Dr. Bowditch, President of the American Academy. xlvii 
The first volume of Dr. Bowditch’s Commentary is concluded 
with a valuable summary of Spherical Trigonometry. 
After this particular account of the first volume of this great work, 
I shall notice very briefly only a few of the more important additions 
of Dr. Bowditch to the succeeding volumes. 
In a note on the Third Book (Chap. 1, § 3) he mentions, in pass- 
ing, an important improvement he had made in a particular notation, 
and which he had adopted, in his Commentary on La Place, many 
years previously to the publication of a method used by an eminent 
French mathematician*, which is substantially like that of Dr. Bow- 
ditch, and is now in general use. 
He next notices (in Book III. ch. 2, §8) La Place’s remarkable 
omission of an important term in one of his formulas, as originally 
published ; and, what will appear most surprising is, that this defect 
appears to have remained unnoticed by mathematicians for nearly half 
acentury. Asimilar omission occurs afterwards (chap. 5, § 38), and 
both of these Dr. Bowditch has supplied in the text, as being essen- 
tial to the formula. In his Note on the last-mentioned case, he has 
also given a method of his own for ascertaining the value of the 
radius vector of an ellipsoid, being more general than that of La 
Place, and the same which he had many years before published in 
the Academy’s Memoirs. ¢ 
Dr. Bowditch had peculiar skill in bringing any proposed formula 
to the test by means of extremely neat and simple cases. Of this 
there is a striking example in this second volume;{ in which he 
shows by this test, that a rule proposed by an eminent English 
mathematician § is defective. I have understood, that Dr. Bowditch 
sometimes, among his intimate friends, alluded to this case as one of 
* Baron Fourier, Secretary of the Institute of France. 
t Vol. IV. p. 45. tf) BS 207. § Mr. Ivory. 
