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round the axis of its rotation, we see that, relatively to the shell, 
the liquid will have performed less than a complete period of its 
retrograde revolution by the difference (27 r/co - 27 r/e) ; or by the 
fraction (1 - co/e) of the period of the fluid relatively to the shell. 
In the extreme case of a = b = c (the ellipsoid a sphere), to = e and 
the retrograde motion of the fluid relatively to the shell is one com- 
plete revolution, in the period of the forward revolution of the 
shell : that is to say, the fluid is perfectly left behind, and remains 
unmoved while the shell turns. In the other extreme case of any 
one or any two of the quantities a, 6, c being infinitely small, w is 
infinitely small : that is to say, the fluid makes an infinitely small 
fraction of its retrograde revolution during the time of one turn of 
the shell in the direction which we are calling forward. It must 
not from this be inferred that the fluid moves very nearly, as if 
solid, with the shell. On the contrary, it experiences large dis- 
tortion even in the first complete turn of the shell, and largely 
increasing to a maximum in the course of the first quarter period of 
the liquid relatively to the shell. 
{To be continued .) 
2. The Sacral Index in Yarious Eaces of Mankind. By 
Professor Wrn. Turner, M.B., F.B.S. 
In a paper on “The Index of the Pelvic Brim as a basis of 
Classification,” which I read in September at the meeting of the 
British Association in Aberdeen, and published in the Journal of 
Anatomy and Physiology , October 1885, I briefly referred to varia- 
tions in the length and breadth of the sacrum in different races of 
men, and pointed out that in some races the length exceeded the 
breadth, and that in others an opposite relation prevailed. These 
differences may be expressed numerically by computing a sacral 
index by the following formula : 
sacral breadth x 100 
sacral length 
When the sacral index is above 100 the breadth of the bone is 
greater than the length, when the index is below 100 the sacrum 
