504 Miscellanea 



If we wish to apply Jlakeliam's hypothcsis to a table we can tjike a normal curve, mviltiply 

 by q^ (the probability of dying in a year), and then fit the expression just given to the figures 

 we obtiiin. The best way to do this will be by moiuents about the origin of the normal ourve 

 chosen for the exposed and, writing /x, and fL., for the.se, we have 



h^l^AZ^ and N.Jli±^\ 

 Ml 



'2- X 



which is the complete Solution. As Makehara's hypothesis only holds good for part of t\ mortality 

 table we must choo.sc our e.\i>o.scd curve so that the death.s re.sultiiig therefrom will be insignilicant 

 bclow say 25 in youth and above 8."> in old age. U.sing (t = 8;5 and SOö a.s origin I niade a trial 

 with the //•" Mortality Table {Institute of Actuaries, Healthy Male Lires). I gnniiied the deaths 

 corresponding to this assumed normal curve for every five years of age and using Sheppard's 



adjustmcnt for the second moment, found /i = 6-4703 years, and hence log,(,c=-2log,je= •040464. 



The gi-aduation in the Text Book for actuaries uses 'OyOeöT and 1'rofe.ssor Pearson gave 

 ■040640.") in Biumetrika, Vol. I. Part 3. We thus reach an e.\treuiely easy method of satis- 

 factorily finding c. 



Using the sanie normal curve and proccss with the graihiated .sickne.ss rates I found 

 '''gio'^='0'lß'-''^0^ '^■"1 t'i*^ resulting rates gave a good agreement from age 30 to age 80. An 

 attenii)t to ht the whole sickness table was made by taking (r=12'5 and 47"5 as origin and 

 the valnc of logj^c was found to be -040133 but the result was misatisfactory as regarda 

 graduation. 



The fact that Makoham's hypothesis fits Sutton's sicknes-s t;vblc to the same extent as it 

 does a mortalitj- table is further eviiiunce of the close relationship existing betweeu the two 

 classes of t;ibles. 



III. Craniological Notes. 



(iv) Humogeneitij und Heterogeneity in Grania. 

 By Charles S. Myers. 



Professor Pearson's vigorous denunciation* of niy criticismt of Miss Fawcett's menioirj on 

 the Naqada skulls gives me a welcome opportunity of strengthening the po.sition I took up. 



(i) It may be remembered that, in order to dctermine whether or not the Naqada material 

 belonged to a homogeneous race, Miss Fawcett compared the variability of skuU-leugths (and 

 of other nieasuroments, which for brovity's .sake I have here to neglect) in the Naqada series 

 with the variabilities in fo>ir serie.s, which were considered to be of an admittcdly homogeneous 

 character, viz., in a Bavarian, an Aino, a French and an English serie.s. The variabilities of 

 .skuU-lengths in these four sories were found to be 6-088, 5-936, 7-202 and 6-446 respectively. 

 Now, taking the skull-lengths of a mi.xed series of Australian, Guanche, Eskimo and Chinese 

 skulls, I obtained a variability of 8-389; whereupon I concludcd that if a sniall series, which wjis 

 as hetcrogcneous as could be conceived, showcd a skuU-length variability of 8389, such material 

 as contained variabilities ranging between 5722 (in the Naqada .serio.s) and 7202 (in the French 

 series) could nt)t rea.sonably be tenucd homogeneous. That infcrcnce, I thought and still think, 



* Biometrika, Vul. ii., pp. 34.5^:147. t .V<i;i, Februnrj-, l'J03, pp. 2Ö— 32. 



X Biometrika, Vol. i., pp. 408 — 467. 



