238 Coast Survey of the United States. 
tion for the philosophic accuracy and elegance of their execution, 
but by means of which he arrived at a ratio independent and ex- 
clusive. His purpose was to establish an authentic standard 
with bars of recognized authority. Had the subject required fur- 
ther research, no one could hesitate to admit his results, as every 
one must admire the zeal, learning, and fidelity he displayed. 
But the legal ratio is in fact the only one admissible. ‘This is an 
evident truth. When the metre ceased to be considered the ten- 
millionth part of the quadrant of the meridian, it became equally 
with the toise a mere iron bar, having no other value than that 
assigned it by law; and that value was a permanent one, which 
no individual experiments could be permitted to change. 
On this point there can be no higher authority than that of 
M. Bessel, which it may be well to quote. ‘Mr. Hassler de- 
duced from several comparisons the value of the metre in parts 
of the toise. But this I consider as not allowable, for the ratio 
between the two is determined by law, by which the metre has 
received its true definition. If certain copies of these metres do 
not agree together, it shows that the law is not exactly fulfilled by 
them ; and as it is much more difficult to transfer to another me- 
tallic bar 443-296 lines of the toise than the whole length of the 
toise, the value of the metre is a circuitous and unprofitable way, 
as long as the toise is as easily obtained as it was at the time of 
the construction of the metre.” 
Mr. Hassler’s ratio differed from the legal ratio (443-296) by 
— 0-015 lines of the toise, an amount quite serious when multi- 
plied by frequent repetitions. 
At the primary stations last year Dr. Bache made use for the 
first time of vertical angles for determining differences of heights. 
For this the triangulation at the north offers a fine field; but the 
features of the coast at the south will preclude its frequent appli- 
cation there. This method will be continued. The effect of 
refraction near the surface may be investigated by a series of ob- 
servations, and these angles can be measured at a time of day 
when it would be impracticable to observe the horizontal angles. 
Anew system of magnetic observations has been introduced 
into the coast survey. The declination of the magnetic needle, 
which is of indispensable practical utility, is to be carefully as- 
certained at every important station of the work. It is needless 
to say, however much the subject may have been neglected hith- 
