This manuscript is a set of class notes presumed taken by a student (R. Nachwitz?) attending lectures by Professors Schneider and Karl Ludwig Meissner on Civil Engineering topics given at the Collegium Carolinum in Braunschweig, Germany during 1849-50. Topics covered in technical mechanics included effect of friction, strength of materials, mechanics of gear teeth, analysis of fire hoses and nozzles, vibration in structures. The general topic of “Baukunst” (Art of Building/ Architecture) was covered by Prof. Meissner and dealt with design of actual structures, emphasis on railroad engineering such as embankments and arch bridges. The marginalia in the text illustrates many interesting structures and equations. The handwritten text is in Frakturschrift. The lectures provide an excellent insight into the extent of German engineering education the students received during a critical period in the Collegium Carolinum –Braunschweig, the first such German institution founded in 1745 devoted solely to technical topics.

Translation of page 130 and two lines of page 131 which are part of the last sentence on page 130. The translation was made more or less to correspond to the lines of the original except that, for easier understanding, the text of the original handwritten class notes was smoothed out by filling in needed punctuation marks, some apparently missing words, definitions, and completing many abbreviated sentences. Additional explanations are shown in brackets [---].

Reference is made to the two sketches on the original 130.

“Should the failure (collapse) of one or the other vault be prevented, One half of the vault must be in equilibrium with the other half. The distance from the center of gravity line to the support point m is φ for the first case, and δfor the second.
The distance of the horizontal force F (from m) is g, and y in the second case.
[Note: With the structure and the failure being symmetrical, there is no vertical force at the crown, and P being the weight of the stone, equilibrium requires that] Fg = Pφ from which follows that F = Pφ/g, in the first case, and Fʹy = Pδ from which it follows that Fʹ = Pʹδ/y, in the second case.
The expressions for F and Fʹ can result in as many different values as there are points on the Intrador (???).
The problem is then to determine the location of point m so that F is A maximum, and, in the second case, Fʹ is a minimum.

These two considerations lead to the following conclusions:

(1) A heavy vault without any outside loading, that is, the one that has to carry only the weight of its own stones, must be in equilibrium if the horizontal force falls between the values of the maximum from Pφ/g and the minimum of Pʹδ/y.

(2) In a stable vault there are no fracture joints, that is, there are no joints that open towards inside or outside, because the horizontal force falls within the wall thickness.

(3) The actual horizontal force at the crown (apex) depends neither on the support reactions nor on the lower vault outline (??) but only on the parts (components) which lie between the fracture joint and the end [crown?].

[Four more conclusions and further explanations follow on later pages.] Alexis Ostapenko, translator