o, and if we putz= -x^q, this becomes 



x^ + ^x- I =0. This is identical with the former ii a = ?~ ; so 



qi • p 



we can calculate a very easily, then read off the real values of 

 X, and finally take %=■ - x "ijq. 



II. For the quartic, take the cmwz y — x"^ ^ x^ and a straight 



line the equation of which is -4-^=1. Then the abscissse of 

 a 



the intersections of the curve and the straight line are the real 



roots of x*'->!-x'^-\- ~x-b = o. Now the general quartic is at 



a 

 once reducible to the form c*+/3'^ + ^j2! + r=o, and if we put 



z — xJp, this becomes x* + x^ + ^x + -5=0. This is identical 



^■^ pi p^ 



with the former if a = -_, b= - —; so we can calculate a 



q \l p P* 



and b very easily, then read off the real values of x, and finally 

 take z = x :Jp. 



For the quartic, we can take also the parabola j/ = Jf' and a 

 circle (;«;- a )2+^^ = p2. T. Hayashi. 



Matsuyama Chugakko, lyo, Japan, December 28, 1900. 



"The Principles of Magnetism and Electricity." 



There are two points occurring in the review (p. 434) of 

 "The Principles of Magnetism and Electricity" in which the 

 author appears to me to be correct, though the examples are 

 given as instancing errors into which he has fallen. The re- 

 viewer states, "The author measures magnetic force in dynes 

 and difference of potential in ergs," thereby apparently implying 

 that this is incorrect. Surely these are usual units for express- 

 ing these quantities. Again, the author is taken to task for 

 stating that in the case of a dynamo or motor armature, " owing 

 to the self-induction of each section, a certain amount of eriergy 

 is used twice in each revolution to establish the current in it. 

 This energy is lost so far as the external circuit or the effective 

 output of the machine is concerned." Whilst with a dynamo 

 running sparklessly with copper brushes this is only partially 

 true, the difficulty of obtaining the return of the energy thus 

 absorbed is in practice so great that we see on a very large 

 proportion of machines that carbon brushes are used, the 

 object of which is to enable this energy to be wasted without 

 an actual spark, and it is well known that machines with 

 carbon brushes thus working have a higher rise of temperature 

 from the waste of power than when true electrodynamic com- 

 mutation takes place. Actual measurements of power absorbed 

 have also shown a waste of power from this cause sometimes 

 exceeding 5 per cent, of the output of the machine. 



London, March 12. Llewelyn B. Atkinson. 



Through the courtesy of the Editor I am able to reply to 

 the letter of Mr. Llewelyn B. Atkinson, in which he challenges 

 two of my criticisms in the review of "The Principles of Mag- 

 netism and Electricity," by Mr. P. L. Gray. Mr. Atkinson 

 states that I " apparently imply " that measuring magnetic 

 force in dynes, and difference of potential in ergs, is incorrect. 

 To prevent any misconception, I now wish to state quite definitely 

 that I regard the above method of measurement as hopelessly 

 and absolutely wrong. If it be correct, then magnetic force is 

 a quantity whose dimensions are identical with those of dyna- 

 mical force, and difference of potential a quantity of the dimen- 

 sions of energy. If Mr. Atkinson is satisfied with these con- 

 clusions, and is prepared to uphold them, I have no further 

 remarks to offer on the subject. I may, however, point out that 

 measuring difference of potential in ergs is about as logical a 

 proceeding as measuring difference of (gravitational) level in 

 ft. -lbs. Some eccentric people might, no doubt, be found to 

 uphold this latter proceeding. But a falsehood does not become 

 a truth merely because a number of people give their unreason- 

 ing assent to it. 



With regard to the second criticism, that relating to the pro- 

 cess of commutation in a dynamo, I still maintain that the 

 statement in Mr. P. L. Gray's book is misleading and incorrect 

 in its generality, and Mr. Atkinson practically admits as much 

 in his letter. Nothing is said by Mr. Gray as to the particular 

 statement in question being intended to apply to carbon brushes 

 under certain conditions of use. It is a general statement, made 

 without any qualifications, and as such is incorrect. 



The Reviewer. 



