838 
NATURE 
[JUNE 23, 1923 

series of positive integral powers. So far as relates to 
selection of subject matter in the form of examples 
and applications, ‘‘Common Sense of the Calculus ” 
exactly meets the case. We should be glad if Mr. 
Brewster would republish this collection based on a 
different method of dealing with infinitesimals. He 
would probably find that instead of making his book 
larger it would be possible even to make it smaller. 
The “terms of second order” which give so much 
trouble in this treatment can be got rid of completely 
by adopting the definition of “limiting equality ” 
mentioned in a letter to NATURE of February 10, as 
the interpretation of such formule as dy=f1(x)dx. 
“Zero” is a dangerous quantity to put in the hands 
of a beginner, and so are quantities which “may be 
neglected,” and it was only a year ago that we had 
a student trying to take mathematical honours who 
said that two quantities da and db were “of the 
same order, therefore they are equal” ! On the other 
hand, we have found it possible to condense into five 
or six pages of stencilled notes all the information 
required to explain differentiation and integration and 
to introduce such differentials as dx, dy, ds, dr, rd0, 
$7°d0, and even dx dy and dx dy dz in a form in which 
finite quotients and sums of products can be built up 
in perfect safety, second-order quantities being tabooed, 
but ds?=dx?+dy*=dy?+(rd0)? being legitimate. A 
recent paper by Prof. Alfred Lodge in the Mathematical 
Gazette evidently is based on the same principle. 
G. HEB. 

Christopher Wren and the Tom Tower. 
“Tom Tower,” Christ Church, Oxford. Some Letters 
of S’ Christopher Wren to John Fell, Bishop of 
Oxford. Witherto Unpublished. Now set forth 
and Annotated by W. Douglas Carée; with a 
chapter by Prof. H. H. Turner, and another by 
Arthur Cochrane. Pp. xii+127+28 plates. (Oxford: 
Clarendon Press; London: Oxford University 
Press, 1923.) 255. net. 
HIS book was published in honour of the bi- 
centenary of Wren’s death. on February 25. 
The author had been called upon to direct some 
necessary repairs to the buildings of Christ Church 
College, particularly to the ‘Tom Tower,” when his 
attention was directed to some unpublished letters 
and documents dealing with the original design and 
building of the tower, and these have now been 
published in the present volume. In addition to a 
contemporary copy of the contract between the 
College treasurer and the contractor for the building 
of the tower, there are seven autograph letters written 
by Wren to John Fell, Bishop of Oxford, the first 
NO. 2799, VOL. 111] 


dated May 26, 1681, andthe last September 9, 1682, 
when the work was nearing completion. The last 
letter is reproduced in facsimile, showing Wren’s firm 
and very distinct handwriting. 
An analysis of each letter follows, and Prof. H. H. 
Turner has supplied a commentary to the sixth and 
most interesting one. This letter (dated from White- 
hall, December 3, 1681) is a reply to a proposal on the 
part of the bishop, that the tower should be converted 
into an observatory. Wren is too polite to reject 
the proposal altogether, but gives good reasons why 
it should not be hastily adopted. It would inyolve a 
change in the whole design; the bell would have to 
be lowered so as to heighten the loft, and it might 
then not be well heard. The Gothic roof, agreeing 
with the rest of the College buildings, would have to 
be abandoned, and a flat roof with a horizontal 
balustrade substituted, while instead of windows there 
would have to be wooden shutters without mullions 
or bars. In addition to these objections from the 
point of view of an architect, Wren next produces 
others from the point of view of an astronomer, and 
here also he could speak with authority, having held 
the office of Savilian professor of astronomy for twelve 
years (1661-73) until pressure of other work obliged 
him to relinquish it. ¢ 
“Give me leave to add that such a room as this 
will be when built, is no way necessary for observations, 
as now they are managed. Were I to set up the 
Trade again I was once well acquainted with, and 
I think the world doth or may justly own some improve- 
ments of it to me, I should require nothing else but 
these things. First a large mural quadrant fixt to 
a wall truly built in the meridian, and this is best 
in an open court or garden, 2” a pole to raise large 
telescopes and manage them, and the like place is — 
properest for this also. 3°” a quadrant to take 
distances fixt to a foot so as it may turn to all sort 
of planes . . . must be housed for its better preserva- 
tion, but the best house will be a little house of boards 
and no other roof but what may be taken quite off 
when the instrument is used. . . . We built indeed 
an Observatory at Greenwich not unlike what your 
tower will prove, it was for the Observators habitation 
and a little for pomp; it is the instruments in the 
court after the manner I have described which are 
used, the room keeps the clocks and the instruments 
that are laid by.” 
en 
a 
This statement as to what an observatory ought 
to be like is very interesting, as showing that Wren 
thoroughly agreed with Flamsteed about the require- 
ments of practical astronomy. Therefore Oxford did 
not get an observatory on this occasion (there were 
only two University Observatories in existence at that 
time, at Copenhagen and at Leyden), and nearly a 
hundred years had to pass, before the Radcliffe 
Observatory was built, including a very big tower ! 
