July 27, 1905] 



NA TURE 



295 



under the face and the right arm straight down. Both 

 were probably female, and upon the breast of one was a 

 line bronze pin seven inches long with three pendant 

 ornaments, and three discs of bronze, one plated with gold. 

 Other bronzes of great interest were found with the second 

 skeleton. 



I do not write to describe the bones and ornaments, but 

 to make public the conduct of the Luton authority. A 

 most intelligent workman lives close to the site of the 

 discovery — one Thomas Cumberland — a man who has 

 studied the antiquities of the district for many years, and 

 to whom antiquaries are indebted for great and freely 

 given assistance. This man was on the spot at once, and 

 clearly and correctly stated the age of the bones and 

 ornaments as British or late Celtic. Notwithstanding this 

 information, the local police insisted on an inquest, 

 although the bones were broken to pieces and in the 

 highest degree friable. I went to the nursery and con- 

 firmed Mr. Cumberland's "determination, made drawings 

 of the bronzes, and such an examination of the bones 

 as circumstances would permit. The coroner refused to 

 hold an inquest, and so had no authority to make any 

 order, but he wrote and " suggested " that the bones 

 should be buried in the parish churchyard. .Armed with 

 this "suggestion," the relieving officer ordered an under- 

 taker to carry off the bones, which he did, in spite of the 

 protest of the nurseryman, who informed him that they 

 had been given to me and were niv property. He was 

 ordered to put the bones in coflRns and bury them in the 

 churchyard of Biscot. The undertaker took the bones to 

 his shop at Luton. I at once applied to the relieving 

 officer for permission to examine and measure some of the 

 bones. I clearly explained to him the nature and import- 

 ance of the discovery, and the trifling nature of the favour 

 asked. This official replied in a curt and rude manner, 

 and simply said, " I have no authority ; you must apply 

 to the coroner." 



I repeatedly wrote to the undertaker to delay the 

 funeral for a few days. I twice wrote to the coroner 

 in an urgent but most respectful manner, and pointed 

 out the importance of the discovery, which, indeed, is 

 quite unique in this district, but all to no purpose. He 

 said he had not given the " order " for burial, and he 

 refused to interfere, but he wrote to the undertaker and 

 said, " I can give no consent or authority in any way, but 

 must leave you to carry out the arrangement which has 

 been come to with you." I wrote letters for six days to 

 the different persons concerned, but to no effect : they 

 would have a funeral, and the police now actually de- 

 manded the bronzes from the owner. The property is free- 

 hold. 



Well, on Wednesday last the two coffins were screwed up 

 at Luton and taken in a hearse to Biscot churchyard, 

 where the vicar, in the presence of a policeman, officiated. 

 Shining breastplates were screwed on to the coffins in- 

 scribed. " Bones found at Leagrave, Julv 1905." Amongst 

 the bones in the coffins were several non-human examples, 

 a rib bone of a sheep, a piece of a rib of beef, a bone of 

 a rabbit, and another of roebuck. 



nunstable. Worthingtoni G. Smith. 



Graphical Solution of Cubic snd Quartic Equations. 



Some years ago you published some interesting com- 

 munications in regard to the graphical solution of cubic 

 and quartic equations (vol. Ixi. p. 5^, vol. Ixiii. pp. 515 

 and 609, vol. Ixiv. p. 5). The solutions then given give 

 only the real roots of the equation. I therefore take the 

 liberty of directing attention to the following method, 

 which gives the roots of cubic and quartic equations 

 whether the roots are real or complex, and may be applied 

 to equations of higher degree, with more complicated 

 results. 



A cubic equation with real coefficients may be reduced 

 by a simple real transformation to the form 



3'-(-l3S-f-I = 0, 



where q is real, and since the sum of the roots of this 

 equation is zero, they may be written in the form 

 — 2y 



y+ s!x 



If, now, we foim the symmetric functions, we have 



3y--i-.v=-(j 



2(y'-.\-y) = i. 

 Hence if we draw the fi.xed curve 



y' — -xy — a = o, 

 the coordinates of the points where it is cut by the 

 movable parabola 



3y=-f-.v + (j = o 



give the roots of the equation 



2='-|-q2-M=o, 

 i.e. if .%•„ and y„ are the coordinates of any such point, 

 -aVo and y„+ n'x^ are the roots of the given equation. 



In like manner a quartic equation with real coefficients 

 may be put into the form 



where 13 and s are real, and its roots may be put into the 

 form _ 



II + v'to , 

 — 1;+ v'to. 

 and, forming the symmetric functions, we have 



2.v" ■¥ w.^-V w^= - q (') 



2J'(Wi - If;) = - I (^^ 



v*-(Wy^-^w,^v''- + w{w^ = s (3) 



and if we put 



4t;^ = y 



(to, — TU;)"=X 



w'e find by simple elimination 



A.-y = i, (y + q)--(x-|-4s) = o. 

 Hence the intersections of the fixed hyperbola with the 

 movable parabola give values for x and y from which v, 

 TO,, and TO3 may be calculated. 



If we eliminate x from the two equations last written, we 

 have 



y^ -(- aqy- -(- q-y - 4sy — I = o. 



Hence there is always at least one positive value for y, 

 therefore a real value of -J \ also, since .\y = i, a positive 

 value for x, therefore a real value for •zu, — to, ; and since 

 from (i) TO,-|-TO, is real, real values for to, and to.. 



' ' H. IvAH Thomsen. 



1928 Mt. Royal Terrace, Baltimore, Md., June 7. 



NO. 1865, VOL. 72] 



7H£ PRESENT POSITION OF THE CANCER 

 PROBLEM. 



THE term " cancer " is in common parlance indis- 

 criminately applied to all tumours the growth 

 of which is unlimited and generally rapid, which tend 

 to recur after removal by operation, and particularly 

 which reproduce their like (the secondary or metastatic 

 growths) in parts of the body remote from the original 

 seat of disease. Pathologically there are various 

 forms of " cancer," or malignant disease, but there is 

 no need to deal with these here, and it may be stated 

 that there is no sharp line of demarcation between 

 the so-called benign and the malignant growths ; there 

 is a series of connecting links between the two. 

 Malignant disease is an important cause of death. 

 According to the last published report of the Registrar 

 General (1903), the death-rate from this cause per 

 1000 living was 0.87; for comparison that for pul- 

 monary tuberculosis (consumption) may be quoted; 

 this was 1-2. 



Moreover, it is a common belief that cancer is on 

 the increase ; people remark how much more frequently 

 it is heard of now than formerly, and apparently the 

 statistics support this view, for the cancer death-rate, 

 which was 056 in 1884, has steadily increased, and is 

 now 0-87, as stated above. Competent statisticians, 

 however, doubt whether the increase is real or only 

 apparent, and partly due to more accurate diagnosis 

 and to a greater tendency to seek medical advice. 

 During the last two or three decades surgery has made 



