The Mystery of the Downs

by John R. Watson; Arthur J. Rees

“‘Surely every man walketh in a vain shew: surely they are disquieted in vain: he heapeth up riches, and knoweth not who shall gather.’”

“Appropriate enough,” commented Marsland.

“There remained the final 6, under the 396, to be explained, before I was able to start on the table which had been used to build up the cryptogram. The fact that the figures in the outside circle start at 6 indicated that there was some connection between it and the inner 6. I came to the conclusion that the inner 6 meant one of two things: either the designer preferred to start from the number 6 because he thought the figure 1 was too clear an indication of the commencement of his cryptogram, or else he made his start from the sixth letter of the text. I thought the former the likelier solution, but I tried them both, to make sure. The first five figures on the latter solution gave me a recurring Y, which indicated that I was on the wrong track because it was essential there should be no recurring letters. There are no recurring letters in the other key, as the table shows:

6	7	8	9	10	11		12	13	14	15	16		17	18	19
S	u	r	e	l	y		e	v	e	r	y		m	a	n
1	2	3	4	5	6		7	8	9	10	11		12	13	14
20	21	22	23	24	25	26		27	28		29		30	31	32	33
w	a	l	k	e	t	h		i	n		a		v	a	i	n
15	16	17	18	19	20	21		22	23		24		25	26	27	28
34	35	36	37		38	39	40	41	42	43		44	45	46	47
s	h	e	w:		s	u	r	e	l	y		t	h	e	y
29	30	31	32		33	34	35	36	37	38		39	40	41	42
48	49	50		51	52	53	54	55	56	57	58	59	60		61	62
a	r	e		d	i	s	q	u	i	e	t	e	d		i	n
43	44	45		46	47	48	49	50	51	52	53	54	55		56	57
63	64	65	66		67	68		69	70	71	72	73	74	75
v	a	i	n:		h	e		h	e	a	p	e	t	h
58	59	60	61		62	63		64	65	66	67	68	69	70
76	77		78	79	80	81	82	83		84	85	86
u	p		r	i	c	h	e	s		a	n	d
71	72		73	74	75	76	77	78		79	80	81
87	88	89	90	91	92	93		94	95	96		97	98	99
k	n	o	w	e	t	h		n	o	t		w	h	o
82	83	84	85	86	87	88		89	90	91		92	93	94
100	101	102	103	104		105	106	107	108	109	110
s	h	a	l	l		g	a	t	h	e	r
95	96	97	98	99		100	101	102	103	104	105

“The circle of figures taken in their ascending order and starting with the second six, run thus:

6, 8, 9, 10, 11, 13, 17, 19, 20, 21, 23, 25, 26, 27, 39, 51, 54, 72, 80, 89.

Now, assuming that my interpretation of the solitary six in the circle is correct—that the old man started from six because he thought the use of the figure one gave away too much—we will substitute for these figures the letters which appear underneath them in the table. The substitution gives us the following row of letters:

S R E L Y V M N W A K T H I U D Q P C O S

“This is the line of letters from which we will endeavour to reconstruct the old man’s cryptogram. We can, I think, go forward with the assurance that they are the actual letters represented by the cryptogram, for several reasons. There are no recurring letters, and they represent every letter in the text in consecutive order, with three exceptions which are capable of a simple explanation. The U has been taken from the second ‘surely’ instead of the first, to mislead the solver. Otherwise you would have surely for the first five numbers, which would be too clear an indication. The same reason exists for making A the tenth letter instead of the eighth; which would reveal the word ‘man.’ The final letter—the ‘G’ in ‘gather’—has been excluded, for a reason which I will presently explain.”

“What about the second S—the final letter? Do you not call that a recurring letter?” asked Marsland, who was closely examining the table the detective had prepared.