September i6, 1920] 



NATURE 



79 



centuries, and the third with the establishment 

 and consolidation of the Empire. Geography plays 

 a minor part in the book, and the title is therefore 

 likely to be misleading. Nevertheless it is refresh- 

 ing to find a school history in which the author 

 has departed from the time-honourea custom of 

 subdividing his work according to the number of 

 monarchs with whom he intends to deal. 



Letters to the Editor. 



[The Editor does not hold himself responsible for 

 opinions expressed by his correspondents. Neither 

 can he urtdertake to return, or to correspond with 

 the writers of, rejected manuscripts intended for 

 this or any other part of Nature. No notice is 

 taken of anonymous communications .] 



"Spiranthes autumnalis" in Scotland. 



GRE,tT is the debt whirli British botanists— experts 

 and amateurs alike — owe to the authors of the ■" Hand- 

 book of the British Flora." It is scarcely possible to 

 imagine a simpler or more convenient key to the 

 natural orders. But a good deal has been added to 

 our knowledge of British plants since the last revision 

 of the work by Sir Joseph Hooker forty years ago, and 

 it is to be regretted that before the latest edition was 

 published in 1918 it was not passed through the liands 

 of a competent editor to bring the work up to date. 

 For instance, it is stated that the little orchid, 

 Spiranthes autumnalis, is found nowhere north of 

 Yorkshire and Westmorland. I had always accepted 

 this as gosp«-l until last .August, when, while exploring 

 a wood on Speysidc for Linnaea borealis, 1 came upon 

 a little colony of "lady's tress<'s." Since then 1 have 

 received trustworthy information that Spiranthes 

 grows in the valley of the Nairn. 



I do not know w'hethcr this addition to our Scottish 

 flora has been recorded hitherto. 



Herbert Maxwell. 



Monrcith. 



Associated Squares and Derived Simple Squares of 

 Order 5. 



The six different types shown below are distin- 

 guished by the position of the complernentary numbers 

 (1, 25; 2, 24; 3, 23, etc.): 



A B C . 



2510 3 9 18 20 II 522 7 6 4 21 19 IS 



10 25 3 9 18 22 20 5 II 7 



14 2 13 12 24 12 14 13 2 24 



4 19 21 6 15 9 10 3 25 18 



17 8 23 16 I 16 17 23 8 I 



II 20 5 22 7 

 J 14 13 12 24 



ic« 421 6 15 

 8 17 23 16 I 



D 



25 18 3 9 ID 



II 7 5 22 20 



-■ ■!4 >3 " M 



8 I 23 16 17 



19 1521 64 



25 18 3 10 9 35 10 3 18 9 



II 7 5 30 32 19 4 31 15 6 



3 34 13 14 13 3 14 13 34 13 



19 ij 31 4 6 II 30 5 7 33 



8 I 23 17 16 8 17 33 I 16 



Constant 65. 



A is an associated square, and by means of Dr. 

 Planck's meth(Kl of complementary differences it has 

 been found that there arc 3034 squares of this type, 

 and each one can have sixteen inversions, making a 

 total of 48,544 squares. 



B. "By exchanging the first and second numbers in 



NO. 2655, VOL. 106] 



both rows and columns of A, type B is obtained. 

 There are thus 48,544 squares of type B. 



C. By exchanging the first and fourth numbers in 

 both rows and columns of A, type C is obtained. 

 There are thus 48,544 squares of type C. 



D. Every associated square cannot be converted 

 into type D, but by means of Dr. Planck's method of 

 complementary differences the number can be found. 

 It is 972, and each one can have one inversion, 

 making a total of 1944. 



E. But 36. of these 972 can be converted into type E, 

 and each one can have three inversions, making a 

 total of 144. 



F. -Also the same 36 of type D can be converted 

 into type F, and each one, again, can have three 

 inversions, making a total of 144. 



In the last three types, squares can be constructed 

 for each type by taking the columns as the rows and 

 vi£e versa, and I have included these in the totals. 

 This obviates the necessity of including types of 

 squares when these three types are turned round 

 through a quarter of a circle. 

 Totals : 



A ... 48,544 



B ... 48,544 



C ... 48,544 



D ... 1.944 



E ... 144 



F ... 144 



147,864 



These are only six out of thirty-four types of 5th 

 order, making a total of nearly 700,000 squares. 



J. C. Burnett. 

 Barkston, near Grantham, Lines. 



The Spectrum of Nova Cygni III. 



Cloudv and hazy nights have seriously interfered 

 with spectroscopic observations of this nova at Stony- 

 hurst, but some good photographs of the spectrum 

 were obtained with the Whitelow short-focus 

 prismatic camera on the nights of August 29 and 30 

 and September 6 by Father J. Rowland. The spec- 

 trum, the bright band spectrum characteristic of 

 the second stage in the progressive spectra of novse, 

 remained practically the same during that interval. 

 The bright hydrogen bands extended, on the average, 

 over 20 A. units, and consisted each of two com- 

 ponents. There was a bright extension on the violet 

 edge of H(, about A 3870, which was possibly the first 

 sign of the incoming of the nebular band. 



Besides hydrogen, the most prominent radiations 

 were, due to enhanced iron lines, 5316, 5169, 5019, and 

 4924. On September 6, 4924 alone of the four radia- 

 tions named left an impression on an isochromatic 

 plate. Between Hp and H^ were two prominent and 

 very broad bright bands, the first extending from 

 \ 4703 to 4628, and the other marked by throe maxima 

 corresponding to the iron lines A 4584, 4550, and 4516. 

 Between Hy and Hj were three very prominent radia- 

 tions, A 4303 iron, 4228, and 4170, the last being almost 

 as intense as Hj. The K calcium band was also 

 doubled, and extended over about 15 A. units. On 

 .August 29 the spectrum extended far into the violet. 

 On .September 6 the visual magnitude was estimated 

 as lower than the fifth. No obvious change in the 

 spectrum could be detected on n weak impression 

 secured on September 10. The iron line 4934 was 

 still present. Ha was very brilliant. 



A. L. CORTIK. 



.Sfonyhurst College Observatory, Blackburn. 



